Communications

Blockset ®
For Use with Simulink

Computation

Visualization

Programming

User’s Guide
Version 2
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Communications Blockset User’s Guide

 COPYRIGHT 2000 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc.
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by
or for the federal government of the United States. By accepting delivery of the Program, the government
hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR
Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part
252.227-7014. The terms and conditions of The MathWorks, Inc. Software License Agreement shall pertain
to the government’s use and disclosure of the Program and Documentation, and shall supersede any
conflicting contractual terms or conditions. If this license fails to meet the government’s minimum needs or
is inconsistent in any respect with federal procurement law, the government agrees to return the Program
and Documentation, unused, to MathWorks.
MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks, and
Target Language Compiler is a trademark of The MathWorks, Inc.
Other product or brand names are trademarks or registered trademarks of their respective holders.
Printing History: September 2000 New for Version 2 (Release 12)
 Contents

Preface

What Is the Communications Blockset? . . . . . . . . . . . . . . . . . . xii

Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Using This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Expected Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Organization of the Document . . . . . . . . . . . . . . . . . . . . . . . . . . xvi

Configuration Information . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Using the Blockset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Technical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

Scalars, Vectors, and Matrices . . . . . . . . . . . . . . . . . . . . . . . . . xviii
Frame-Based and Sample-Based Signals . . . . . . . . . . . . . . . . xviii

Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx

Getting Started with the Communications Blockset

1
The Example Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Overview of the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Building the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Exploring the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9

Components of the Example . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11

Creating Random Binary Data . . . . . . . . . . . . . . . . . . . . . . . . . 1-11
Encoding Using a Convolutional Code . . . . . . . . . . . . . . . . . . . 1-12
Unbuffering to Convert Vectors to Scalars . . . . . . . . . . . . . . . 1-14
Modulating the Encoded Messages . . . . . . . . . . . . . . . . . . . . . 1-16

i
 Transmitting Along a Noisy Channel . . . . . . . . . . . . . . . . . . . . 1-16
Mapping the Received Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Buffering to Convert Scalars to Vectors . . . . . . . . . . . . . . . . . . 1-20
Decoding the Convolutional Code . . . . . . . . . . . . . . . . . . . . . . . 1-21
Computing the Error Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-24
Displaying the Error Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
Other Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26

Learning More About the Example . . . . . . . . . . . . . . . . . . . . 1-27

Modifying the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-27
For Further Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-28

Using the Communications Blockset

2
Signal Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Processing Vectors and Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Processing Frame-Based and Sample-Based Signals . . . . . . . . 2-4

Communications Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6

Source Features of the Blockset . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Random or Pseudorandom Signals . . . . . . . . . . . . . . . . . . . . . . . 2-6
Nonrandom Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11

Communications Sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12

Sink Features of the Blockset . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Writing to a File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Error Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Eye Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
Scatter Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
Example: Using Eye and Scatter Diagrams . . . . . . . . . . . . . . . 2-14

Source Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16

Source Coding Features of the Blockset . . . . . . . . . . . . . . . . . . 2-16
Representing Quantization Parameters . . . . . . . . . . . . . . . . . . 2-17
Quantizing a Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17
Implementing Differential Pulse Code Modulation . . . . . . . . . 2-21

ii Contents
 Companding a Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-24
Selected Bibliography for Source Coding . . . . . . . . . . . . . . . . . 2-26

Block Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27

Organization of This Section . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
Accessing Block Coding Blocks . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
Block Coding Features of the Blockset . . . . . . . . . . . . . . . . . . . 2-28
Communications Toolbox Support Functions . . . . . . . . . . . . . . 2-29
Channel Coding Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29
Data Formats for Block Coding . . . . . . . . . . . . . . . . . . . . . . . . . 2-29
Using Block Encoders and Decoders Within a Model . . . . . . . 2-32
Examples of Block Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32
Notes on Specific Block Coding Techniques . . . . . . . . . . . . . . . 2-35
Selected Bibliography for Block Coding . . . . . . . . . . . . . . . . . . 2-39

Convolutional Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40

Organization of This Section . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40
Accessing Convolutional Coding Blocks . . . . . . . . . . . . . . . . . . 2-40
Convolutional Coding Features of the Blockset . . . . . . . . . . . . 2-40
Parameters for Convolutional Coding . . . . . . . . . . . . . . . . . . . . 2-41
Examples of Convolutional Coding . . . . . . . . . . . . . . . . . . . . . . 2-42
Selected Bibliography for Convolutional Coding . . . . . . . . . . . 2-45

Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46
Interleaving Features of the Blockset . . . . . . . . . . . . . . . . . . . . 2-46
Block Interleavers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46
Convolutional Interleavers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-47
Selected Bibliography for Interleaving . . . . . . . . . . . . . . . . . . . 2-51

Analog Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-53

Accessing Analog Modulation Blocks . . . . . . . . . . . . . . . . . . . . 2-53
Analog Modulation Features of the Blockset . . . . . . . . . . . . . . 2-53
Baseband Modulated Signals Defined . . . . . . . . . . . . . . . . . . . 2-54
Representing Signals for Analog Modulation . . . . . . . . . . . . . . 2-55
Timing Issues in Analog Modulation . . . . . . . . . . . . . . . . . . . . 2-55
Filter Design Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-59

Digital Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-64

Accessing Digital Modulation Blocks . . . . . . . . . . . . . . . . . . . . 2-64

iii
 Digital Modulation Features of the Blockset . . . . . . . . . . . . . . 2-65
Representing Signals for Digital Modulation . . . . . . . . . . . . . . 2-68
Delays in Digital Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 2-69
Upsampled Signals and Rate Changes . . . . . . . . . . . . . . . . . . . 2-72
Examples of Digital Modulation . . . . . . . . . . . . . . . . . . . . . . . . 2-75
Selected Bibliography for Digital Modulation . . . . . . . . . . . . . 2-83

Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-84
Channel Features of the Blockset . . . . . . . . . . . . . . . . . . . . . . . 2-84
AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-84
Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-85
Binary Symmetric Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-88
Selected Bibliography for Channels . . . . . . . . . . . . . . . . . . . . . 2-89

Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-90
Synchronization Features of the Blockset . . . . . . . . . . . . . . . . 2-90
Overview of PLL Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-91
Implementing an Analog Baseband PLL . . . . . . . . . . . . . . . . . 2-91
Implementing a Digital PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-92
Selected Bibliography for Synchronization . . . . . . . . . . . . . . . 2-92

Function Reference
3
Alphabetical List of Functions . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
comm_links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
commlib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4

Block Reference
4
Communications Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3

Communications Sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5

iv Contents
Source Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7

Channel Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9

Block Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9
Convolutional Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11

Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13
Block Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13
Convolutional Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15

Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18
Digital Baseband Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18
Analog Baseband Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24
Digital Passband Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26
Analog Passband Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31

Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34

Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36

Basic Communications Functions . . . . . . . . . . . . . . . . . . . . . 4-37

Integrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-37
Sequence Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38

Utility Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41

Alphabetical List of Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42

A-Law Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-47
A-Law Expander . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-49
Algebraic Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-51
Algebraic Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-53
APP Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-56
AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-60
Baseband PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64
BCH Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-66
BCH Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-68
Bernoulli Random Binary Generator . . . . . . . . . . . . . . . . . . . . 4-70
Binary Cyclic Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-73
Binary Cyclic Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-75

v
 Binary-Input RS Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-77
Binary Linear Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-79
Binary Linear Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-81
Binary-Output RS Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-82
Binary Symmetric Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-84
Binary Vector Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . 4-86
Bit to Integer Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-89
BPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-90
BPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-92
Charge Pump PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-94
Complex Phase Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-97
Complex Phase Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-98
Continuous-Time Eye and Scatter Diagrams . . . . . . . . . . . . . . 4-99
Convolutional Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . 4-103
Convolutional Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-105
Convolutional Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-107
CPFSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-109
CPFSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . 4-112
CPFSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-115
CPFSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-118
CPM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-121
CPM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . 4-125
CPM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-130
CPM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-134
Data Mapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-139
DBPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-142
DBPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-144
Deinterlacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-146
Derepeat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-147
Descrambler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-150
Differential Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-152
Differential Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-153
Discrete Modulo Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-154
Discrete-Time Eye and Scatter Diagrams . . . . . . . . . . . . . . . 4-156
Discrete-Time VCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-159
DPCM Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-161
DPCM Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-163
DQPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-165
DQPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
DSB AM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . 4-171

vi Contents
DSB AM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . 4-173
DSB AM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . 4-175
DSB AM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . 4-176
DSBSC AM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . 4-178
DSBSC AM Demodulator Passband . . . . . . . . . . . . . . . . . . . . 4-180
DSBSC AM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . 4-182
DSBSC AM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . 4-183
Enabled Quantizer Encode . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-185
Error Rate Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
FM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-194
FM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-196
FM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-198
FM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-200
Gaussian Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-202
General Block Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . 4-205
General Block Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
General Multiplexed Deinterleaver . . . . . . . . . . . . . . . . . . . . 4-208
General Multiplexed Interleaver . . . . . . . . . . . . . . . . . . . . . . . 4-210
General QAM Demodulator Baseband . . . . . . . . . . . . . . . . . . 4-212
General QAM Demodulator Passband . . . . . . . . . . . . . . . . . . 4-214
General QAM Modulator Baseband . . . . . . . . . . . . . . . . . . . . 4-217
General QAM Modulator Passband . . . . . . . . . . . . . . . . . . . . 4-219
GMSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . 4-222
GMSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . 4-225
GMSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-228
GMSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-231
Hamming Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-234
Hamming Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-236
Helical Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-238
Helical Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-241
Insert Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-244
Integer-Input RS Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-246
Integer-Output RS Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-248
Integer to Bit Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-250
Integrate and Dump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-251
Interlacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-253
Linearized Baseband PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-254
Matrix Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-256
Matrix Helical Scan Deinterleaver . . . . . . . . . . . . . . . . . . . . . 4-257
Matrix Helical Scan Interleaver . . . . . . . . . . . . . . . . . . . . . . . 4-259

vii
 Matrix Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-262
M-DPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . 4-264
M-DPSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . 4-267
M-DPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . 4-270
M-DPSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . 4-274
M-FSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-277
M-FSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . 4-280
M-FSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-283
M-FSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-286
Modulo Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-289
M-PAM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-290
M-PAM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . 4-293
M-PAM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-297
M-PAM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . 4-301
M-PSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-305
M-PSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . 4-308
M-PSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-311
M-PSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-316
MSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-319
MSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . 4-321
MSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-324
MSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-326
Mu-Law Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-329
Mu-Law Expander . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-330
Multipath Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . 4-331
OQPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-334
OQPSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . 4-336
OQPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-339
OQPSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . 4-342
Phase-Locked Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-345
PM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-348
PM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-350
PM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-352
PM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-353
PN Sequence Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-355
Poisson Int Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-358
Puncture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-360
QPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . 4-362
QPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-364
Quantizer Decode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-367

viii Contents
Random Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-368
Random-Integer Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-369
Random Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-372
Rayleigh Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-373
Rectangular QAM Demodulator Baseband . . . . . . . . . . . . . . 4-376
Rectangular QAM Demodulator Passband . . . . . . . . . . . . . . . 4-379
Rectangular QAM Modulator Baseband . . . . . . . . . . . . . . . . . 4-383
Rectangular QAM Modulator Passband . . . . . . . . . . . . . . . . . 4-387
Rician Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-391
Rician Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-394
Sampled Quantizer Encode . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-397
Scrambler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-399
SSB AM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . 4-401
SSB AM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . 4-403
SSB AM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-405
SSB AM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . 4-408
Triggered Read From File . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-411
Triggered Write to File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-414
Uniform Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-416
Viterbi Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-419
Voltage-Controlled Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . 4-424
Windowed Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-426

ix
x Contents
Preface
What Is the Communications Blockset? . . . . . . . . .xii

Related Products . . . . . . . . . . . . . . . . . . xiii

Using This Guide . . . . . . . . . . . . . . . . . . . xv

Expected Background . . . . . . . . . . . . . . . . . . xv
Organization of the Document . . . . . . . . . . . . . xvi

Configuration Information . . . . . . . . . . . . . xvii

Using the Blockset . . . . . . . . . . . . . . . . . . xvii

Technical Conventions . . . . . . . . . . . . . . . xviii

Scalars, Vectors, and Matrices . . . . . . . . . . . . . xviii
Frame-Based and Sample-Based Signals . . . . . . . . . xviii

Typographical Conventions . . . . . . . . . . . . . . xx
Preface

What Is the Communications Blockset?

The Communications Blockset is a collection of Simulink® blocks designed for
research, development, system design, analysis, and simulation in the
communications area. You can use the blockset’s ready-to-use blocks directly,
or you can easily modify them to implement your own methods and algorithms.
Blocks in this product can model various processes within communication
systems, including:
• Signal generation
• Source coding
• Error-control coding
• Interleaving
• Modulation/demodulation
• Transmission along a channel
• Synchronization

xii
 Related Products

Related Products
The MathWorks provides several products that are especially relevant to the
kinds of tasks you can perform with the Communications Blockset. They are
listed in the table below. In particular, the Communications Blockset requires
these products:

• MATLAB®
• Simulink
• Signal Processing Toolbox
• Communications Toolbox
• DSP Blockset

For more information about any of these products, see either:

• The online documentation for that product, if it is installed or if you are
reading the documentation from the CD
• The MathWorks Web site, at http://www.mathworks.com; see the “products”
section

Note The toolboxes listed below all include functions that extend MATLAB’s
capabilities. The blocksets all include blocks that extend Simulink’s
capabilities.

Product Description

CDMA Reference Simulink block libraries for the design and

Blockset simulation of the IS-95A wireless
communications standard
Communications Toolbox MATLAB functions for modeling the physical
layer of communications systems

xiii
Preface

Product Description

DSP Blockset Simulink block libraries for the design,

simulation, and prototyping of digital signal
processing systems
Real-Time Workshop® Tool that generates customizable C code from
Simulink models and automatically builds
programs that can run in real time in a variety
of environments

Signal Processing Tool for algorithm development, signal and

Toolbox linear system analysis, and time-series data
modeling

Simulink Interactive, graphical environment for

modeling, simulating, and prototyping
dynamic systems

Stateflow® Tool for graphical modeling and simulation of

complex control logic

xiv
 Using This Guide

Using This Guide

This guide describes how to use the Communications Blockset to simulate
communication systems. It contains tutorial information categorized by type of
communication process, as well as a reference entry for each block in the
blockset.

Expected Background
This guide assumes that you already have background knowledge in the
subject of communications. If you do not yet have this background, then you
can acquire it using a standard communications text or the books listed in one
of this guide’s sections whose titles begin with “Selected Bibliography.”

If You Are a New User

Start with “Getting Started with the Communications Blockset”, which
describes an example in detail. Then read those parts of “Using the
Communications Blockset” that address the functionality that concerns you.
When you find out which blocks you want to use, refer to those parts of “Block
Reference” that describe those blocks.

If You Are an Experienced User

The block reference descriptions in “Block Reference” are probably the most
relevant parts of this guide for you. Each reference description includes a
complete explanation of the block’s parameters and operation. Many reference
descriptions also include examples, a description of the block’s algorithm, and
references to additional reading material.
You might also want to browse through “Getting Started with the
Communications Blockset” and “Using the Communications Blockset” based
on your interests or needs.

xv
Preface

Organization of the Document

This chapter introduces the Communications Toolbox and some of its
important terminology. The table below summarizes the contents of the
remaining chapters.

Chapter Description

“Getting Started with the Discusses an example model in detail to help

Communications you begin learning about the blockset
Blockset”

“Using the Surveys the major libraries of the blockset

Communications and discusses their capabilities and features
Blockset”

“Function Reference” Contains reference entries for the small

number of functions in the blockset

“Block Reference” Shows the contents of each library of the

blockset and contains reference entries for all
blocks

xvi
 Configuration Information

Configuration Information
To determine if the Communications Blockset is installed on your system, type
ver

at the MATLAB prompt. MATLAB displays information about the version of

MATLAB you are running, including a list of installed add-on products and
their version numbers. Check the list to see if the Communications Blockset
appears.
For information about installing the blockset, see the MATLAB Installation
Guide for your platform.

Note For the most up-to-date information about system requirements, see
the system requirements page, available in the support area of the
MathWorks Web site (http://www.mathworks.com/support).

Using the Blockset

To open the Communications Blockset, type
commlib

at the MATLAB prompt.

Double-click on any icon in the main Communications Blockset window to open
the library that the icon represents.

xvii
Preface

Technical Conventions
This section discusses the terminology that this document uses to describe the
signal types that the Communications Blockset supports. To learn how the
blockset processes each kind of signal, see “Signal Support” on page 2-3.

Scalars, Vectors, and Matrices

This document uses the unqualified words scalar and vector in ways that
emphasize a signal’s number of elements, not its strict dimension properties:

• A scalar signal is one that contains a single element. The signal could be a
one-dimensional array with one element, or a matrix of size 1-by-1.
• A vector signal is one that contains one or more elements, arranged in a
series. The signal could be a one-dimensional array, a matrix that has
exactly one column, or a matrix that has exactly one row. The number of
elements in a vector is called its length or, sometimes, its width.

In cases when it is important for a description or schematic to distinguish

among different types of scalar signals or different types of vector signals, this
document mentions the distinctions explicitly. For example, the terms
one-dimensional array, column vector, and row vector distinguish among three
types of vector signals.
The size of a matrix is the pair of numbers that indicate how many rows and
columns the matrix has. The orientation of a two-dimensional vector is its
status as either a row vector or column vector. A one-dimensional array has no
orientation.
A matrix signal that has more than one row and more than one column is called
a full matrix signal.

Frame-Based and Sample-Based Signals

In Simulink, each matrix signal has a “frame attribute” that declares the signal
to be either frame-based or sample-based, but not both. (A one-dimensional
array signal is always sample-based, by definition.) Simulink indicates the
frame attribute visually by using a double connector line in the model window
instead of a single connector line. In general, Simulink interprets frame-based
and sample-based signals as follows:

xviii
 Technical Conventions

• A frame-based signal in the shape of an M-by-1 (column) matrix represents

M successive samples from a single time series.
• A frame-based signal in the shape of a 1-by-N (row) matrix represents a
sample of N independent channels, taken at a single instant in time.
• A sample-based matrix signal might represent a set of bits that collectively
represent an integer, or a set of symbols that collectively represent a code
word, or something else other than a fragment of a single time series.

xix
Preface

Typographical Conventions
This guide uses some or all of these conventions.

Item Convention to Use Example

Example code Monospace font To assign the value 5 to A,

enter
A = 5

Function names/syntax Monospace font The cos function finds the

cosine of each array element.
Syntax line example is
MLGetVar ML_var_name

Keys Boldface with an initial Press the Return key.

capital letter

Literal strings (in syntax Monospace bold for f = freqspace(n,'whole')

descriptions in Reference literals.
chapters)

Mathematical Variables in italics This vector represents the

expressions Functions, operators, and polynomial
constants in standard text. p = x2 + 2x + 3

MATLAB output Monospace font MATLAB responds with

A =

Menu names, menu items, and Boldface with an initial Choose the File menu.
controls capital letter

New terms Italics An array is an ordered

collection of information.

String variables (from a finite Monospace italics sysc = d2c(sysd, 'method')

list)

xx
 1
Getting Started with the
Communications Blockset
The Example Model . . . . . . . . . . . . . . . . . 1-3
Overview of the Simulation . . . . . . . . . . . . . . 1-3
Building the Model . . . . . . . . . . . . . . . . . . 1-5
Exploring the Model . . . . . . . . . . . . . . . . . 1-9

Components of the Example . . . . . . . . . . . . . 1-11

Creating Random Binary Data . . . . . . . . . . . . . 1-11
Encoding Using a Convolutional Code . . . . . . . . . . 1-12
Unbuffering to Convert Vectors to Scalars . . . . . . . . 1-14
Modulating the Encoded Messages . . . . . . . . . . . 1-16
Transmitting Along a Noisy Channel . . . . . . . . . . 1-16
Mapping the Received Data . . . . . . . . . . . . . . 1-18
Buffering to Convert Scalars to Vectors . . . . . . . . . 1-20
Decoding the Convolutional Code . . . . . . . . . . . . 1-21
Computing the Error Rate . . . . . . . . . . . . . . . 1-24
Displaying the Error Rate . . . . . . . . . . . . . . . 1-26
Other Blocks . . . . . . . . . . . . . . . . . . . . 1-26

Learning More About the Example . . . . . . . . . . 1-27

Modifying the Model . . . . . . . . . . . . . . . . . 1-27
For Further Study . . . . . . . . . . . . . . . . . . 1-28
1 Getting Started with the Communications Blockset

This chapter describes a particular example in detail, to help you get started
using the Communications Blockset. The description here assumes very little
prior knowledge of MATLAB or Simulink. It assumes that you have a basic
knowledge about communications subject matter. More specialized knowledge
about convolutional coding might be useful for the two parts marked
“Technical,” but is not essential for using the example to learn about the
Communications Blockset environment.
This chapter:

• Gives an overview of the model

• Discusses how you can explore the model in Simulink before reading about
its components
• Describes the components of the model in detail
• Discusses how you can modify the model after you understand how it works
• Lists sources of further information

The detailed component descriptions also include three digressions about:

• Signal sizes (page 1-12)

• Sample times (page 1-15)
• Data types (page 1-16)

While these digressions relate to specific components of the example model,

they also point out general model-building and model-debugging techniques
that can help you use Simulink more effectively.

1-2
 The Example Model

The Example Model

The figure below shows the example model. You can open it by typing
commblksgettingstarted at the MATLAB prompt.

Tip In this document, you can click on blocks in the figure above to see more
information about how they behave within the example.

Figure 1-1: Example Model

Overview of the Simulation

This example simulation starts by creating a random binary message signal.
The simulation encodes the message into a convolutional code, modulates the
code using the binary phase shift keying (BPSK) technique, and adds white
Gaussian noise to the modulated data in order to simulate a noisy channel.

1-3
1 Getting Started with the Communications Blockset

Then, the simulation decodes the convolutional code while trying to correct as
many noise-induced errors as possible. The decoding also involves some
intermediate steps to prepare the received data for the decoding block. Finally,
the simulation compares the decoded information to the original message
signal in order to compute and display an error rate.
The table below indicates which blocks from the Communications Blockset
appear in the model, the order they appear in the model, and the purpose each
one serves.

Communications Purpose in Example

Blockset Block

Bernoulli Random Create random bits to use as message.

Binary Generator

Convolutional Encoder Encode message using the convolutional coding technique.

BPSK Modulator Modulate encoded message to prepare for transmission.

Baseband

AWGN Channel Transmit data, adding random numbers to simulate a noisy

channel.

Sampled Quantizer Map received data to appropriate three-bit values to prepare for
Encode soft-decision decoding.

Viterbi Decoder Decode the convolutional code using the Viterbi algorithm.

Error Rate Calculation Compute proportion of discrepancies between original and

recovered messages.

The model also uses some blocks from Simulink and the DSP Blockset:

• Unbuffer (DSP Blockset)

• Complex to Real-Imag (Simulink)
• Terminator (Simulink)
• Buffer (DSP Blockset)
• Display (Simulink)

1-4
 The Example Model

Building the Model

This section helps you build the model starting from a blank model window. If
you prefer to open the prebuilt model, then type commblksgettingstarted at
the MATLAB prompt and skip ahead to “Exploring the Model” on page 1-9.

Part 1: Placing the First Block

To start building the model, follow these steps:

1 Type commlib at the MATLAB prompt. This opens the Communications

Blockset main library.

2 From the library’s File menu, select New and then select Model. This opens
a new model window called untitled. You will build the example model in
this window.

3 From the model window’s File menu, select Save. Choose an appropriate
location and filename for the model you are about to build. You should save
the model frequently while you are editing it, to avoid losing any work.

4 In the Communications Blockset main library, double-click on the Comm

Sources icon. This opens the Comm Sources library.

5 In the Comm Sources library, find the icon for the Bernoulli Random Binary
Generator block. Drag it into the model window.

6 In the model window (not the Comm Sources library window), double-click
on the Bernoulli Random Binary Generator icon. This opens the block’s
parameter dialog box, also called its mask.

7 In the mask, type new values in the parameter fields to change the default
parameter values to the ones shown in the right image below.

1-5
1 Getting Started with the Communications Blockset

Default Parameters Desired Parameters for the Example

8 Click on the OK button in the mask.

You have now placed and configured the first block for this example model.

Part 2: Placing Other Blocks

This section tells how to find and configure the other blocks required for the
example model. First open the main libraries of the products that contain those
blocks:

• To open the main DSP Blockset library, type dsplib at the MATLAB prompt.
• To open the main Simulink library, type simulink3 at the MATLAB prompt.

Now, the basic procedure for placing blocks is similar to the procedure you used
for the Bernoulli Random Binary Generator block:

1 From the product’s main library, navigate to the library or sublibrary where
the block resides.

2 Drag the desired block into the model window.

1-6
 The Example Model

3 Double-click on the block in the model window to open its mask.

4 Change the appropriate parameters.

5 Click on the mask’s OK button.

Apply this basic procedure to the blocks listed below. For now, just place each
block anywhere within your model window. The next section gives tips for
connecting the blocks to each other.
Below are the blocks that you should gather and configure in your model
window. Each bullet lists the name and library location of the block, while each
subbullet indicates how to change the parameters from their default values.

From the Communications Blockset Library.

• Convolutional Encoder, from the Convolutional sublibrary of the Channel

Coding library. Use default parameter values.

• BPSK Modulator Baseband, from the PM sublibrary of the Digital Baseband

sublibrary of the Modulation library. Use default parameter values.

• AWGN Channel, from the Channels library

- Set Initial seed to 123456
- Set Es/No to -1
- Set Symbol period to .5

• Sampled Quantizer Encode, from the Source Coding library

- Set Quantization partition to [-.75 -.5 -.25 0 .25 .5 .75]
- Set Quantization codebook to [7 6 5 4 3 2 1 0]
- Set Input signal vector length to 1
- Set Sample time to -1

• Viterbi Decoder, from the Convolutional sublibrary of the Channel Coding

library
- Set Decision type to Soft Decision
- Set Number of soft decision bits to 3
- Set Traceback depth to 48

1-7
1 Getting Started with the Communications Blockset

• Error Rate Calculation, from the Comm Sinks library

- Set Receive delay to 49
- Set Output data to Port

From the DSP Blockset Library.

• Unbuffer, from the Buffers sublibrary of the Signal Management library.

Use the default parameter value.
• Buffer, from the Buffers sublibrary of the Signal Management library
- Set Output buffer size to 2

From the Simulink Library.

• Complex to Real-Imag, from the Math library

- Set Output to Real
• Two copies of Terminator, from the Signals & Systems library
• Display, from the Sinks library
- Use default parameter values, but drag a corner of the icon to make it
three times as tall

Connecting the Blocks

Once you have all the blocks in your model window, you can connect them so
that your model window looks like “Example Model” on page 1-3 (except for the
Info block that appears in that figure). Also, from the model window’s
Simulation menu, choose Simulation parameters; then in the Simulation
Parameters dialog box, set Stop time to inf.
Here are some tips for connecting blocks:
• To connect the output port of one block to the input port of another block,
position the pointer over the first block’s output port and drag the pointer to
the second block’s input port.
• To add a branch to an existing connection line (for example, to connect the
Bernoulli Random Binary Generator block to both the Convolutional
Encoder block and the Error Rate Calculation block), first position the
pointer on the line where you want the branch to start. Then using the right
mouse button, drag the pointer to the place where you want the branch to

1-8
 The Example Model

end. As an alternative to using the right mouse button, you can also use the
left mouse button while holding down the Ctrl key.
• To delete a connection line, first select it by positioning the cursor along the
line and pressing the mouse button. Then select Cut from the model
window’s Edit menu.
• To undo the addition or deletion of a block or line, choose Undo from the
model window’s Edit menu. You can also reverse the effect of an Undo
command by using the Redo option from the model window’s Edit menu.
• To reverse the orientation of a block’s icon, select the block and choose Flip
block from the model window’s Format menu. To rotate a block’s icon, select
the block and choose Rotate block from the model window’s Format menu.

Additional information about modelbuilding is in the section, “Creating a

Model,” in the Using Simulink guide.

Exploring the Model

Once the model is open, you can explore it in several ways. You can begin to
explore even before you run the simulation:

• “Read” the block diagram starting with the Bernoulli Random Binary
Generator block in the upper left corner, following the arrows, and ending
with the Display block in the center.
Note that the block marked “Info” does not function during the simulation
but rather links to the HTML version of this documentation.
• Double-click on any block to see its parameter dialog box. This dialog box
briefly describes the block, shows its parameter values if the block has
parameters, allows you to change any of the parameter values, and also
includes a Help button that links to the detailed HTML reference page for
the block.
• To see the blockset library in which any Communications Blockset block
resides, right-click on the block, select Link options, and then select Go to
library block. This shows you where to find the block if you later want to use
it in your own model. The Link options function is inactive for built-in
Simulink blocks, such as the Display block.

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1 Getting Started with the Communications Blockset

Running the Simulation

Run the simulation by selecting Start from the model window’s Simulation
menu. While the simulation runs, the bottom bar of the model window displays
the time, T, and the Display block in the center of the block diagram displays
three numbers that represent the simulation’s error rate information
(explained below). Once it starts, the simulation runs until you select Stop
from the model window’s Simulation menu.

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 Components of the Example

Components of the Example

This section discusses the purpose, behavior, and relevant parameters of each
block within the example model. Except for two noncomputational blocks
discussed at the end, this section covers blocks in the order in which they
process data in the simulation.

Creating Random Binary Data

The Bernoulli Random Binary Generator block, in the Comm Sources library,
produces the message information for this model. The output of this block is
what the other components of the model encode, modulate, transmit, and
decode in turn.
Double-click on the Bernoulli Random Binary Generator block in the model
window to open the parameter mask dialog box shown below.

Since the Sample time parameter is 1 second, the block generates one binary
number each second. Since the Probability of a zero parameter is 0.5, the
block generates the bits so that 0 and 1 are equally probable. The Initial seed
parameter initializes the random number generator; if you change the Initial
seed parameter, then the block generates a different random sequence.
Because the Frame-based outputs check box is checked, the block produces a
frame-based scalar signal instead of a sample-based scalar signal. This is done

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1 Getting Started with the Communications Blockset

to accommodate the functionality of the Unbuffer and Buffer blocks in a

different part of the model, and illustrates one of several possible ways to
handle signals appropriately throughout the model as a whole. When you run
the simulation or update the diagram, notice that the connector line that leads
out of the Bernoulli Random Binary Generator block is a double line instead of
a single line. This double line indicates a frame-based signal.

Encoding Using a Convolutional Code

The Convolutional Encoder block, in the Convolutional sublibrary of the
Channel Coding library, receives the messages from the Bernoulli Random
Binary Generator block and encodes them into codewords.
While the message data is a scalar bit stream, the encoded data is a stream of
binary length-two vectors. These signal sizes are compatible with the structure
of the particular convolutional code and with the corresponding parameter
configuration of the Convolutional Encoder block.

Digression: Exploring Signal Sizes

This section explains a technique for gathering information about the sizes of
signals in a model. This technique can be useful for determining what
parameters you should use for a block or for diagnosing problems in a model.
To check the sizes of signals in the model, use the Signal dimensions feature
from the model window’s Format menu. In this example, when the signal
dimension display is on, the connector line that leads out of the Convolutional
Encoder block has the annotation [2x1] above it because the signal is a 2-by-1
matrix signal. The connector line that leads into the Convolutional Encoder
block has no annotation above it because it is a scalar. The situation is the
opposite for the Viterbi Decoder block.

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 Components of the Example

Defining the Convolutional Code (Technical)

The feedforward convolutional encoder in this example is depicted below.

First output
+

Input z-1 z-1 z-1 z-1 z-1 z-1

Second output

Each summing node represents modulo-2 addition. Each box marked z-1
represents a memory register that holds the input values from previous sample
times. Since there are six memory registers, the output at a given time depends
on seven input values, including the current one. Thus the constraint length of
the code is 7. Since the code has one input and two outputs, the code rate is 1/2.
A pair of octal numbers called the code generator indicates the connections from
the memory registers to the modulo-2 summing nodes. The pair [171 133]
describes the encoder in the figure.
The Trellis structure parameter in the Convolutional Encoder block tells the
block which code to use when processing data. In this case, the poly2trellis
function, in the Communications Toolbox, converts the constraint length and
the pair of octal numbers into a valid trellis structure that the block uses in its
processing.

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1 Getting Started with the Communications Blockset

Computing the Code Generator. The code generator is a 1-by-2 matrix of octal
numbers because the encoder has one input and two outputs. The first element
in the matrix indicates which input values contribute to the first output, and
the second element in the matrix indicates which input values contribute to the
second output.
For example, the first output in the encoder diagram is the modulo-2 sum of the
rightmost and the four leftmost elements in the diagram’s array of input
values. The seven-digit binary number 1111001 captures this information, and
is equivalent to the octal number 171. The octal number 171 thus becomes the
first entry of the code generator matrix. Here, each triplet of bits uses the
leftmost bit as the most significant bit.
The second output corresponds to the binary number 1011011, which is
equivalent to the octal number 133. The code generator is therefore [171 133].

Unbuffering to Convert Vectors to Scalars

After the Convolutional Encoder block encodes the data, the goal is to modulate
the codewords. However, the codewords are vectors of length two, while this
model chooses to modulate, transmit, and quantize only scalar data. Thus an
intermediate step converts the vector codewords into a scalar signal. The
Unbuffer block, in the DSP Blockset, performs this intermediate step. To check
the sizes of the input and output of the Unbuffer block, try the technique
mentioned in “Digression: Exploring Signal Sizes” on page 1-12.

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 Components of the Example

The Unbuffer block is a multirate block, which means that its input sample
rate differs from its output sample rate. In this case, the Unbuffer block
receives one length-two codeword every second and outputs a scalar every half
second.

Digression: Exploring Sample Times

Because sample times are important in communication system simulation, this
section explains two techniques for gathering information about the sample
times of components of a model. These techniques can be useful for determining
what parameters you should use for a block or for diagnosing problems in a
model.

Exact Sample Time of a Signal. To check the sample time of any signal in the
model, attach a Probe block to the signal’s line. The Probe block resides in
Simulink’s Signals & Systems library. Simply drag a Probe block into the
model window, attach its input port to the signal line you want to examine, and
then update the diagram by selecting Update diagram from the model
window’s Edit menu. The first number after the Ts or Tf notation on the Probe
block’s icon is the length of time between updates of that signal. (In the case of
frame-based signals, the Tf notation indicates that the number shown is the
period of the entire frame signal, not the period of each row of the frame.) For
more information, see the reference entry for the Probe block in the Simulink
documentation set. In this model, a Probe block attached to the line that leads
out of the Unbuffer block shows a sample time of 0.5 second.

Relative Sample Times in the Model. Another way to explore sample times is to turn
on the sample time coloring feature for the whole model. Use the Sample time
colors option in the model window’s Format menu to toggle the coloring
feature on and off. If sample time coloring is on, then blocks with the same
sample time have the same color. In this example, the Unbuffer block becomes
yellow because it is a multirate block. Also, the blocks before and after the

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1 Getting Started with the Communications Blockset

Unbuffer block have different colors because they have different sample times.
For more information about sample times, refer to Simulink documentation.

Modulating the Encoded Messages

The BPSK Modulator Baseband block, in the Digital Baseband Modulation
sublibrary of the Modulation library, modulates the scalar stream of coded
data. It simulates binary phase shift keying (BPSK) modulation. The output of
the BPSK Modulator Baseband block is a complex Simulink signal, even
though the BPSK-modulated values happen to be real.

Digression: Exploring Data Types

To check the data types of signals in a model, use the Port data types feature
from the model window’s Format menu. In this example, when this feature is
on, the connector line that leads out of the BPSK Modulator Baseband block
has a label “double (c)” above it to indicate that it is a complex double-precision
signal. By contrast, the connector line that leads into the BPSK Modulator
Baseband block is labeled “double” to indicate that it is a real double-precision
signal.

Transmitting Along a Noisy Channel

After modulation, the data is ready for transmission. The AWGN Channel
block, in the Channels library, simulates a noisy channel by adding white

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 Components of the Example

Gaussian noise to the data stream. The AWGN Channel block uses a Gaussian
distribution whose variance is determined using these mask parameters:

• Es/No, which is - 1 decibel in this example

• Input signal power, which is 1 watt because BPSK modulation produces
values of -1 and 1
• Symbol period, which is .5 second

The AWGN Channel block can compute the variance in other ways as well, but
this example chooses this mode by setting the Mode parameter to Signal to
noise ratio (Es/No).
Like the Bernoulli Random Binary Generator block, the AWGN Channel block
requires an Initial seed parameter that initializes the random number
generator. If you change the Initial seed parameter, then the block generates
a different random sequence. The Initial seed parameters of the AWGN
Channel block and the Bernoulli Random Binary Generator block do not need
to match.

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1 Getting Started with the Communications Blockset

Note The input to the AWGN Channel block is a complex Simulink signal,
not a real one (See “Digression: Exploring Data Types” on page 1-16.). This
causes the AWGN Channel block to add complex noise, dividing the calculated
variance equally between the real and imaginary components.

Mapping the Received Data

The received data, that is, the output of the AWGN Channel block, consists of
complex numbers that are close to -1 and 1. In order to reconstruct the original
binary message, the receiver part of the model must decode the convolutional
code. Although the Viterbi Decoder block is designed for convolutional
decoding, it expects its input data to have a particular format. The purpose of
the mapping task is to transform the output of the AWGN Channel block into
a format that the Viterbi Decoder block can interpret properly.
Specifically, the Viterbi Decoder block is configured here to process integer
input values between 0 and 7. The mapping procedure includes these two
tasks:

1 Convert the received data signal to a real signal by removing its imaginary
part. It is reasonable to assume that the imaginary part of the received data
does not contain essential information, because the imaginary part of the
transmitted data is zero (ignoring small roundoff errors) and because the
channel noise is not very powerful.

2 Map the resulting real signal to an integer between 0 and 7, to prepare for
the soft-decision algorithm described in the next section.

Converting to Real Data

The Complex to Real-Imag block, in Simulink’s Math library, performs step 1
above. Since its Output parameter is set to Real, the block outputs only the
real part of its input.

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 Components of the Example

Mapping to Decision Values

The Sampled Quantizer Encode block, in the Source Coding library, performs
step 2 above. This block classifies each real input value based on whether it is
greater or less than the partition values in the Quantization partition
parameter. The block then outputs a value from the Quantization codebook
parameter that depends on the classification.
As the section “Defining the Decoding Process (Technical)” on page 1-22
explains, the Viterbi Decoder requires input values that are integers between
0 and 23-1 in order to decode using three-bit soft decisions. Therefore, the
Quantization codebook parameter is a vector containing the eight integers
between 0 and 7. Since the input to the Sampled Quantizer Encode block is
close to the values -1 and 1, it is reasonable to select the seven partition values
to be -.75, -.5, -.25, 0, .25, .5, and .75. This means that the first classification
group consists of numbers less than or equal to -.75, the second classification
group consists of numbers between -.75 and -.5 (including -.5), and so on, until
the eighth classification group consists of numbers greater than .75. Finally,
the elements of the Quantization codebook and Quantization partition
vectors are ordered so that an input value of -1 maps to an output value of 7
and an input value of 1 maps to an output value of 0. The combination of this
mapping and the Viterbi Decoder block’s decision mapping reverses the BPSK
modulation that the BPSK Modulator Baseband block performs on the
transmitting side of this model.

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1 Getting Started with the Communications Blockset

Buffering to Convert Scalars to Vectors

The output of the Sampled Quantizer Encode block has values tailored to the
Viterbi Decoder block’s expectations. However, it is not yet ready for decoding
because it is a scalar, whereas the convolutional code in this example uses
codewords that are vectors of length two. The Buffer block, from the DSP
Blockset, converts the scalar output of the Sampled Quantizer Encode block
into a length-two vector signal. The output of the Buffer block is suitable input
for the Viterbi Decoder block.
The Buffer block’s outputs have length two because its Output buffer size
parameter is 2. The block combines its inputs over the first two sample times
into a single vector output; then it combines its input over the third and fourth
sample times into the subsequent single vector output, and so on.
Like the Unbuffer block, the Buffer block is a multirate block. The period of the
Buffer block’s output is twice as long as the period of its input. For more about
how to check sample times of blocks, see “Digression: Exploring Sample Times”
on page 1-15.

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 Components of the Example

Decoding the Convolutional Code

Now that the received data is properly mapped to length-two vectors of 3-bit
decision values, the Viterbi Decoder block can decode it. The Viterbi Decoder
block resides in the Convolutional sublibrary of the Channel Coding library.
The Trellis structure parameter in the Viterbi Decoder block defines the
encoder and therefore matches the corresponding parameter in the model’s
Convolutional Encoder block. For more information about this parameter, see
“Encoding Using a Convolutional Code” on page 1-12.
Other parameters in the Viterbi Decoder block are specific to the decoding
process. The block uses soft decisions with 23 different input values because the
Decision type parameter is Soft Decision and the Number of soft decision
bits parameter is 3.

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1 Getting Started with the Communications Blockset

Defining the Decoding Process (Technical)

This section elaborates on some more advanced aspects of the decoding in this
example. It discusses how the Viterbi Decoder block interprets its inputs, how
the interpretation influences the mapping done by the blocks that precede the
Viterbi Decoder block, and what the Traceback depth parameter means.

Soft-Decision Interpretation of Data. When the Decision type parameter is set to

Soft Decision, the Viterbi Decoder block requires input values between 0 and
2b-1, where b is the Number of soft decision bits parameter. The block
interprets 0 as the most confident decision that the codeword bit is a zero and
interprets 2b-1 as the most confident decision that the codeword bit is a one.
The values in between these extremes represent less confident decisions.

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 Components of the Example

The table below lists the interpretations of the eight possible input values for
this example.

Table 1-1: Decision Values for 3-Bit Soft Decisions

Decision Value Interpretation

0 Most confident 0

1 Second most confident 0

2 Third most confident 0

3 Least confident 0

4 Least confident 1

5 Third most confident 1

6 Second most confident 1

7 Most confident 1

How Decoder’s Interpretation Influences Choice of Mapping. The table above helps
explain the design of the mapping process described in “Mapping the Received
Data” on page 1-18. For example, if the original message contains a 1, then the
Viterbi Decoder block makes a correct decision if and only if it receives an input
between 4 and 7. On the other hand, the 1 in the message gets mapped to -1 by
the BPSK Modulator Baseband block and to a number near -1 by the AWGN
Channel block. This means that the Sampled Quantizer Encode block should
be configured so as to map input numbers near -1 to output numbers between
4 and 7. As the Quantization partition and Quantization codebook
parameters for the Sampled Quantizer Encode block indicate, it maps input
numbers less than 0 to output numbers between 4 and 7. The schematic below
suggests how knowledge about the modulator, channel, and decoder decisions
(solid arrows) can help you design intermediate steps like the mapping
procedure (dashed arrow).

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1 Getting Started with the Communications Blockset

Decoder
BPSK AWGN Mapping Interpretation
1 -1 near -1 4, 5, 6, or 7 1
Code bit Symbol Decision value Recovered
Code bit

Decoder
BPSK AWGN Mapping Interpretation
0 1 near 1 0, 1, 2, or 3 0
Code bit Symbol Decision value Recovered
Code bit

Figure 1-2: Processing and Recovery of Code Bits

Traceback Depth Parameter. The Traceback depth parameter in the Viterbi

Decoder block represents the length of the decoding delay. Typically, people
aim for a traceback depth of about five or six times the constraint length, which
would be 35 or 42 in this example. However, some hardware implementations
offer options of 48 and 96. This example chooses 48 because that is closer to the
targets (35 and 42) than 96 is.

Computing the Error Rate

The Error Rate Calculation block, in the Comm Sinks library, compares the
original message from the Bernoulli Random Binary Generator block with the
recovered message from the Viterbi Decoder block, and produces error
statistics. The Error Rate Calculation block produces a length-three vector
whose elements are:

• The error rate, which is the quotient of the next two quantities below
• The total number of errors, that is, comparisons between unequal elements
• The total number of comparisons that the block made

Since the block’s Output data parameter is Port, the block sends its error
statistics to the output port. At the output port, a Display block receives and
displays the error statistics.

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 Components of the Example

Delay in Received Data

One subtlety of the Error Rate Calculation block’s configuration is the Receive
delay parameter. This parameter is nonzero because a given message bit and
its corresponding recovered bit are separated in time by a nonzero amount of
simulation time. The Receive delay parameter tells the block which elements
of its input signals to compare when checking for errors.

Tip If you build your own model using the Error Rate Calculation block and
get an error rate close to .5 for binary data, then you should check whether the
Receive delay value is the correct delay for the model.

In this case, the Receive delay value is 49 samples, which is one more than the
Traceback depth value (48) in the Viterbi Decoder block. The extra
one-sample delay comes from the initial delay in the Buffer block. Because the

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1 Getting Started with the Communications Blockset

Buffer block must collect two scalar samples before it can output one vector, its
first meaningful output occurs at time 1 second, not time 0.

Displaying the Error Rate

The Display block, in Simulink’s Sinks library, receives the length-three
output of the Error Rate Calculation block and displays it while the simulation
runs. The three fields represent the error rate, the total number of errors, and
the total number of comparisons that the Error Rate Calculation block made
during the simulation. The total number of comparisons depends on how long
you let the simulation run. The simulation runs until you end it.

Other Blocks
The Terminator and Info blocks do not perform a function during the
simulation, yet they serve other purposes.

Terminator Blocks
The Terminator blocks, from Simulink’s Signals & Systems library, attach to
output ports whose signals are not used in the rest of the model. Simulink
warns you if it finds an output port that is not attached to another block.
Terminator blocks prevent warnings from occurring.

Info Block
The block marked “Info” is a customized version of Simulink’s Model Info block.
It is customized so that double-clicking on it displays the HTML version of this
documentation in the Help browser.

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 Learning More About the Example

Learning More About the Example

After you understand how the model works, you can learn even more about it
and about how the Communications Blockset works by modifying the model or
by reading other sources of information. This section suggests modifications
and reference sources that might be helpful.

Modifying the Model

The table below describes some changes that you can make in the model and
how to implement such changes. Changes that require a greater understanding
of the blocks or techniques involved appear towards the end of the table.

Table 1-2: Ideas for Modifying the Example Model

Description of Modification of Model

Change

Change sequences of Change the Initial seed parameter in the Bernoulli Random Binary
random numbers Generator block and/or the AWGN Channel block to another positive
integer.

Change distribution Change the Probability of a zero parameter in the Bernoulli Random
of random numbers Binary Generator block to another number between 0 and 1.
in message signal

Change amount of Change the Es/No parameter in the AWGN Channel block to another
noise in channel real number. Alternatively, change the Mode parameter to Signal to
noise ratio (SNR) or Variance from mask and set the associated SNR
or Variance parameter, respectively.

Change traceback Change the Traceback depth parameter in the Viterbi Decoder block
depth in decoder to another positive integer, and also change the Receive delay
parameter in the Error Rate Calculation block to that integer plus one.

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1 Getting Started with the Communications Blockset

Table 1-2: Ideas for Modifying the Example Model (Continued)

Description of Modification of Model

Change

Change convolutional Change the Trellis structure parameters in both the Convolutional
code Encoder and Viterbi Decoder blocks. For example, change it to
poly2trellis(9,[753 561]).

Note that if the new code rate is not 1/2, then you might need to change
other parts of the model to ensure that the signal sizes and sample
times are appropriate throughout the model.

Change number of Change the Number of soft decision bits in the Viterbi Decoder block,
soft-decision bits and also change the Quantization partition and Quantization
codebook parameters in the Sampled Quantizer Encode block. For
example, change these three parameters to 2, [-.5 0 .5], and
[3 2 1 0], respectively.

More generally, the length of Quantization partition must be one less

than the length of Quantization codebook, and the values in
Quantization codebook must be between 0 and 2b-1, where b is the
Number of soft decision bits parameter.

For Further Study

For more information about the communications techniques in this example,
see a reference text such as the ones listed below. The book by Clark and Cain
is particularly useful for convolutional coding.
[1] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[2] Couch, Leon W. II. Digital and Analog Communication Systems. New York:
Macmillan Publishing Company, 1990.
[3] Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan. Simulation
of Communication Systems. New York: Plenum Press, 1992.
[4] Sklar, Bernard. Digital Communications: Fundamentals and Applications.
Englewood Cliffs, N.J.: Prentice-Hall, 1988.

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 Learning More About the Example

To learn more about how to use the Communications Blockset, continue

reading this guide. “Using the Communications Blockset” covers each of the
core blockset libraries in turn.
To learn more about a particular block in this model, see its block reference
page. Communications Blockset reference pages make up the “Block
Reference” chapter in this document. If you have the model open, then you can
click on the Help button in the block’s dialog box to display the reference page.
You can also click on a Communications Blockset block name below to see its
reference page:

• Bernoulli Random Binary Generator

• Convolutional Encoder
• BPSK Modulator Baseband
• AWGN Channel
• Sampled Quantizer Encode
• Viterbi Decoder
• Error Rate Calculation
• Display (Simulink)

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1 Getting Started with the Communications Blockset

1-30
 2
Using the
Communications Blockset
Signal Support . . . . . . . . . . . . . . . . . . . 2-3

Communications Sources . . . . . . . . . . . . . . 2-6

Communications Sinks . . . . . . . . . . . . . . . 2-12

Source Coding . . . . . . . . . . . . . . . . . . . 2-16

Block Coding . . . . . . . . . . . . . . . . . . . . 2-27

Convolutional Coding . . . . . . . . . . . . . . . . 2-40

Interleaving . . . . . . . . . . . . . . . . . . . . 2-46

Analog Modulation . . . . . . . . . . . . . . . . . 2-53

Digital Modulation . . . . . . . . . . . . . . . . . 2-64

Channels . . . . . . . . . . . . . . . . . . . . . 2-84

Synchronization . . . . . . . . . . . . . . . . . . 2-90
2 Using the Communications Blockset

This chapter describes and illustrates how to implement communication

techniques using the blocks in the Communications Blockset. The first
section, “Signal Support,” discusses the types of signals that this blockset
supports. Each subsequent section corresponds to one of the core
libraries within the Communications Blockset. These sections are:

• “Communications Sources” on page 2-6

• “Communications Sinks” on page 2-12
• “Source Coding” on page 2-16
• “Block Coding” on page 2-27
• “Convolutional Coding” on page 2-40
• “Interleaving” on page 2-46
• “Analog Modulation” on page 2-53
• “Digital Modulation” on page 2-64
• “Channels” on page 2-84
• “Synchronization” on page 2-90

For descriptions of individual blocks, see their entries in Chapter 4,

“Block Reference.” For background or theoretical information about
communications techniques, see the works listed in the “Selected
Bibliography...” sections that appear in this chapter.

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 Signal Support

2. Using the Communications Blockset

Signal Support
As of Release 12, Simulink supports matrix signals in addition to
one-dimensional arrays, and frame-based signals in addition to sample-based
signals. This section describes how the Communications Blockset processes
certain kinds of matrix and frame-based signals. To learn the terminology that
this document uses to describe signal attributes, see “Technical Conventions”
on page xviii.

Processing Vectors and Matrices

These rules indicate the shapes of sample-based signals that Communications
Blockset blocks can process:

• Most blocks do not process matrix signals that have more than one row and
more than one column.
• In their numerical computations, blocks that process scalars do not
distinguish between one-dimensional scalars and one-by-one matrices. If the
block produces a scalar output from a scalar input, then the block preserves
dimension.
• If a block can process sample-based vectors, then:

- The numerical computations do not distinguish between one-dimensional

arrays, M-by-1 matrices, and 1-by-N matrices.
- The block output preserves dimension and orientation.
- The block treats elements of the input vector as a collection that arises
naturally from the block’s operation (for example, a collection of symbols
that jointly represent a codeword), or as samples from independent
channels. The block does not assume that the elements of the input vector
are successive samples from a single time series.
Some blocks process vectors but require them to be frame-based. For more
information about processing frame-based signals, see “Processing
Frame-Based and Sample-Based Signals” on page 2-4.

To find out whether a block processes scalar signals, vector signals, or both,
refer to its entry in the reference section.

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2 Using the Communications Blockset

Illustrations of Scalar and Vector Processing

The figures below depict the preservation of dimension and orientation when a
block processes scalars (without oversampling) and vectors. To display signal
dimensions in your model, turn on the Signal dimensions option in the model
window’s Format menu.

Processing Frame-Based and Sample-Based Signals

All one-dimensional arrays are sample-based, but a matrix signal can be either
frame-based or sample-based. A frame-based signal in the shape of an N-by-1
matrix represents a series of N successive samples from a single time series.
The Communications Blockset processes some frame-based signals and is
compatible with the DSP Blockset. However, the Communications Blockset
omits some frame-based features, and many blocks are not specifically
optimized for frame-based processing.

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 Signal Support

These rules indicate how most Communications Blockset blocks handle

frame-based matrix signals:

• Most blocks do not process frame-based matrix signals that have more than
one row and more than one column.
• Most blocks do not process frame-based row vectors and do not support
multichannel functionality.
• Blocks that process continuous-time signals do not process frame-based
inputs. Such blocks include the analog modulation blocks and the analog
phase-locked loop blocks.
• Blocks for which a frame-based multichannel operation would make sense,
even if the blocks do not currently support such operation, reject
sample-based vectors because their interpretation is ambiguous.
Frame-based vectors, however, have an unambiguous interpretation. Blocks
interpret a frame-based row vector as multiple channels at a single instant
of time, and interpret a frame-based column vector as multiple samples from
a single time series (that is, a single channel).
• Some blocks, such as the digital baseband modulation blocks, can produce
multiple output values for each value of a scalar input signal. In such cases,
a frame-based one-by-one matrix input results in a frame-based column
vector output. By contrast, a sample-based scalar input results in a
sample-based scalar output with a smaller sample time.

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Communications Sources
Every communication system contains one or more sources. You can find
sources in Simulink’s Sources library, in the DSP Blockset’s DSP Sources
library, and in the Communication Blockset’s Comm Sources library.
You can open the Comm Sources library by double-clicking on its icon in the
main Communications Blockset library (commlib), or by typing
commsource2

at the MATLAB prompt.

Source Features of the Blockset

Blocks in this library can:

• Generate random or pseudorandom signals

• Generate nonrandom signals by reading from a file or by simulating a
voltage-controlled oscillator (VCO)

This section describes these capabilities, considering first random and then
nonrandom signals.

Random or Pseudorandom Signals

Random signals are useful for simulating noise, errors, or signal sources.
Besides using built-in Simulink blocks such as the Random Number block, you
can also use blocks in the Comm Sources library of the Communications
Blockset to generate:

• Random bits
• Random integers
• Pseudorandom integers
• Random real numbers

This section discusses the sample time parameter, seed parameter and signal
attribute parameters that are common to many random source blocks, and
then discusses each category of random source.

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 Communications Sources

Sample Time Parameter for Random Sources

Each of the random source blocks requires you to set a Sample time parameter
in the block mask. If you configure the block to produce a sample-based signal,
then this parameter is the time interval between successive updates of the
signal. If you configure the block to produce a frame-based matrix signal, then
the Sample time parameter is the time interval between successive rows of the
frame-based matrix.
If you use a Simulink Probe block to query the period of a frame-based output
from a random source block in the Comm Sources library, then note that the
Probe block reports the period of the entire frame, not the period of each sample
in a given channel of the frame. The equation below relates the quantities
involved for a single-channel signal.
A seconds/frame = (B seconds/sample)*(S samples/frame)
where:

• A is the number shown in the Probe block after the Tf notation.

• B is the random source block’s Sample time parameter.
• S is the random source block’s Samples per frame parameter.

Seed Parameter for Random Sources

Each of the random source blocks requires you to set a seed in the block mask.
This is the initial seed that the random number generator uses when forming
its sequence of numbers. If you choose a constant seed, then the block produces
the same noise sequence each time you start the simulation. The sequence will
be different from that produced with a different constant seed. If you want the
noise to be different each time you start the simulation, then you can use a
varying seed such as cputime.

Signal Attribute Parameters for Random Sources

In most random source blocks, the output can be a frame-based matrix, a
sample-based row or column vector, or a sample-based one-dimensional array.

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The table below indicates how to set certain block parameters depending on the
kind of signal you want to generate.

Signal Attributes Parameter Settings

Sample-based,
one-dimensional

Sample-based row
vector

Also, any vector parameters in the block should

be rows, not columns.

Sample-based column
vector

Also, any vector parameters in the block should

be columns, not rows.

Frame-based

Also, set Samples per frame to the number of

samples in each output frame, that is, the
number of rows in the signal.

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 Communications Sources

The Frame-based outputs and Interpret vector parameters as 1-D check

boxes are mutually exclusive, because frame-based signals and
one-dimensional signals are mutually exclusive. The Samples per frame
parameter field is active only if the Frame-based outputs check box is
checked.

Example. The model in the figure below illustrates that one random source
block can produce various kinds of signals. The annotations in the model
indicate how each copy of the block is configured. Notice how each block’s
configuration affects the type of connector line (single or double) and the signal
dimensions that appear above each connector line. In the case of the Rayleigh
Noise Generator block, the first two block parameters (Sigma and Initial seed)
determine the number of channels in the output; for analogous indicators in
other random source blocks, see their individual reference entries.

Random Bits
The Bernoulli Random Binary Generator and Binary Vector Noise Generator
blocks both generate random bits, but differ in the way that you specify the

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distribution of 1s. As a result, the Bernoulli Random Binary Generator block is

suitable for representing sources, while the Binary Vector Noise Generator
block is more appropriate for modeling channel errors.
The Bernoulli Random Binary Generator block considers each element of the
signal to be an independent Bernoulli random variable. Also, different
elements need not be identically distributed.
The Binary Vector Noise Generator block constructs a random binary signal
using a two-stage process. First, using information that you provide in the
block mask, it determines how many 1s will appear. Then it determines where
to place the required number of 1s, so that each possible arrangement has
equal probability.
For example, if you set the Binary vector length parameter to 4, set the
Probabilities parameter to 1, and uncheck the Frame-based outputs check
box, then the block generates binary vectors of length 4, each of which contains
exactly one 1. You might use these parameters to perturb a binary code that
consists of four-bit codewords. Adding the random vector to your code vector
(modulo 2) would introduce exactly one error into each codeword. Alternatively,
to perturb each codeword by introducing one error with probability 0.4 and two
errors with probability 0.6, set the Probabilities parameter to [0.4, 0.6]
instead of 1.
Note that the Probabilities parameter of the Binary Vector Noise Generator
block affects only the number of 1s in each vector, not their placement.

Random Integers
The Random-Integer Generator and Poisson Int Generator blocks both
generate vectors containing random nonnegative integers. The
Random-Integer Generator block uses a uniform distribution on a bounded
range that you specify in the block mask. The Poisson Int Generator block uses
a Poisson distribution to determine its output. In particular, the output can
include any nonnegative integer.

Pseudorandom Symbols
The PN Sequence Generator block generates a sequence of pseudorandom
symbols. Such a sequence can be used in a pseudorandom scrambler and
descrambler, or in a direct-sequence spread-spectrum system.

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 Communications Sources

Random Real Numbers

You can use one of several blocks to generate random real numbers, depending
on what distribution you want to use. The choices are listed in the table below.

Distribution Block

Gaussian Gaussian Noise Generator

Rayleigh Rayleigh Noise Generator

Rician Rician Noise Generator

Uniform on a bounded interval Uniform Noise Generator

The particular mask parameters depend on the block. See each block’s
individual entry in the reference section for details.

Nonrandom Signals
Blocks in the Comm Sources library can create nonrandom signals by reading
from a file or by simulating a voltage-controlled oscillator (VCO):

• The Triggered Read from File block reads a record from a file whenever an
input trigger signal has a rising edge. You can set up the block to read at
every rising edge of the trigger, or every kth rising edge of the trigger for a
positive number k.
• A voltage-controlled oscillator is one part of a phase-locked loop. The
Voltage-Controlled Oscillator and Discrete-Time VCO blocks implement
voltage-controlled oscillators. These blocks produce continuous-time and
discrete-time output signals, respectively. Each block’s output signal is
sinusoidal, and changes its frequency in response to the amplitude
variations of the input signal.

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Communications Sinks
The Communications Blockset provides sinks and display devices that
facilitate analysis of communication system performance. You can open the
Comm Sinks library by double-clicking on its icon in the main Communications
Blockset library (commlib), or by typing
commsink2

at the MATLAB prompt.

Sink Features of the Blockset

Blocks in this library can:

• Write to a file when trigger events occur

• Compute error statistics
• Plot an eye diagram
• Generate a scatter diagram

This section describes these capabilities. Other sinks are in Simulink’s Sinks
library and in the DSP Blockset’s DSP Sinks library.

Writing to a File
The Triggered Write to File block writes data to a file whenever an input
trigger signal has a rising edge. You can set up the block to write at every rising
edge of the trigger, or every kth rising edge of the trigger for a positive number
k. The data can have an ASCII, integer, or floating-point format. If the
destination file already exists, then this block overwrites it. For more details,
see the reference page for the Triggered Write to File block.
For untriggered writing of MAT files, use Simulink’s To File block.

Error Statistics
The Error Rate Calculation block compares input data from a transmitter with
input data from a receiver. It calculates these error statistics:
• The error rate
• The number of error events
• The total number of input events

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 Communications Sinks

The block reports these statistics either as final values in the workspace or as
running statistics at an output port.
You can use this block either with binary inputs to compute the bit error rate,
or with symbol inputs to compute the symbol error rate. You can use
frame-based or sample-based data. Also, if you use frame-based data, then you
can have the block consider certain samples and ignore others.
The example in the section “Examples of Convolutional Coding” on page 2-42
illustrates the use of the Error Rate Calculation block.

Eye Diagrams
An eye diagram is a simple and convenient tool for studying the effects of
intersymbol interference and other channel impairments in digital
transmission. When this blockset constructs an eye diagram, it plots the
received signal against time on a fixed-interval axis. At the end of the fixed
interval, it wraps around to the beginning of the time axis. Thus the diagram
consists of many overlapping curves. One way to use an eye diagram is to look
for the place where the “eye” is most widely opened, and use that point as the
decision point when demapping a demodulated signal to recover a digital
message.
The two blocks, Continuous-Time Eye and Scatter Diagrams and
Discrete-Time Eye and Scatter Diagrams, both produce eye diagrams. One
processes continuous-time signals and the other processes discrete-time
signals. The blocks also differ in the way you determine the decision timing: the
Continuous-Time Eye and Scatter Diagrams block draws a vertical line to
indicate a decision every time a trigger signal has a rising edge, whereas the
Discrete-Time Eye and Scatter Diagrams block draws a similar line
periodically according to a mask parameter.
An example appears in “Example: Using Eye and Scatter Diagrams” on
page 2-14.

Scatter Diagrams
A scatter diagram of a signal plots the signal’s value at a given decision point.
In the best case, the decision point should be at the time when the eye of the
signal’s eye diagram is the most widely open.

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2 Using the Communications Blockset

The two blocks, Continuous-Time Eye and Scatter Diagrams and

Discrete-Time Eye and Scatter Diagrams, both produce scatter diagrams. One
processes continuous-time signals and the other processes discrete-time
signals. They also differ in the way you determine the decision timing: the
Continuous-Time Eye and Scatter Diagrams block plots a new point every time
a trigger signal has a rising edge, whereas the Discrete-Time Eye and Scatter
Diagrams block plots new points periodically according to a mask parameter.

Example: Using Eye and Scatter Diagrams

The model below creates an eye diagram and scatter diagram from a complex
sinusoidal signal. Because the decision time interval is almost, but not exactly,
an integer multiple of the period of the sinusoid, the diagram exhibits drift over
time. More specifically, successive traces in the eye diagram and successive
points in the scatter diagram are near each other but do not overlap.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Sine Wave, in the DSP Blockset DSP Sources library (not the Sine Wave
block in the Simulink Sources library)
- Set Frequency to .502
- Set Output complexity to Complex
• Discrete-Time Eye and Scatter Diagrams
- Set Diagram type to Eye and Scatter Diagrams
- Set Sample time for plot update to 1/30

Running the model produces the plots below. In the eye diagram, one set of
traces represents the real part of the signal and the other set of traces
represents the imaginary part of the signal.

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Communications Sinks

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2 Using the Communications Blockset

Source Coding
Source coding, also known as quantization or signal formatting, is a way of
processing data in order to reduce redundancy or prepare it for later
processing. Analog-to-digital conversion and data compression are two
categories of source coding.
Source coding divides into two basic procedures: source encoding and source
decoding. Source encoding converts a source signal into a digital signal using a
quantization method. The symbols in the resulting signal are nonnegative
integers in some finite range. Source decoding recovers the original
information from the source coded signal.
For background material on the subject of source coding, see the works listed
in “Selected Bibliography for Source Coding” on page 2-26.

Source Coding Features of the Blockset

This blockset supports scalar quantization, predictive quantization,
companders, and differential coding. It does not support vector quantization.
You can open the Source Coding library by double-clicking on its icon in the
main Communications Blockset library (commlib), or by typing
commsrccod2

at the MATLAB prompt.

Blocks in the Source Coding library can:
• Use a partition and codebook to quantize a signal
• Implement differential pulse code modulation (DPCM)
• Compand a signal using a µ-law or A-law compressor or expander
• Encode or decode a signal using differential coding

Supporting functions in the Communications Toolbox also allow you to

optimize source coding parameters for a set of training data. See the sections
“Optimizing Quantization Parameters” and “Optimizing DPCM Parameters”
in the Communications Toolbox User’s Guide for more information about such
capabilities.

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 Source Coding

Representing Quantization Parameters

Scalar quantization is a process that maps all inputs within a specified range
to a common value. It maps inputs in a different range of values to a different
common value. In effect, scalar quantization digitizes an analog signal. Two
parameters determine a quantization: a partition and a codebook. This section
describes how blocks represent these parameters.

Partitions
A quantization partition defines several contiguous, nonoverlapping ranges of
values within the set of real numbers. To specify a partition as a parameter,
list the distinct endpoints of the different ranges in a vector.
For example, if the partition separates the real number line into the sets

• {x: x ≤ 0}
• {x: 0< x ≤ 1}
• {x: 1 < x ≤ 3}
• {x: 3 < x}

then you can represent the partition as the three-element vector

[0,1,3]

Notice that the length of the partition vector is one less than the number of
partition intervals.

Codebooks
A codebook tells the quantizer which common value to assign to inputs that fall
into each range of the partition. Represent a codebook as a vector whose length
is the same as the number of partition intervals. For example, the vector
[-1,0.5,2,3]

is one possible codebook for the partition [0,1,3].

Quantizing a Signal
This section shows how the Sampled Quantizer Encode, Enabled Quantizer
Encode, and Quantizer Decode blocks use the partition and codebook
parameters. (The Enabled Quantizer Encode block does not appear in an
example, but its behavior is similar to that of the Sampled Quantizer Encode

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2 Using the Communications Blockset

block.) The examples here are analogous to “Scalar Quantization Example 1”

and “Scalar Quantization Example 2” in the Communications Toolbox User’s
Guide.

Scalar Quantization Example 1

The figure below shows how the Sampled Quantizer Encode block uses the
partition and codebook as defined above to map a real vector to a new vector
whose entries are either -1, 0.5, 2, or 3. In the Scope window, the bottom signal
is the quantization of the (original) top signal.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Signal From Workspace, in the DSP Blockset DSP Sources library

- Set Signal to [-2.4,-1,-.2,0,.2,1,1.2,1.9,2,2.9,3,3.5]'
• Sampled Quantizer Encode
- Set Quantization partition to [0, 1, 3]
- Set Quantization codebook to [-1, 0.5, 2, 3]
- Set Input signal vector length to 1
- Set Sample time to 1
• Terminator, in the Simulink Signals & Systems library

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 Source Coding

• Scope, in the Simulink Sinks library

- After double-clicking on the block to open it, click on the Properties icon
and set Number of axes to 2.
Connect the blocks as shown in the figure. Also, from the model window’s
Simulation menu, choose Simulation parameters; then in the Simulation
Parameters dialog box, set Stop time to 12. Running the model produces a
scope image similar to the one in the figure. (To make the axis ranges and title
exactly match those in the figure, right-click on each plot area in the scope and
select Axes properties.)

Scalar Quantization Example 2

This example, shown in the figure below, illustrates the nature of scalar
quantization more clearly. It quantizes a sampled sine wave and plots the
original (top) and quantized (bottom) signals. The plot contrasts the smooth
sine curve with the polygonal curve of the quantized signal. The vertical
coordinate of each flat part of the polygonal curve is a value in the
Quantization codebook vector.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Sine Wave, in the Simulink Sources library (not the Sine Wave block in the
DSP Blockset DSP Sources library)

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2 Using the Communications Blockset

• Sampled Quantizer Encode

- Set Quantization partition to [-1:.2:1]
- Set Quantization codebook to [-1.2:.2:1]
- Set Input signal vector length to 1
• Terminator, in the Simulink Signals & Systems library
• Scope, in the Simulink Sinks library
- After double-clicking on the block to open it, click on the Properties icon
and set Number of axes to 2.
Connect the blocks as shown in the figure. Also, from the model window’s
Simulation menu, choose Simulation parameters; then in the Simulation
Parameters dialog box, set Stop time to 2*pi. Running the model produces the
scope image as shown in the figure. (To make the axis ranges and title exactly
match those in the figure, right-click on each plot area in the scope and select
Axes properties.)

Determining Which Interval Each Input Is in

The Sampled Quantizer Encode block also returns a signal, at the first output
port, that tells which interval each input is in. For example, the model below
shows that the input entries lie within the intervals labeled 0, 6, and 5,
respectively. Here, the 0th interval consists of real numbers less than or equal
to 3; the 6th interval consists of real numbers greater than 8 but less than or
equal to 9; and the 5th interval consists of real numbers greater than 7 but less
than or equal to 8.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Constant, in the Simulink Sources library

- Set Constant value to [2, 9, 8]
• Sampled Quantizer Encode
- Set Quantization partition to [3, 4, 5, 6, 7, 8, 9]

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 Source Coding

- Set Quantization codebook to any vector whose length exceeds the

length of Quantization Partition by one
- Set Input signal vector length to 3
• Terminator, in the Simulink Signals & Systems library
• Display, in the Simulink Sinks library
- Drag the bottom edge of the icon to make the display big enough for three
entries
Connect the blocks as shown above. Running the model produces the display
numbers as shown in the figure.
You can continue this example by branching the first output of the Sampled
Quantizer Encode block, connecting one branch to the input port of the
Quantizer Decode block, and connecting the output of the Quantizer Decode
block to another Display block. If the two source coding blocks’ Quantization
codebook parameters match, then the output of the Quantizer Decode block
will be the same as the second output of the Sampled Quantizer Encode block.
Thus the Quantizer Decode block partially duplicates the functionality of the
Sampled Quantizer Encode block, but requires different input data and fewer
parameters.

Implementing Differential Pulse Code Modulation

The quantization in the section “Quantizing a Signal” on page 2-17 requires no
a priori knowledge about the transmitted signal. In practice, you can often
make educated guesses about the present signal based on past signal
transmissions. Using such educated guesses to help quantize a signal is known
as predictive quantization. The most common predictive quantization method
is differential pulse code modulation (DPCM). The DPCM Encoder and DPCM
Decoder blocks can help you implement a DPCM predictive quantizer.

DPCM Terminology
To determine an encoder for such a quantizer, you must supply not only a
partition and codebook as described in “Representing Quantization
Parameters” on page 2-17, but also a predictor. The predictor is a function that
the DPCM encoder uses to produce the educated guess at each step. Instead of
quantizing x itself, the encoder quantizes the predictive error, which is the
difference between the educated guess and the actual value. The special case
when the numerator is linear and the denominator is 1 is called delta
modulation.

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2 Using the Communications Blockset

For more information about how DPCM works, see [1] in “Selected
Bibliography for Source Coding” on page 2-26, or look underneath the masks of
the DPCM Encoder and DPCM Decoder blocks.

Representing Predictors
This blockset implements predictors using an IIR filter. Just as you can specify
a filter using a rational function of z-1, you specify the predictor by giving its
numerator and denominator. In block masks, the numerator and denominator
are vectors that list the coefficients in order of ascending powers of z-1.
The numerator’s constant term must be zero. This makes sense conceptually
because the filter’s output is meant to predict the present signal without
actually knowing its value.
In most applications, the denominator is the constant function 1.

Coded and Decoded Signals

If you encode a given signal using DPCM, then two resulting signals are the
quantization index and the quantization-encoded signal. These correspond
exactly to the two outputs of an ordinary quantization encoder. In both
instances, the quantization index tells which partition interval a signal lies in,
and the quantization-encoded signal tells which codebook values correspond to
those partition intervals.
To use the DPCM Decoder block to recover a message that has been through
the DPCM Encoder block, connect the quantization index signal, not the
quantization-encoded signal, to the input port of the DPCM Decoder block.
The DPCM Decoder block outputs two signals. The first output is the
attempted recovery of the message that first entered the DPCM encoder
(assuming the encoder and decoder have matching parameters). The second
output comes directly from the underlying quantization decoder. It represents
the quantized predictive error, not the recovered message itself.

Example: Using DPCM Encoding and Decoding

A simple special case of DPCM quantizes the difference between the signal’s
current value and its value at the previous step. Thus the predicted value
equals the actual value at the previous step. The model below implements this
scheme. It encodes a sine wave, decodes it, and plots both the original and
decoded signals.

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 Source Coding

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Sine Wave, in the DSP Blockset DSP Sources library (not the Sine Wave
block in the Simulink Sources library)
- Set Frequency to 3
- Set Sample time to .01
• DPCM Encoder
- Set Predictor numerator to [0, 1]
- Set Quantization partition to [-10:9]/10
- Set Quantization codebook to [-10:10]/10
- Set Sample time to .01
• DPCM Decoder
- Set Predictor numerator, Quantization codebook, and Sample time to
the values given for the DPCM Encoder block
• Terminator, in the Simulink Signals & Systems library
• Scope, in the Simulink Sinks library
- After double-clicking on the block to open it, click on the Properties icon
and set Number of axes to 2.
Connect the blocks as shown in the figure. Also, from the model window’s
Simulation menu, choose Simulation parameters; then in the Simulation
Parameters dialog box, set Stop time to 1.
Running the model produces scope images similar to those below. (To make the
axis ranges and titles exactly match those below, right-click on each plot area
in the scope and select Axes properties.)

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Companding a Signal
In certain applications, such as speech processing, it is common to use a
logarithm computation, called a compressor, before quantizing. The inverse
operation of a compressor is called an expander. The combination of a
compressor and expander is called a compander.
This blockset supports two kinds of companders: µ-law and A-law companders.
The reference pages for the A-Law Compressor, A-Law Expander, Mu-Law
Compressor, and Mu-Law Expander blocks list the relevant expander and
compressor laws.

Example: Using a µ-Law Compander

This example quantizes an exponential signal in two ways and compares the
resulting mean square distortions. To create the signal in the MATLAB
workspace, execute these commands:
sig = -4:.1:4;
sig = exp(sig'); % Exponential signal to quantize

Now, the model in the figure below performs two computations. One
computation uses the Sampled Quantizer Encode block with a partition
consisting of length-one intervals. The second computation uses the Mu-Law
Compressor block to implement a µ-law compressor, the Sampled Quantizer

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 Source Coding

Encode block to quantize the compressed data and, finally, the Mu-Law
Expander block to expand the quantized data.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Signal From Workspace, in the DSP Blockset DSP Sources library

- Set Signal to sig
• Mu-Law Compressor
- Set Peak signal magnitude to max(sig)
• Mux, in the Simulink Signals & Systems library
• Sampled Quantizer Encode, in the Source Coding library
- Set Quantization partition to 0:floor(max(sig))
- Set Quantization codebook to 0:ceil(max(sig))
- Set Sample time to 1
• Terminator, in the Simulink Signals & Systems library
• Demux, in the Simulink Signals & Systems library
• Mu-Law Expander
- Set Peak signal magnitude to ceil(max(sig))
• Two copies of To Workspace, in the Simulink Sinks library
- Set Variable name to nocompander and withcompander, respectively, in
the two copies of this block
- Set Save format to Array in each of the two copies of this block
Connect the blocks as shown above. Also, from the model window’s Simulation
menu, choose Simulation parameters; then in the Simulation Parameters
dialog box, set Stop time to 80. Run the model, then execute these commands:

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distor = sum((nocompander-sig).^2)/length(sig);
distor2 = sum((withcompander-sig).^2)/length(sig);
[distor distor2]

ans =

0.5348 0.0397

This output shows that the distortion is smaller for the second scheme. This is
because equal-length intervals are well suited to the logarithm of the data but
not as well suited to the data itself.

Selected Bibliography for Source Coding

[1] Kondoz, A. M. Digital Speech. Chichester, England: John Wiley & Sons,
1994.
[2] Sklar, Bernard. Digital Communications: Fundamentals and Applications.
Englewood Cliffs, N.J.: Prentice-Hall, 1988.

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 Block Coding

Block Coding
Error-control coding techniques detect and possibly correct errors that occur
when messages are transmitted in a digital communication system. To
accomplish this, the encoder transmits not only the information symbols but
also extra redundant symbols. The decoder interprets what it receives, using
the redundant symbols to detect and possibly correct whatever errors occurred
during transmission. You might use error-control coding if your transmission
channel is very noisy or if your data is very sensitive to noise. Depending on the
nature of the data or noise, you might choose a specific type of error-control
coding.
Block coding is a special case of error-control coding. Block coding techniques
maps a fixed number of message symbols to a fixed number of code symbols. A
block coder treats each block of data independently and is a memoryless device.

Organization of This Section

These topics provide background information:

• “Accessing Block Coding Blocks” on page 2-27

• “Block Coding Features of the Blockset” on page 2-28
• “Communications Toolbox Support Functions” on page 2-29
• “Channel Coding Terminology” on page 2-29

These topics describe how to simulate linear block coding:

• “Data Formats for Block Coding” on page 2-29

• “Using Block Encoders and Decoders Within a Model” on page 2-32
• “Examples of Block Coding” on page 2-32
• “Notes on Specific Block Coding Techniques” on page 2-35

For background material on the subject of block coding, see the works listed in
“Selected Bibliography for Block Coding” on page 2-39.

Accessing Block Coding Blocks

You can open the Channel Coding library by double-clicking on its icon in the
main Communications Blockset library (commlib), or by typing
commfeccod2

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2 Using the Communications Blockset

at the MATLAB prompt.

Then you can open the Block sublibrary by double-clicking on its icon in the
Channel Coding library, or by typing
commblkcod2

at the MATLAB prompt.

Block Coding Features of the Blockset

The class of block coding techniques includes categories shown in the diagram
below.

Linear block codes

Cyclic codes

BCH codes

Hamming codes Reed-Solomon codes

The Communications Blockset supports general linear block codes. It also

includes blocks that process cyclic, BCH, Hamming, and Reed-Solomon codes
(which are all special kinds of linear block codes). Blocks in the blockset can
encode or decode a message using one of the techniques mentioned above. The
Reed-Solomon and BCH decoders indicate how many errors they detected
while decoding. The Reed-Solomon coding blocks also let you decide whether to
use symbols or bits as your data.

Note The blocks in this blockset are designed for error-control codes that use
an alphabet having 2 or 2m symbols.

2-28
 Block Coding

Communications Toolbox Support Functions

Functions in the Communications Toolbox can support the Communications
Blockset simulation blocks by:
• Determining characteristics of a technique, such as error-correction
capability or possible message lengths
• Performing lower-level computations associated with a technique, such as:
- Computing a truth table
- Computing a generator or parity-check matrix
- Converting between generator and parity-check matrices
- Computing a generator polynomial
For more information about error-control coding capabilities of the
Communications Toolbox, see the section “Block Coding” in the
Communications Toolbox User’s Guide.

Channel Coding Terminology

Throughout this section, the information to be encoded consists of message
symbols and the code that is produced consists of codewords.
Each block of K message symbols is encoded into a codeword that consists of N
message symbols. K is called the message length, N is called the codeword
length, and the code is called an [N,K] code.

Data Formats for Block Coding

Each message or codeword is an ordered grouping of symbols. Each block in the
Block Coding sublibrary processes one word in each time step, as described in
“Binary Format (All Coding Methods)” below. Reed-Solomon coding blocks also
let you choose between binary and integer data, as described in “Integer
Format (Reed-Solomon only)” on page 2-31.

Binary Format (All Coding Methods)

You can structure messages and codewords as binary vector signals, where
each vector represents a message word or a codeword. At a given time, the
encoder receives an entire message word, encodes it, and outputs the entire
codeword. The message and code signals share the same sample time.

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2 Using the Communications Blockset

The figure below illustrates this situation. In this example, the encoder
receives a four-bit message and produces a five-bit codeword at time 0. It
repeats this process with a new message at time 1.

0 0 0 1
1 1 0 0
message Encoder 1 1 code
1 0
0 0 1 0
0 0
t=1 t=0
t=1 t=0

For all coding techniques except Reed-Solomon, the message vector must have
length K and the corresponding code vector has length N. For Reed-Solomon
codes, the message vector must have length M*K and the corresponding code
vector has length M*N. Here M is an integer greater than or equal to 3 that
satisfies N = 2M-1.
If the input to a block coding block is a frame-based vector, then it must be a
column vector instead of a row vector.
To produce sample-based messages in the binary format, you can configure the
Bernoulli Random Binary Generator block so that its Probability of a zero
parameter is a vector whose length is that of the signal you want to create. To
produce frame-based messages in the binary format, you can configure the
same block so that its Probability of a zero parameter is a scalar and its
Samples per frame parameter is the length of the signal you want to create.

Using Serial Signals. If you prefer to structure messages and codewords as scalar
signals, where several samples jointly form a message word or codeword, then
you can use the Buffer and Unbuffer blocks in the DSP Blockset. Be aware that
buffering involves latency and multirate processing. See the reference page for
the Buffer block for more details. If your model computes error rates, then the
initial delay in the coding-buffering combination influences the Receive delay
parameter in the Error Rate Calculation block. If you are unsure about the
sample times of signals in your model, then selecting Sample time colors from
the model’s Format menu, or attaching Probe blocks (from the Simulink
Signals & Systems library) to connector lines might help.

2-30
 Block Coding

Integer Format (Reed-Solomon only)

A message word for an [N,K] Reed-Solomon code consists of M*K bits, which
you can interpret as K symbols between 0 and 2M. Here N = 2M-1 and M is an
integer greater than or equal to 3. The integer format for Reed-Solomon codes
lets you structure messages and codewords as integer signals instead of binary
signals. (If the input is a frame-based vector, then it must be a column vector
instead of a row vector.)

Note In this context, Simulink expects the first bit to be the least significant
bit in the symbol. “First” means the smallest index in a vector or the smallest
time for a series of scalars.

The figure below illustrates the equivalence between binary and integer
signals for a Reed-Solomon encoder. The case for the decoder would be similar.

t=0 t=0
0 6
1 7
1 4
1 0
1 Vector of 5 4 Integer format
1 three-bit symbols versus
0 Binary format
0 Vector of 3*5 bits
1
0
0
0
0
0
1

To produce sample-based messages in the integer format, you can configure the
Random-Integer Generator block so that M-ary number and Initial seed
parameters are vectors of the desired length and all entries of the M-ary
number vector are 2M. To produce frame-based messages in the integer
format, you can configure the same block so that its M-ary number and Initial
seed parameters are scalars and its Samples per frame parameter is the
length of the signal you want to create.

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2 Using the Communications Blockset

Using Block Encoders and Decoders Within a Model

Once you have configured the coding blocks, a few tips will help you place them
correctly within your model:
• If a block has multiple outputs, then the first one is always the stream of
coding data.
The Reed-Solomon and BCH blocks have an error counter as a second output.
• Be sure the signal sizes are appropriate for the mask parameters. For
example, if you use the Binary Cyclic Encoder block and set Message
length K to 4, then the input signal must be a vector of length 4.
If you are unsure about the size of signals in your model, then selecting
Signal dimensions from the model’s Format menu may help.

Examples of Block Coding

This section presents two example models. The first example processes a
Hamming code using the binary format and the second example processes a
Reed-Solomon code using the integer format.

Example: Hamming Code in Binary Format

This example shows very simply how to use an encoder and decoder. It
illustrates the appropriate vector lengths of the code and message signals for
the coding blocks. Also, because the Error Rate Calculation block accepts only
scalars or frame-based column vectors as the transmitted and received signals,
this example uses frame-based column vectors throughout. (It thus avoids
having to change signal attributes using a block such as Convert 1-D to 2-D.)

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Bernoulli Random Binary Generator, in the Comm Sources library

- Set Probability of a zero to .5

2-32
 Block Coding

- Set Initial seed to any positive integer scalar

- Check the Frame-based outputs check box
- Set Samples per frame to 4
• Hamming Encoder, with default parameter values
• Hamming Decoder, with default parameter values
• Error Rate Calculation, in the Comm Sinks library, with default parameter
values

Connect the blocks as in the figure above. Also, use the Signal dimensions
feature from the model window’s Format menu. After possibly updating the
diagram if necessary (Update diagram from the Edit menu), the connector
lines show relevant signal attributes. The connector lines are double lines to
indicate frame-based signals, and the annotations next to the lines show that
the signals are column vectors of appropriate sizes.

Example: Reed-Solomon Code in Integer Format

This example uses a Reed-Solomon code in integer format. It illustrates the
appropriate vector lengths of the code and message signals for the coding
blocks. It also exhibits error correction, using a very simplistic way of
introducing errors into each codeword.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Random-Integer Generator, in the Comm Sources library

- Set M-ary number to 15
- Set Initial seed to any vector containing 5 positive integers
- Check the Interpret vector parameters as 1-D check box

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2 Using the Communications Blockset

• Integer-Input RS Encoder
- Set Codeword length N to 15
• Gain, in the Simulink Math library
- Set Gain to [0 0 0 0 0, ones(1,10)]
• Integer-Output RS Decoder
- Set Codeword length N to 15
• Scope, in the Simulink Sinks library. Get two copies of this block.
• Sum, in the Simulink Math library
- Set List of signs to |-+
Connect the blocks as in the figure above. Also, from the model window’s
Simulation menu, choose Simulation parameters; then in the Simulation
Parameters dialog box, set Stop time to 500.
The vector length numbers appear on the connecting lines only if you select
Signal dimensions from the model’s Format menu. Notice that the encoder
accepts a vector of length 5 (which is K in this case) and produces a vector of
length 15 (which is N in this case). The decoder does the opposite. Also, the
Initial seed parameter in the Random-Integer Generator block is a vector of
length 5 because it must generate a message word of length 5.
Running the model produces the scope images below. Your plot of the error
counts might differ somewhat, depending on your Initial seed value in the
Random-Integer Generator block. (To make the axis range exactly match that
of the left scope in the figure, right-click on the plot area in the scope and select
Axes properties.)

2-34
 Block Coding

Difference Between Original Message and Recovered Message Number of Errors Before Correction

The plot on the right is the number of errors that the decoder detected while
trying to recover the message. Often the number is five because the Gain block
replaces the first five symbols in each codeword with zeros. However, the
number of errors is less than five whenever a correct codeword contains one or
more zeroes in the first five places.
The plot on the left is the difference between the original message and the
recovered message; since the decoder was able to correct all errors that
occurred, each of the five data streams in the plot is zero.

Notes on Specific Block Coding Techniques

Although the Block Coding sublibrary is somewhat uniform in its look and feel,
the various coding techniques are not identical. This section describes special
options and restrictions that apply to parameters and signals for the coding
technique categories in this sublibrary. You should read the part that applies
to the coding technique you want to use: generic linear block code, cyclic code,
Hamming code, BCH code, or Reed-Solomon code.

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2 Using the Communications Blockset

Generic Linear Block Codes

Encoding a message using a generic linear block code requires a generator
matrix. Decoding the code requires the generator matrix and possibly a truth
table. In order to use the Binary Linear Encoder and Binary Linear Decoder
blocks, you must understand the Generator matrix and Error-correction
truth table parameters.

Generator Matrix. The process of encoding a message into an [N,K] linear block
code is determined by a K-by-N generator matrix G. Specifically, a 1-by-K
message vector v is encoded into the 1-by-N codeword vector vG. If G has the
form [Ik, P] or [P, Ik], where P is some K-by-(N-K) matrix and Ik is the K-by-K
identity matrix, then G is said to be in standard form. (Some authors, such as
Clark and Cain [1], use the first standard form, while others, such as Lin and
Costello [2], use the second.) The linear block coding blocks in this blockset
require the Generator matrix mask parameter to be in standard form.

Decoding Table. A decoding table tells a decoder how to correct errors that might
have corrupted the code during transmission. Hamming codes can correct any
single-symbol error in any codeword. Other codes can correct, or partially
correct, errors that corrupt more than one symbol in a given codeword.
The Binary Linear Decoder block allows you to specify a decoding table in the
Error-correction truth table parameter. Represent a decoding table as a
matrix with N columns and 2N-K rows. Each row gives a correction vector for
one received codeword vector.
If you do not want to specify a decoding table explicitly, then set that parameter
to 0. This causes the block to compute a decoding table using the syndtable
function in the Communications Toolbox.

Cyclic Codes
For cyclic codes, the codeword length N must have the form 2M-1, where M is
an integer greater than or equal to 3.

Generator Polynomials. Cyclic codes have special algebraic properties that allow
a polynomial to determine the coding process completely. This so-called
generator polynomial is a degree-(N-K) divisor of the polynomial xN-1. Van Lint
[4] explains how a generator polynomial determines a cyclic code.
The Binary Cyclic Encoder and Binary Cyclic Decoder blocks allow you to
specify a generator polynomial as the second mask parameter, instead of

2-36
 Block Coding

specifying K there. The blocks represent a generator polynomial using a vector

that lists the polynomial’s coefficients in order of ascending powers of the
variable. You can find generator polynomials for cyclic codes using the
cyclpoly function in the Communications Toolbox.

If you do not want to specify a generator polynomial, then set the second mask
parameter to the value of K.

Hamming Codes
For Hamming codes, the codeword length N must have the form 2M-1, where
M is an integer greater than or equal to 3. The message length K must equal
N-M.

Primitive Polynomials. Hamming codes rely on algebraic fields that have 2M

elements (or, more generally, pM elements for a prime number p). Elements of
such fields are named relative to a distinguished element of the field that is
called a primitive element. The minimal polynomial of a primitive element is
called a primitive polynomial. The Hamming Encoder and Hamming Decoder
blocks allow you to specify a primitive polynomial for the finite field that they
use for computations. If you want to specify this polynomial, then do so in the
second mask parameter field. The blocks represent a primitive polynomial
using a vector that lists the polynomial’s coefficients in order of ascending
powers of the variable. You can find generator polynomials for Galois fields
using the gfprimfd function in the Communications Toolbox.
If you do not want to specify a primitive polynomial, then set the second mask
parameter to the value of K.

BCH Codes
For BCH codes, the codeword length N must have the form 2M-1, where M is
an integer greater than or equal to 3. The message length K can have only
particular values. To see which values of K are valid for a given N, use the
bchpoly function in the Communications Toolbox. For example, in the output
below, the second column lists all possible message lengths that correspond to
a codeword length of 31. The third column lists the corresponding
error-correction capabilities.
params = bchpoly(31)

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2 Using the Communications Blockset

params =

31 26 1
31 21 2
31 16 3
31 11 5
31 6 7

No known analytic formula describes the relationship among the codeword

length, message length, and error-correction capability for BCH codes.

Error Information. The BCH Decoder block allows you to state the
error-correction capability of the code, as the Error-correction capability T
parameter. Providing the value here speeds the computation. If you do not
know the code’s error-correction capability, then setting this parameter to zero
causes the block to calculate the error-correction capability when initializing.
You can find out the error-correction capability using the bchpoly function in
the Communications Toolbox.
The BCH Decoder block also returns error-related information during the
simulation. The second output signal indicates the number of errors that the
block detected in the input codeword. A negative integer in the second output
indicates that the block detected more errors than it could correct using the
coding scheme.

Reed-Solomon Codes
Reed-Solomon codes are useful for correcting errors that occur in bursts. The
codeword length N of a Reed-Solomon code must have the form 2M-1, where M
is an integer greater than or equal to 3. The error correction capability of a
Reed-Solomon code is floor((N-K)/2). Since N is an odd number, the coding
is more efficient when the message length K is also odd.

Effect of Nonbinary Symbols. One difference between Reed-Solomon codes and the
other codes supported in this blockset is that Reed-Solomon codes process
symbols in GF(2M) instead of GF(2). Each such symbol is specified by M bits.
The nonbinary nature of the Reed-Solomon code symbols causes the
Reed-Solomon blocks to differ from other coding blocks in these ways:

• You can use the integer format, via the Integer-Input RS Encoder and
Integer-Output RS Decoder blocks.

2-38
 Block Coding

• The binary format forms a message from M*K (not K) samples and a
codeword from M*N (not N) samples.
• The binary format expects the vector lengths to be M*K (not K) for messages
and M*N (not N) for codewords.

Error Information. The Reed-Solomon decoding blocks (Binary-Output RS

Decoder and Integer-Output RS Decoder) return error-related information
during the simulation. The second output signal indicates the number of errors
that the block detected in the input codeword. A negative integer in the second
output indicates that the block detected more errors than it could correct using
the coding scheme.

Selected Bibliography for Block Coding

[1] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[2] Lin, Shu and Daniel J. Costello, Jr. Error Control Coding: Fundamentals
and Applications. Englewood Cliffs, N.J.: Prentice-Hall, 1983.
[3] Peterson, W. Wesley and E. J. Weldon, Jr. Error-correcting Codes, 2nd ed.
Cambridge, Mass.: MIT Press, 1972.
[4] van Lint, J. H. Introduction to Coding Theory. New York: Springer-Verlag,
1982.

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2 Using the Communications Blockset

Convolutional Coding
Convolutional coding is a special case of error-control coding. Unlike a block
coder, a convolutional coder is not a memoryless device. Even though a
convolutional coder accepts a fixed number of message symbols and produces a
fixed number of code symbols, its computations depend not only on the current
set of input symbols but on some of the previous input symbols.

Organization of This Section

• Describes how to access the Convolutional sublibrary of Channel Coding
• Summarizes the software’s capabilities
• Discusses parameters for convolutional coding (polynomial description and
trellis description)
• Gives examples of convolutional coding

For background material on the subject of convolutional coding, see the works
listed in “Selected Bibliography for Convolutional Coding” on page 2-45.

Accessing Convolutional Coding Blocks

You can open the Channel Coding library by double-clicking on its icon in the
main Communications Blockset library (commlib), or by typing
commfeccod2

at the MATLAB prompt.

Then you can open the Convolutional sublibrary by double-clicking on its icon
in the Channel Coding library, or by typing
commconvcod2

at the MATLAB prompt.

Convolutional Coding Features of the Blockset

The Communications Blockset supports feedforward or feedback binary
convolutional codes that can be described by a trellis structure or a set of
generator polynomials. It uses the Viterbi algorithm to implement
hard-decision and soft-decision decoding.

2-40
 Convolutional Coding

The blockset also includes an a posteriori probability decoder, which can be

useful for processing turbo codes.

Parameters for Convolutional Coding

To process convolutional codes (including turbo codes), use the Convolutional
Encoder, Viterbi Decoder, and/or APP Decoder blocks in the Convolutional
sublibrary. If a mask parameter is required in both the encoder and the
decoder, then use the same value in both blocks.
The blocks in the Convolutional sublibrary assume that you use one of two
different representations of a convolutional encoder:

• If you design your encoder using a diagram with shift registers and modulo-2
adders, then you can compute the code generator polynomial matrix and
subsequently use the poly2trellis function (in the Communications
Toolbox) to generate the corresponding trellis structure mask parameter
automatically. For an example, see “Example: A Rate 2/3 Feedforward
Convolutional Encoder” on page 2-42.
• If you design your encoder using a trellis diagram, then you can construct the
trellis structure in MATLAB and use it as the mask parameter.

Details about these representations are in the sections, “Polynomial

Description of a Convolutional Encoder” and “Trellis Description of a
Convolutional Encoder,” in the Communications Toolbox User’s Guide.

Using the Polynomial Description in Blocks

To use the polynomial description with the Convolutional Encoder, Viterbi
Decoder, or APP Decoder blocks, you can use the utility function poly2trellis,
from the Communications Toolbox. This function accepts a polynomial
description and converts it into a trellis description. For example, the command
below computes the trellis description of an encoder whose constraint length is
five and whose generator polynomials are 35 and 31.
trellis = poly2trellis(5,[35 31]);

To use this encoder with one of the convolutional coding blocks, simply place a
poly2trellis command such as
poly2trellis(5,[35 31]);

in the Trellis structure parameter field.

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2 Using the Communications Blockset

Examples of Convolutional Coding

The model below uses a rate 2/3 feedforward encoder, and the accompanying
description explains how to determine the coding blocks’ parameters from a
schematic of the encoder. It also illustrates the use of the Error Rate
Calculation block with a receive delay.
Another example using blocks from the Convolutional Coding library is the
model in “Getting Started with the Communications Blockset” on page 1-1,
which uses a quantizer and the Viterbi Decoder block to implement
soft-decision Viterbi decoding. This model also illustrates the use of the Error
Rate Calculation block with a receive delay.

Example: A Rate 2/3 Feedforward Convolutional Encoder

This example uses the rate 2/3 feedforward convolutional encoder depicted in
the figure below.

z-1 z-1 z-1 z-1

z-1 z-1 z-1

How to Determine Coding Parameters. The Convolutional Encoder and Viterbi

Decoder blocks can implement this code if their parameters have the
appropriate values.
The encoder’s constraint length is a vector of length 2 since the encoder has two
inputs. The elements of this vector indicate the number of bits stored in each

2-42
 Convolutional Coding

shift register, including the current input bits. Counting memory spaces in
each shift register in the diagram and adding one for the current inputs leads
to a constraint length of [5 4].
To determine the code generator parameter as a 2-by-3 matrix of octal
numbers, use the element in the ith row and jth column to indicate how the ith
input contributes to the jth output. For example, to compute the element in the
second row and third column, notice that the leftmost and two rightmost
elements in the second shift register of the diagram feed into the sum that
forms the third output. Capture this information as the binary number 1011,
which is equivalent to the octal number 13. The full value of the code generator
matrix is [27 33 0; 0 5 13].
To use the constraint length and code generator parameters in the
Convolutional Encoder and Viterbi Decoder blocks, use the poly2trellis
function to convert those parameters into a trellis structure.

How to Simulate the Encoder. Below is a model that simulates this encoder.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Bernoulli Random Binary Generator, in the Comm Sources library

- Set Probability of a zero to .5
- Set Initial seed to any positive integer scalar
- Set Sample time to .5
- Check the Frame-based outputs check box
- Set Samples per frame to 2
• Convolutional Encoder
- Set Trellis structure to poly2trellis([5 4],[27 33 0; 0 5 13])

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2 Using the Communications Blockset

• An additional copy of the Bernoulli Random Binary Generator, in the Comm

Sources library
- Set Probability of a zero to .05
- Set Initial seed to any positive integer scalar
- Set Sample time to 1/3
- Check the Frame-based outputs check box
- Set Samples per frame to 3
• Sum, in the Simulink Math library, with default parameter values
• Viterbi Decoder
- Set Trellis structure to poly2trellis([5 4],[27 33 0; 0 5 13])
- Set Decision type to Hard Decision
• Error Rate Calculation, in the Comm Sinks library
- Set Receive delay to 68
- Set Output data to Port
• Display, in the Simulink Sinks library
- Drag the bottom edge of the icon to make the display big enough for three
entries
Connect the blocks as in the figure, using the first Bernoulli Random Binary
Generator block at the far left. Also, from the model window’s Simulation
menu, choose Simulation parameters; then in the Simulation Parameters
dialog box, set Stop time to 500.

Notes on the Model. The matrix size annotations appear on the connecting lines
only if you select Signal Dimensions from the model’s Format menu. Notice
that the encoder accepts a 2-by-1 frame-based vector and produces a 3-by-1
frame-based vector, while the decoder does the opposite. The Samples per
frame parameter in the first Bernoulli Random Binary Generator block is 2
because the block must generate a message word of length 2, while that
parameter in the second Bernoulli Random Binary Generator block is 3
because the block must perturb a codeword of length 3.
Also notice that the Receive delay parameter in the Error Rate Calculation
block is 68, which is the vector length (2) of the recovered message times the
Traceback depth value (34) in the Viterbi Decoder block. If you examined the
transmitted and received signals as matrices in the MATLAB workspace, then
you would see that the first 34 rows of the recovered message consists of zeros,

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 Convolutional Coding

while subsequent rows are the decoded messages. Thus the delay in the
received signal is 34 vectors of length 2, or 68 samples.
Running the model produces display output similar to that shown in the figure.
The three numbers in the Display block indicate the error rate, the total
number of errors, and the total number of comparisons that the Error Rate
Calculation block made during the simulation. (The first two numbers vary
depending on your Initial seed value in the Bernoulli Random Binary
Generator blocks.) Because the simulation runs from time 0 to time 500, the
block compares 501 pairs of vectors of length 2, hence 1002 pairs of samples.
However, 68 of the received samples constitute the initial delay, so the total
number of comparisons by the end of the simulation is 934.

Selected Bibliography for Convolutional Coding

[1] Benedetto, Sergio and Guido Montorsi. “Performance of Continuous and
Blockwise Decoded Turbo Codes.” IEEE Communications Letters, vol. 1, May
1997. 77-79.
[2] Benedetto, S., G. Montorsi, D. Divsalar, and F. Pollara. “A Soft-Input
Soft-Output Maximum A Posterior (MAP) Module to Decode Parallel and
Serial Concatenated Codes.” JPL TMO Progress Report, vol. 42-127, November
1996. [This electronic journal is available at http://tmo.jpl.nasa.gov/tmo/
progress_report/index.html.]

[3] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[4] Gitlin, Richard D., Jeremiah F. Hayes, and Stephen B. Weinstein. Data
Communications Principles. New York: Plenum, 1992.
[5] Viterbi, Andrew J. “An Intuitive Justification and a Simplified
Implementation of the MAP Decoder for Convolutional Codes.” IEEE Journal
on Selected Areas in Communications, vol. 16, February 1998. 260-264.

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2 Using the Communications Blockset

2. Using the Communications Blockset

Interleaving
An interleaver permutes symbols according to a mapping. A corresponding
deinterleaver uses the inverse mapping to restore the original sequence of
symbols. Interleaving and deinterleaving can be useful for reducing errors
caused by burst errors in a communication system.
You can open the Interleaving library by double-clicking on its icon in the main
Communications Blockset library (commlib), or by typing
comminterleave2

at the MATLAB prompt.

Then you can open the interleaving sublibraries by double-clicking on their
icons in the Interleaving library, or by typing these commands at the MATLAB
prompt.
commblkintrlv2
commcnvintrlv2

Interleaving Features of the Blockset

This blockset provides interleavers in two broad categories:

• Block interleavers. This category includes matrix, random, algebraic, and

helical scan interleavers as special cases.
• Convolutional interleavers. This category includes a helical interleaver as a
special case, as well as a general multiplexed interleaver.

In typical usage of all interleaver/deinterleaver pairs in this blockset, the

parameters of the deinterleaver match those of the interleaver.
For background information about interleavers, see the works listed in
“Selected Bibliography for Interleaving” on page 2-51.

Block Interleavers
A block interleaver accepts a set of symbols and rearranges them, without
repeating or omitting any of the symbols in the set. The number of symbols in
each set is fixed for a given interleaver. The interleaver’s operation on a set of
symbols is independent of its operation on all other sets of symbols.

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 Interleaving

Types of Block Interleavers

The set of block interleavers in this library includes a general
interleaver/deinterleaver pair as well as several special cases. Each
special-case block uses the same computational code that its more general
counterpart uses, but provides an interface that is more suitable for the special
case.
The Matrix Interleaver block accomplishes block interleaving by filling a
matrix with the input symbols row by row and then sending the matrix
contents to the output port column by column. For example, if the interleaver
uses a 2-by-3 matrix to do its internal computations, then for an input of
[1 2 3 4 5 6] the block produces an output of [1 4 2 5 3 6].

The Random Interleaver block chooses a permutation table randomly using the
Initial seed parameter that you provide in the block mask. By using the same
Initial seed value in the corresponding Random Deinterleaver block, you can
restore the permuted symbols to their original ordering.
The Algebraic Interleaver block uses a permutation table that is algebraically
derived. It supports Takeshita-Costello interleavers and Welch-Costas
interleavers. These interleavers are described in [4].

Convolutional Interleavers
A convolutional interleaver consists of a set of shift registers, each with a fixed
delay. In a typical convolutional interleaver, the delays are nonnegative
integer multiples of a fixed integer (although a general multiplexed interleaver
allows arbitrary delay values). Each new symbol from the input signal feeds
into the next shift register and the oldest symbol in that register becomes part
of the output signal. The schematic below depicts the structure of a
convolutional interleaver by showing the set of shift registers and their delay
values D(1), D(2),...,D(N). The blocks in this library have mask parameters that
indicate the delay for each shift register. The delay is measured in samples.

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2 Using the Communications Blockset

z-D(1)

z-D(2) The kth shift register holds D(k) symbols,

Input Output where k=1, 2,...,N.

z-D(N)

This section discusses:

• The types of convolutional interleavers included in the library

• The delay between the original sequence and the restored sequence
• An example that uses a convolutional interleaver

Types of Convolutional Interleavers

The set of convolutional interleavers in this library includes a general
interleaver/deinterleaver pair as well as several special cases. Each
special-case block uses the same computational code that its more general
counterpart uses, but provides an interface that is more suitable for the special
case.
The most general block in this library is the General Multiplexed Interleaver
block, which allows arbitrary delay values for the set of shift registers. To
implement the schematic above using this block, you would use an Interleaver
delay parameter of [D(1); D(2); ...; D(N)].
More specific is the Convolutional Interleaver block, in which the delay value
for the kth shift register is (k-1) times the block’s Register length step
parameter. The number of shift registers in this block is the value of the Rows
of shift registers parameter.
Finally, the Helical Interleaver block supports a special case of convolutional
interleaving that fills an array with symbols in a helical fashion and empties
the array row by row. To configure this interleaver, use the Number of
columns of helical array parameter to set the width of the array, and use the
Group size and Helical array step size parameters to determine how symbols

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 Interleaving

are placed in the array. See the reference page for the Helical Interleaver block
for more details and an example.

Delay Between Original and Restored Sequences

After a sequence of symbols passes through a convolutional interleaver and a
corresponding convolutional deinterleaver, the restored sequence lags behind
the original sequence. The delay, measured in symbols, between the original
and restored sequences is
(Number of shift registers) * (Maximum delay among all shift registers)
for the most general multiplexed interleaver. If your model incurs an
additional delay between the interleaver output and the deinterleaver input,
then the restored sequence lags behind the original sequence by the sum of the
additional delay and the amount in the formula above.

Note For proper synchronization, the delay in your model between the
interleaver output and the deinterleaver input must be an integer multiple of
the number of shift registers. You can use the Integer Delay block in the DSP
Blockset to adjust delays manually, if necessary.

Convolutional Interleaver block. In the special case implemented by the

Convolutional Interleaver/Convolutional Deinterleaver pair, note that the
number of shift registers is the Rows of shift registers parameter, while the
maximum delay among all shift registers is
(Register length step)*(Rows of shift registers-1)

Helical Interleaver block. In the special case implemented by the Helical

Interleaver/Helical Deinterleaver pair, the delay between the restored
sequence and the original sequence is

s(C – 1)
CN --------------------
-
N
where C is the Number of columns in helical array parameter, N is the
Group size parameter, and s is the Helical array step size parameter.

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Example: Convolutional Interleavers

The example below illustrates convolutional interleaving and deinterleaving
using a sequence of consecutive integers. It also illustrates the inherent delay
and the effect of the interleaving blocks’ initial conditions.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Ramp, in the Simulink Sources library. Use default parameters.

• Zero-Order Hold, in the Simulink Discrete library. Use default parameters.
• Convolutional Interleaver
- Set Rows of shift registers to 3
- Set Initial conditions to [-1 -2 -3]'
• Convolutional Deinterleaver
- Set Rows of shift registers to 3
- Set Initial conditions to [-1 -2 -3]'
• Two copies of To Workspace, in the Simulink Sinks library
- Set Variable name to interleaved and restored, respectively, in the two
copies of this block
- Set Save format to Array in each of the two copies of this block
Connect the blocks as shown above. Also, from the model window’s Simulation
menu, choose Simulation parameters; then in the Simulation Parameters
dialog box, set Stop time to 20. Run the simulation, then execute this
command.
comparison = [[0:20]', interleaved, restored]

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 Interleaving

comparison =

0 0 -1
1 -2 -2
2 -3 -3
3 3 -1
4 -2 -2
5 -3 -3
6 6 -1
7 1 -2
8 -3 -3
9 9 -1
10 4 -2
11 -3 -3
12 12 0
13 7 1
14 2 2
15 15 3
16 10 4
17 5 5
18 18 6
19 13 7
20 8 8

In this output, the first column contains the original symbol sequence. The
second column contains the interleaved sequence, while the third column
contains the restored sequence.
The negative numbers in the interleaved and restored sequences come from the
interleaving blocks’ initial conditions, not from the original data. The first of
the original symbols appears in the restored sequence only after a delay of 12
symbols. The delay of the interleaver-deinterleaver combination is the product
of the number of shift registers (3) and the maximum delay among all shift
registers (4).

Selected Bibliography for Interleaving

[1] Berlekamp, E. R. and P. Tong. “Improved Interleavers for Algebraic Block
Codes.” U. S. Patent 4559625, Dec. 17, 1985.

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[2] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[3] Forney, G., D., Jr. “Burst-Correcting Codes for the Classic Bursty Channel.”
IEEE Transactions on Communications, vol. COM-19, October 1971. 772-781.
[4] Heegard, Chris and Stephen B. Wicker. Turbo Coding. Boston: Kluwer
Academic Publishers, 1999.
[5] Ramsey, J. L. “Realization of Optimum Interleavers.” IEEE Transactions on
Information Theory, IT-16 (3), May 1970. 338-345.
[6] Takeshita, O. Y. and D. J. Costello, Jr. “New Classes Of Algebraic
Interleavers for Turbo-Codes.” Proc. 1998 IEEE International Symposium on
Information Theory, Boston, Aug. 16-21, 1998. 419.

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 Analog Modulation

Analog Modulation
In most media for communication, only a fixed range of frequencies is available
for transmission. One way to communicate a message signal whose frequency
spectrum does not fall within that fixed frequency range, or one that is
otherwise unsuitable for the channel, is to alter a transmittable signal
according to the information in your message signal. This alteration is called
modulation, and it is the modulated signal that you transmit. The receiver
then recovers the original signal through a process called demodulation. This
section describes how to modulate and demodulate analog signals with the
Communications Blockset. After giving instructions for accessing the analog
modulation blocks, it goes on to discuss these topics:

• “Analog Modulation Features of the Blockset” on page 2-53

• “Baseband Modulated Signals Defined” on page 2-54
• “Representing Signals for Analog Modulation” on page 2-55
• “Timing Issues in Analog Modulation” on page 2-55
• “Filter Design Issues” on page 2-59

Accessing Analog Modulation Blocks

You can open the Modulation library by double-clicking on its icon in the main
Communications Blockset library (commlib), or by typing
commmod2

at the MATLAB prompt.

Then you can open the Analog Baseband and Analog Passband sublibraries by
double-clicking on their icons in the Modulation library, or by typing these
commands at the MATLAB prompt.
commanabbnd2
commanapbnd2

Analog Modulation Features of the Blockset

The figure below shows the modulation techniques that the Communications
Blockset supports for analog signals. As the figure suggests, some categories of
techniques include named special cases.

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Analog modulation methods

Amplitude Frequency Phase

modulation (AM) modulation (FM) modulation (PM)

Single-sideband Double-sideband
suppressed-carrier suppressed-carrier
(SSB) (DSB-SC)

For a given modulation technique, two ways to simulate modulation techniques

are called baseband and passband. Baseband simulation, also known as the
lowpass equivalent method, requires less computation. This blockset supports
both baseband and passband simulation. Since baseband simulation is more
prevalent, this guide focuses more on baseband simulation.
The modulation and demodulation blocks also let you control such features as
the initial phase of the modulated signal and post-demodulation filtering.

Baseband Modulated Signals Defined

A baseband representation of a modulated signal is often more convenient for
simulation than the passband representation is. Suppose the modulated signal
has the waveform

Y 1 ( t ) cos ( 2πf c t + θ ) – Y 2 ( t ) sin ( 2πf c t + θ )

where Y1 and Y2 are amplitude terms, fc is the carrier frequency and θ is the
carrier signal’s initial phase. A baseband simulation recognizes that this
equals

 jθ j2πf c t
Re  ( Y 1 ( t ) + jY 2 ( t ) )e  e
î þ

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 Analog Modulation

and models only the part inside the curly brackets. Here j is the square root of
-1. The complex vector y is a sampling of the complex signal (Y1(t) + jY2(t)) ejθ.

Representing Signals for Analog Modulation

Analog modulation blocks in this blockset process only sample-based scalar
signals. The data types of inputs and outputs are depicted in the figure below.

Baseband complex Baseband

real real
Modulator Demodulator

Passband real Passband

real real
Modulator Demodulator

Timing Issues in Analog Modulation

A few timing issues are important for simulating analog modulation with this
blockset. The sections below illustrate choices of signal sample times and
simulation step sizes.

Signal Sample Times

All analog demodulators in this blockset produce discrete-time, not
continuous-time, output. These blocks require you to specify the output sample
time as a mask parameter. In addition, some analog modulators require you to
specify the sample time as a mask parameter. Modulators in this category are
FM Modulator Baseband, FM Modulator Passband, SSB AM Modulator
Baseband, and SSB AM Modulator Passband.

Example Using a Modulator. In the figure below, both Probe blocks show a sample
time of 1 second in their icons. (The display Ts:[1 0] indicates a sample time
of 1 second and a sample time offset of 0.) Setting the Sample time parameter
in the FM Modulator Baseband block to 1 is appropriate because the input to
this block also has a sample time of 1 second.

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2 Using the Communications Blockset

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Sine Wave, in the Simulink Sources library (not the Sine Wave block in the
DSP Blockset DSP Sources library)
- Set Sample time to 1
• FM Modulator Baseband, in the Analog Baseband sublibrary of the
Modulation library
- Set Sample time to 1
• Two copies of Probe, in the Simulink Signals & Systems library
- Uncheck all boxes except Probe sample time
Connect the blocks as in the figure. Then select Update diagram from the
model window’s Edit menu, which updates the display on each Probe block’s
icon. (Running the model is not instructive because it does not represent a
complete system.)

Simulation Step Sizes

If you use passband modulation with continuous-time signals, then you need to
set the simulation step size, based on the carrier frequency. By the Nyquist
theorem, the simulation sampling rate must be at least twice as large as the
modulation carrier frequency. Equivalently, the simulation step size must be
no larger than half the modulation carrier period.
When you begin a new model, Simulink automatically determines the default
step size. To change the step size from the default to a different value, use this
procedure:

1 Select Simulation parameters from the model window’s Simulation menu

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 Analog Modulation

2 Select the Solver panel

3 Set the Max step size and Initial step size parameters to numerical values
(that is, not auto) that are appropriate for your model.

In some situations, Simulink automatically corrects a faulty simulation step

size. For example, if a signal in your model has a sample time of .1 second and
you set the model’s Max step size parameter to 1, then running the model
produces this response in the command window.
Warning: Maximum step size (1) is larger than the fastest discrete
sampling period (0.1) time. Setting maximum step size to 0.1.

Example Using Step Size Relative to Carrier Period. The model below illustrates why
the simulation step size in a passband simulation must be appropriate for a
given carrier frequency. The first Scope image shows the correct result of
modulating a constant signal using double-sideband suppressed-carrier
amplitude modulation, while the second Scope image shows incorrect results.
The incorrect results occur because the simulation step size is too large relative
to the modulation carrier frequency.
In this case, the DSBSC AM Modulator Passband block uses a Carrier
frequency parameter of 100. That is, the carrier’s period is .01 second and an
appropriate simulation step size is no larger than .005. Therefore, a simulation
step size of .01 second is too large to satisfy the Nyquist criterion. However, a
simulation step size of .001 second is sufficiently small.

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2 Using the Communications Blockset

Correct results;
simulation step size of
.001 is small compared
to carrier period

Carrier frequency = 100 Hz

Incorrect results;
simulation step size
of .01 is too large

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather these blocks with their default parameters:
• Constant, in the Simulink Sources library
• DSBSC AM Modulator Passband, in the Analog Passband sublibrary of the
Modulation library
• Scope, in the Simulink Sinks library

Connect the blocks as in the figure. Also, from the model window’s Simulation
menu, choose Simulation parameters; then in the Simulation Parameters
dialog box, set Stop time to 1.

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 Analog Modulation

To generate the correct results as in the first Scope image in the figure, return
to the Simulation Parameters dialog box and set both the Max step size and
Initial step size parameters to .001. Then run the model and use the Scope
window’s zooming tools to study the sinusoidal output curve. You can also
generate incorrect results as in the second Scope image in the figure, by
changing the Max step size and Initial step size parameters to .01 and
running the model again.

Filter Design Issues

After demodulating, you might want to filter out the carrier signal, especially
if you are using passband simulation. The Signal Processing Toolbox provides
functions that can help you design your filter, such as butter, cheby1, cheby2,
and ellip. Different demodulation methods have different properties, and you
might need to test your application with several filters before deciding which is
most suitable. This section mentions two issues that relate to the use of filters:
cutoff frequency and time lag.

Example: Varying the Filter’s Cutoff Frequency

In many situations, a suitable cutoff frequency is half the carrier frequency.
Since the carrier frequency must be higher than the bandwidth of the message
signal, a cutoff frequency chosen in this way limits the bandwidth of the
message signal. If the cutoff frequency is too high, then the carrier frequency
may not be filtered out. If the cutoff frequency is too low, then it might narrow
the bandwidth of the message signal.
The example below modulates a sawtooth message signal, demodulates the
resulting signal using a Butterworth filter, and plots the original and recovered
signals. The Butterworth filter is implemented within the SSB AM
Demodulator Passband block.

Before building the model, first execute this command at the MATLAB prompt.
[num,den] = butter(2,25*.01); % Design Butterworth filter.

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Here, 2 is the order of the Butterworth filter, 25 is the carrier signal frequency
and .01 is the sample time of the signal in Simulink. The variables num and den
represent the numerator and denominator, respectively, of the filter’s transfer
function. These variables reside in the MATLAB workspace, where Simulink
can access them during the simulation. The butter function is in the Signal
Processing Toolbox.
Now to open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Signal Generator, in the Simulink Sources library

- Set Wave form to Sawtooth
- Set Amplitude to 4
- Set Frequency to .3
• Zero-Order Hold, in the Simulink Discrete library
- Set Sample time to .01
• SSB AM Modulator Passband, in the Analog Passband sublibrary of the
Modulation library
- Set Carrier frequency to 25
- Set Time delay for Hilbert transform filter to .1
- Set Sample time to .01
• SSB AM Demodulator Passband, in the Analog Passband sublibrary of the
Modulation library
- Set Carrier frequency to 25
- Set Lowpass filter numerator to num
- Set Lowpass filter denominator to den
- Set Sample time to .01
• Scope, in the Simulink Sinks library

- After double-clicking on the block to open it, click on the Properties icon
and set Number of axes to 2
Connect the blocks as in the figure. Running the model produces the scope
image below. The image reflects the original and recovered signals, with a
moderate filter cutoff.

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 Analog Modulation

Other Filter Cutoffs. To see the effect of a lowpass filter with a higher cutoff
frequency, type
[num,den] = butter(2,25*.01*3.9); % Design Butterworth filter.

at the MATLAB prompt and then run the simulation again. The new result is
the left image in the figure below. The higher cutoff frequency allows the
carrier signal to interfere with the demodulated signal.
To see the effect of a lowpass filter with a lower cutoff frequency, type
[num,den] = butter(2,25*.01/4); % Design Butterworth filter.

at the MATLAB prompt and then run the simulation again. The new result is
the right image in the figure below. The lower cutoff frequency narrows the
bandwidth of the demodulated signal.

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Example: Time Lag from Filtering

There is invariably a delay between a demodulated signal and the original
received signal. Both the filter order and the filter parameters directly affect
the length of this delay. The example below illustrates the delay by plotting a
signal before modulation and after demodulation. The curve with amplitude
one is the original sine wave and the other curve is the recovered signal.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Sine Wave, in the DSP Blockset DSP Sources library (not the Sine Wave
block in the Simulink Sources library)
- Set Frequency to 1

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 Analog Modulation

• PM Modulator Baseband, in the Analog Baseband sublibrary of the

Modulation library. Use default parameters.
• PM Demodulator Baseband, in the Analog Baseband sublibrary of the
Modulation library. Use default parameters.
• Mux, in the Simulink Signals & Systems library
• Scope, in the Simulink Sinks library

Connect the blocks as in the figure. Also, from the model window’s Simulation
menu, choose Simulation parameters; then in the Simulation Parameters
dialog box, set Stop time to 5. Running the model produces the scope image
below.

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Digital Modulation
Like analog modulation, digital modulation alters a transmittable signal
according to the information in a message signal. However, in this case, the
message signal is a discrete-time signal that can assume finitely many values.
This section describes how to modulate and demodulate digital signals with the
Communications Blockset. After giving instructions for accessing the digital
modulation blocks, it goes on to discuss these topics:

• “Digital Modulation Features of the Blockset” on page 2-65

• “Representing Signals for Digital Modulation” on page 2-68
• “Delays in Digital Modulation” on page 2-69
• “Upsampled Signals and Rate Changes” on page 2-72
• “Examples of Digital Modulation” on page 2-75

For background material on the subject of digital modulation, see the works
listed in “Selected Bibliography for Digital Modulation” on page 2-83.

Accessing Digital Modulation Blocks

You can open the Modulation library by double-clicking on its icon in the main
Communications Blockset library (commlib), or by typing
commmod2

at the MATLAB prompt.

Then you can open the Digital Baseband and Digital Passband sublibraries by
double-clicking on their icons in the Modulation library, or by typing these
commands at the MATLAB prompt.
commdigbbnd2
commdigpbnd2

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 Digital Modulation

The Digital Baseband and Digital Passband libraries have sublibraries of their
own. You can open each of these sublibraries by double-clicking on the icon
listed in the table below, or by typing its name at the MATLAB prompt.

Table 2-1: Sublibraries of Digital Baseband and Digital Passband

Kind of Modulation Icon in Digital Name of Sublibrary

Baseband or Digital Model
Passband Library

Amplitude modulation AM commdigbbndam2,

commdigpbndam2

Phase modulation PM commdigbbndpm2,

commdigpbndpm2

Frequency modulation FM commdigbbndfm2,

commdigpbndfm2

Continuous phase CPM commdigbbndcpm2,

modulation commdigpbndcpm2

Digital Modulation Features of the Blockset

The figure below shows the modulation techniques that the Communications
Blockset supports for digital data. All of the methods at the far right are
implemented in both passband and baseband blocks.

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Pulse amplitude modulation (PAM)

Amplitude
modulation Quadrature amplitude modulation (QAM

Phase shift keying (PSK)

Phase Differential phase shift keying (DPSK)
Modulation modulation
methods for Offset phase shift keying
digital data
Frequency Frequency shift keying (FSK)
modulation
Gaussian minimum shift keying (GMSK)
Continuous Minimum shift keying (MSK)
phase
modulation Continuous phase
frequency shift keying (CPFSK)

General and Specific Modulation Methods

Some digital modulation sublibraries contain blocks that implement special
cases of a more general technique and are, in fact, special cases of a more
general block. These special-case blocks use the same computational code that
their general counterparts use, but provide an interface that is either simpler
or more suitable for the special case. The table below lists special-case
modulators, their general counterparts, and the conditions under which the
two are equivalent. The situation is analogous for demodulators.

Table 2-2: General and Specific Blocks

General Modulator Specific Modulator Specific Conditions

General QAM Rectangular QAM Predefined constellation

Modulator Baseband, Modulator Baseband, containing 2K points on a
General QAM Rectangular QAM rectangular lattice
Modulator Passband Modulator Passband

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 Digital Modulation

Table 2-2: General and Specific Blocks

General Modulator Specific Modulator Specific Conditions

M-PSK Modulator BPSK Modulator M-ary number

Baseband Baseband parameter is 2.
QPSK Modulator M-ary number
Baseband parameter is 4.

M-DPSK Modulator DBPSK Modulator M-ary number

Baseband Baseband parameter is 2.

DQPSK Modulator M-ary number

Baseband parameter is 4.

CPM Modulator GMSK Modulator M-ary number

Baseband, CPM Baseband, GMSK parameter is 2,
Modulator Passband Modulator Passband Frequency pulse shape
parameter is Gaussian.

MSK Modulator M-ary number

Baseband, MSK parameter is 2,
Modulator Passband Frequency pulse shape
parameter is
Rectangular, Pulse
length parameter is 1.

CPFSK Modulator Frequency pulse shape

Baseband, CPFSK parameter is
Modulator Passband Rectangular, Pulse
length parameter is 1.

Furthermore, the CPFSK Modulator Baseband and CPFSK Modulator

Passband blocks are similar to the M-FSK Modulator Baseband and M-FSK
Modulator Passband blocks, respectively, when the M-FSK blocks use
continuous phase transitions. However, the M-FSK features of this blockset
differ from the CPFSK features in their mask interfaces and in the
demodulator implementations.

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Representing Signals for Digital Modulation

All digital modulation blocks process only discrete-time signals. The data types
of inputs and outputs are depicted in the figure below.

Baseband complex Baseband

real real
Modulator Demodulator

Passband real Passband

real real
Modulator Demodulator

Note If you are simulating baseband modulation using a method that

produces real-valued data (such as pulse amplitude modulation) and if you
want the modulated signal to be a real Simulink signal instead of a complex
Simulink signal, then you can use the corresponding passband block with a
Carrier frequency parameter of zero.

Binary-Valued and Integer-Valued Signals

Some digital modulation blocks can accept either integers or binary
representations of such integers. The corresponding demodulation blocks can
output either integers or their binary representations. This section describes
how modulation blocks process binary inputs; the case for demodulation blocks
is the reverse.
If a modulator block’s Input type parameter is set to Bit, then the block
accepts binary representations of integers between 0 and M-1. It modulates
each group of K bits, called a binary word. Also, these rules apply to the binary
input mode:

• For baseband modulation, the input vector length must be an integer

multiple of K. If the input is frame-based, then it must be a column vector.
• For passband modulation, the input must have length K and must be
sample-based.

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 Digital Modulation

In binary input mode, the Constellation ordering (or Symbol set ordering,
depending on the type of modulation) parameter indicates how the block maps
a group of K input bits to a corresponding integer. If this parameter is set to
Binary, then the block maps [u(1) u(2) ... u(K)] to the integer

å u ( i )2 K – i
i=1

and subsequently behaves as if this integer were the input value. Notice that
u(1) is the most significant bit.
For example, if M = 8, Constellation ordering (or Symbol set ordering) is set
to Binary, and the binary input word is [1 1 0], then the block internally
converts [1 1 0] to the integer 6. The block produces the same output as in the
case when the input is 6 and the Input type parameter is Integer.
If Constellation ordering (or Symbol set ordering) is set to Gray, then the
block uses a Gray-coded arrangement. The explicit mapping is described in
“Algorithm” on the reference page for the M-PSK Modulator Baseband block.

Delays in Digital Modulation

Digital modulation and demodulation blocks sometimes incur delays between
their inputs and outputs, depending on their configuration and on properties of
their signals. The table below lists sources of delay and the situations in which

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they occur. If more than one situation applies to a given model, then the
separate delays are additive.

Table 2-3: Delays Resulting from Digital Modulation or Demodulation

Modulation or Situation in Which Amount of Delay

Demodulation Type Delay Occurs

All demodulators in Samples per symbol One output period

AM, PM, and FM parameter is greater
sublibraries, except than 1, and the input is
OQPSK sample-based.

All demodulators in Sample-based input, D+1 output periods

CPM sublibrary D = Traceback length
parameter

Frame-based input, D output periods

D = Traceback length
parameter

All passband Always One output period

demodulators

OQPSK Modulator Always One output symbol,

Baseband, OQPSK which is half the
Modulator Passband input period

OQPSK Demodulator Always Three input

Baseband, OQPSK symbols, which is 3/2
Demodulator Passband times the output
period

As a result of delays, data that enters a modulation or demodulation block at

time T appears in the output at time T+delay. In particular, if your simulation
computes error statistics or compares transmitted with received data, then it
must take the delay into account when performing such computations or
comparisons.

First Output Sample in DPSK Demodulation. In addition to the delays mentioned

above, the DPSK, DQPSK, and DBPSK demodulators produce output whose

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 Digital Modulation

first sample is unrelated to the input. This is related to the differential

modulation technique, not the particular implementation of it.

Example: Delays From Demodulation

Demodulation in the model below causes the demodulated signal to lag,
compared to the unmodulated signal. This delay is typical for sample-based
data that the modulator upsamples. When computing error statistics, the
model accounts for the delay by setting the Error Rate Calculation block’s
Receive delay parameter to 1. If the Receive delay parameter had a different
value, then the error rate showing at the top of the Display block would be close
to 1/2.

Note If this model used the OQPSK method instead of DBPSK, then the
proper Receive delay parameter would be 2 instead of 1.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Random-Integer Generator, in the Comm Sources library

- Set M-ary number to 2
- Set Initial seed to any positive integer scalar
• DBPSK Modulator Baseband, in the PM sublibrary of the Digital Baseband
sublibrary of Modulation
- Set Samples per symbol to 8
• AWGN Channel, in the Channels library
- Set Es/No to 4
• DBPSK Demodulator Baseband, in the PM sublibrary of the Digital
Baseband sublibrary of Modulation
- Set Samples per symbol to 8

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• Error Rate Calculation, in the Comm Sinks library

- Set Receive delay to 1
- Set Computation delay to 1
- Set Output data to Port
• Display, in the Simulink Sinks library
- Drag the bottom edge of the icon to make the display big enough for three
entries
Connect the blocks as shown above. Also, from the model window’s Simulation
menu, choose Simulation parameters; then in the Simulation Parameters
dialog box, set Stop time to 100. Then run the model and observe the error rate
at the top of the Display block’s icon. Your error rate will vary depending on
your Initial seed value in the Random-Integer Generator block.

Upsampled Signals and Rate Changes

Digital baseband modulation blocks can output an upsampled version of the
modulated signal, while digital baseband demodulation blocks can accept an
upsampled version of the modulated signal as input. Each block’s Samples per
symbol parameter, S, is the upsampling factor in both cases. It must be a
positive integer. Depending on whether the signal is frame-based or
sample-based, the block either changes the signal’s vector size or its sample
time, as the table below indicates. Only the OQPSK blocks deviate from the
information in the table, in that S is replaced by 2S in the scaling factors.

Table 2-4: Processing of Upsampled Modulated Data (Except OQPSK Method)

Computation Input Frame Result

Type Status

Modulation Frame-based Output vector length is S times the number of integers or

binary words in the input vector. Output sample time equals
the input sample time.

Modulation Sample-based Output vector is a scalar. Output sample time is 1/S times the
input sample time.

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 Digital Modulation

Table 2-4: Processing of Upsampled Modulated Data (Except OQPSK Method)

Computation Input Frame Result

Type Status

Demodulation Frame-based Number of integers or binary words in the output vector is 1/S
times the number of samples in the input vector. Output
sample time equals the input sample time.

Demodulation Sample-based Output signal contains one integer or one binary word.
Output sample time is S times the input sample time.

Furthermore, if S > 1 and the demodulator is from the AM,

PM, or FM sublibrary, then the demodulated signal is delayed
by one output sample period. There is no delay if S = 1 or if
the demodulator is from the CPM sublibrary.

Digital passband blocks can also process upsampled data, but only as an
intermediate internal format. For more information about this, see the
description of the Baseband samples per symbol parameter on the reference
page for any digital passband modulation block. Also note that passband blocks
process only sample-based data, not frame-based data.

Illustrations of Size or Rate Changes

The schematics below illustrate how a baseband modulator (other than
OQPSK) upsamples a triplet of frame-based and sample-based integers. In
both cases, the Samples per symbol parameter is 2.

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2 Using the Communications Blockset

Frame-Based Upsampling
1
1
0
Modulator -1 Output sample time = Input sample time
4
-1 Output length = 2* (# of input integers)
2
j
j
Frame-based column vectors

Sample-Based Upsampling

Modulator Output sample time = (Input sample time)/2

2 4 0 j j -1 -1 1 1
Output length = # of input integers

t=2 t=1 t=0 t=2 t=1 t=0

Sample-based scalars in input and output t=1/2

The schematics below illustrate how a demodulator (other than OQPSK or one
from the CPM sublibrary) processes three doubly-sampled symbols using both
frame-based and sample-based inputs. In both cases, the Samples per symbol
parameter is 2. Notice that the sample-based schematic includes an output
delay of one sample period.

Frame-Based Upsampled Input

1
1
0
-1 Demodulator Output sample time = Input sample time
4
-1 Output length = (# of input samples)/2
2
j
j
Frame-based column vectors

Sample-Based Upsampled Input

Demodulator Output sample time = 2*(Input sample time)

j j -1 -1 1 1 2 4 0 0
Scalar input and output
First output element represents delay
t=2 t=1 t=0 t=3 t=2 t=1 t=0
t=1/2 (delay)

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 Digital Modulation

Examples of Digital Modulation

This section builds a few simple example models to illustrate the modulation
methods and how the Communications Blockset allows you to implement them.
The examples are:
• “DQPSK Signal Constellation Points and Transitions” on page 2-75
• “Rectangular QAM Modulation and Scatter Diagram” on page 2-76
• “Phase Tree for Continuous Phase Modulation” on page 2-78
• “Passband Digital Modulation” on page 2-81

DQPSK Signal Constellation Points and Transitions

The model below plots the output of the DQPSK Modulator Baseband block.
The image shows the possible transitions from each symbol in the DQPSK
signal constellation to the next symbol.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Random-Integer Generator, in the Comm Sources library

- Set M-ary number to 4
- Set Initial seed to any positive integer scalar
- Set Sample time to .01
• DQPSK Modulator Baseband, in the PM sublibrary of the Digital Baseband
sublibrary of Modulation
• Complex to Real-Imag, in the Simulink Math library
• XY Graph, in the Simulink Sinks library

Use the blocks’ default parameters unless otherwise instructed. Connect the
blocks as in the figure. Running the model produces the plot below. The plot
reflects the transitions among the eight DQPSK constellation points.

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This plot illustrates π/4-DQPSK modulation, because the default Phase offset
parameter in the DQPSK Modulator Baseband block is pi/4. To see how the
phase offset influences the signal constellation, change the Phase offset
parameter in the DQPSK Modulator Baseband block to pi/8 or another value.
Run the model again and observe how the plot changes.

Rectangular QAM Modulation and Scatter Diagram

The model below uses the M-QAM Modulator Baseband block to modulate
random data. After passing the symbols through a noisy channel, the model
produces a scatter diagram of the noisy data. The diagram suggests what the
underlying signal constellation looks like and shows that the noise distorts the
modulated signal from the constellation.

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 Digital Modulation

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Random-Integer Generator, in the Comm Sources library

- Set M-ary number to 16
- Set Initial seed to any positive integer scalar
- Set Sample time to .1
• Rectangular QAM Modulator Baseband, in the AM sublibrary of the Digital
Baseband sublibrary of Modulation
- Set Normalization method to Peak Power
• AWGN Channel, in the Channels library
- Set Es/No to 20
- Set Symbol period to .1
• Discrete-Time Eye and Scatter Diagrams, in the Comm Sinks library
- Set Trace period to .1
- Set Decision point to .07
- Set Lower and upper bounds of diagram to [-1.1 1.1]
- Set Diagram type to Scatter Diagram

Running the model produces a scatter diagram like the one below. Your plot
might look somewhat different, depending on your Initial seed value in the
Random-Integer Generator block. Because the modulation technique is
16-QAM, the plot shows 16 clusters of points. If there were no noise, then the
plot would show the 16 exact constellation points instead of clusters around the
constellation points.

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2 Using the Communications Blockset

Phase Tree for Continuous Phase Modulation

This example plots a phase tree associated with a continuous phase modulation
scheme. A phase tree is a diagram that superimposes many curves, each of
which plots the phase of a modulated signal over time. The distinct curves
result from different inputs to the modulator.
This example uses the CPM Modulator Baseband block for its numerical
computations. The block is configured so that it uses a raised cosine filter pulse
shape. The example also illustrates how you can use Simulink and MATLAB
together. The example uses MATLAB commands to run a series of simulations
with different input signals, to collect the simulation results, and to plot the
full data set.

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 Digital Modulation

The first step of this example is to build the model. To open the completed
model, click here in the MATLAB Help browser. To build the model, gather and
configure these blocks:

• DSP Constant, in the DSP Sources library

- Set Constant value to s (which will be in the MATLAB workspace)
- Check the Frame-based output check box
• CPM Modulator Baseband
- Set M-ary number to 2
- Set Modulation index to 2/3
- Set Frequency pulse shape to Raised Cosine
- Set Pulse length to 2
• To Workspace, in the Simulink Sinks library
- Set Variable name to x
- Set Save format to Array
Do not run the model, since the variable s is not yet defined in the MATLAB
workspace. Instead, save the model to a directory on your MATLAB path, using
the filename doc_phasetree.
The second step of this example is to execute these commands in MATLAB.
% Parameters from the CPM Modulator Baseband block
M_ary_number = 2;
modulation_index = 2/3;
pulse_length = 2;
samples_per_symbol = 8;
opts = simset('SrcWorkspace','Current',...
'DstWorkspace','Current');

L = 5; % Symbols to display
pmat = [];

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2 Using the Communications Blockset

for ip_sig = 0:(M_ary_number^L)-1

s = de2bi(ip_sig,L,M_ary_number,'left-msb');
% Apply the mapping of the input symbol to the CPM
% symbol 0 -> -(M-1), 1 -> -(M-2), etc.
s = 2*s'+1-M_ary_number;
sim('doc_phasetree', .9, opts); % Run model to generate x.
pmat(:,ip_sig+1) = unwrap(angle(x(:))); % Next column of pmat
end;
pmat = pmat/(pi*modulation_index);
t = (0:L*samples_per_symbol-1)'/samples_per_symbol;
plot(t,pmat); figure(gcf); % Plot phase tree.

The resulting plot is below. Each curve represents a different instance of

simulating the CPM Modulator Baseband block with a distinct (constant) input
signal.

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 Digital Modulation

Passband Digital Modulation

The example below uses passband phase shift keying modulation and displays
the spectrum of the modulated signal. The M-PSK Modulator Passband block’s
parameters satisfy necessary requirements for passband simulation because:

• The input signal’s sampling rate of 10 is less than the carrier frequency of
100.
• The modulated signal’s sampling rate of 3000 exceeds the sum of twice the
carrier frequency and twice the input sampling rate.
• The input sample time of 1/10 is an integer multiple of the output sample
time of 1/3000, while the modulated signal is not oversampled.

These requirements are mentioned on the reference page for the M-PSK
Modulator Passband block.

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:

• Bernoulli Random Binary Generator, in the Comm Sources library.

- Set Probability of a zero to [.5, .5]
- Set Initial seed to any row vector containing 2 positive integers
- Set Sample time to .1
• M-PSK Modulator Passband, in the PM sublibrary of the Digital Passband
sublibrary of Modulation
- Set M-ary number to 4
- Set Input type to Bit
- Set Symbol period to .1
- Set Carrier frequency to 1000
- Set Carrier initial phase to pi/4
- Set Output sample time to 1/3000

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2 Using the Communications Blockset

• Buffer, in the DSP Blockset Buffers sublibrary of the Signal Management

library
- Set Output buffer size to 1024
• Magnitude FFT, in the DSP Blockset Power Spectrum Estimation sublibrary
of the Estimation library
- Check the Inherit FFT length from input dimensions check box
• Mean, in the DSP Blockset Statistics library
- Check the Running mean check box
- Set Reset port to None
• Vector Scope, in the DSP Blockset DSP Sinks library
- Set Input domain to Frequency
- Check the Axis properties check box
- Set Frequency range to [-Fs/2...Fs/2]
- Set Maximum Y-limit to 100
Connect the blocks as in the figure above. Running the model produces the
spectral plot below.

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 Digital Modulation

You might want to vary the modulation technique to see how this plot would
change. For example, you can try replacing the M-PSK Modulator Passband
block with the M-DPSK Modulator Passband or OQPSK Modulator Passband
block.

Selected Bibliography for Digital Modulation

[1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.
[2] Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan. Simulation
of Communication Systems. New York: Plenum Press, 1992.
[3] Pawula, R. F. "On M-ary DPSK Transmission Over Terrestrial and Satellite
Channels." IEEE Transactions on Communications, vol. COM-32, July 1984.
752-761.
[4] Smith, Joel G. "Odd-Bit Quadrature Amplitude-Shift Keying." IEEE
Transactions on Communications, vol. COM-23, March 1975. 385-389.

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2 Using the Communications Blockset

2. Using the Communications Blockset

Channels
Communication channels introduce noise, fading, interference, and other
distortions into the signals that they transmit. Simulating a communication
system involves modeling a channel based on mathematical descriptions of the
channel. Different transmission media have different properties and are
modeled differently. In a simulation, the channel model usually fits directly
between the transmitter and receiver, as shown below.

Transmitter Channel Receiver

Channel Features of the Blockset

This blockset provides several channel models for binary, real, and complex
signals. You can open the Channels library by double-clicking on its icon in the
main Communications Blockset library (commlib), or by typing
commchan2

at the MATLAB prompt.

This section describes the capabilities of the Channels library’s blocks, by
considering these channels:

• Additive white Gaussian noise (AWGN) channel

• Rayleigh and Rician fading channels that model real-world mobile
communication effects

• Binary symmetric channel (BSC)

AWGN Channel
An AWGN channel adds white Gaussian noise to the signal that passes
through it. Gaussian noise is discussed on the reference page for the Gaussian
Noise Generator block. The AWGN Channel block can process either
sample-based or frame-based data, and it lets you specify the variance of the
noise in one of four ways:

• Directly as a mask parameter

• Directly as an input signal

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 Channels

• Indirectly via a signal-to-noise ratio parameter

• Indirectly via an Es/No parameter

An example using the AWGN Channel block is in “Getting Started with the
Communications Blockset” on page 1-1.

Fading Channels
The Channels library includes Rayleigh and Rician fading blocks that can
simulate real-world phenomena in mobile communications. These phenomena
include multipath scattering effects in the Rayleigh case, as well as Doppler
shifts that arise from relative motion between the transmitter and receiver.
This section discusses:

• How to categorize the possible paths along which a signal can travel from the
transmitter to the receiver in the situation that you want to model
• How to choose and configure a fading channel block based on the
categorization
• An example that uses fading channels

Categorizing Signal Paths

The figure below depicts the two types of paths between a moving transmitter
and a stationary receiver. The solid line is a direct line-of-sight path, which
might or might not exist in your situation. Each dotted line is a reflected path
that the signal travels when it reflects from one of the shaded shapes. The
shaded shapes represent obstacles such as buildings or trees.

Reflected Path 1
Receiver
th
Direct Pa
h 2
Pat

Transmitter
ed
lect
Ref

The situation in the figure is just an example. In general, you should analyze
your system by considering these questions:

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2 Using the Communications Blockset

• Are there any reflected paths along which a signal can travel from
transmitter to receiver? If so, how many?
• Is there a direct path from transmitter to receiver?
• What is the relative motion between the transmitter and receiver?

The first two questions will help you choose which fading channel block(s) to
use in your simulation, while the third question will help you choose
appropriate parameters for the blocks.

Choosing and Configuring a Fading Channel Block

Once you categorize the types of signal paths in the situation you want to
model, use the table below to determine the appropriate block (or blocks) for
your simulation.

Table 2-5: Choosing a Fading Channel Block Based on Signal Paths

Signal Path(s) Channel Block

Direct line-of-sight path from transmitter to Rician Fading Channel

receiver

One or more reflected paths from Multipath Rayleigh Fading

transmitter to receiver Channel

If a signal can use more than one reflected path, then a single instance of the
Multipath Rayleigh Fading Channel block can model all of them
simultaneously. The number of paths that the block uses is the length of either
the Delay vector or the Gain vector parameter, whichever length is larger. (If
both of these parameters are vectors, then they must have the same length; if
exactly one of these parameters is a scalar, then the block expands it into a
vector whose size matches that of the other vector parameter.)
The relative motion between the transmitter and receiver influences the values
of the blocks’ parameters. For more details, see their reference pages, as well
as the works listed in “Selected Bibliography for Channels” on page 2-89 if
necessary.

Example: Using Fading Channels

The reference page for the Multipath Rayleigh Fading Channel block includes
an example that illustrates the channel’s effect on a constant signal.

2-86
 Channels

Another example is the model below, which uses both the Multipath Rayleigh
Fading Channel and the Rician Fading Channel blocks in parallel. This
combination of blocks simulates a mobile communication link in which the
transmitted signal can travel to the receiver along a direct path as well as along
three indirect paths. (The number of indirect paths is three because the
Multipath Rayleigh Fading Channel block’s Gain vector parameter is a vector
of length three. Although the Delay vector parameter is a scalar, its value is
applied to each of the three paths.)

To open the completed model, click here in the MATLAB Help browser. To
build the model, gather and configure these blocks:
• DSP Constant, in the DSP Blockset DSP Sources library
- Set Constant value to j*ones(10000,1)
- Check the Frame-based output check box
- Set Frame period to .01
• Rician Fading Channel, with default parameter values
• Multipath Rayleigh Fading Channel
- Set Delay vector to [0 2e-6 3e-6]
- Set Gain vector to [0 -3 1]
• Sum, in the Simulink Math library
• To Workspace, in the Simulink Sinks directory
- Set Save format to Array
Connect the blocks as shown above. Also, from the model window’s Simulation
menu, choose Simulation parameters; then in the Simulation Parameters
dialog box, set Stop time to 0.6.

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2 Using the Communications Blockset

Tip To reduce execution time by logging less data to the workspace, set the
Decimation parameter in the To Workspace block to 100. Then the variable
simout will contain fewer entries, but its graph will look similar.

Run the model. After the simulation stops, plot the faded signal’s power (versus
sample number) by executing this command at the MATLAB prompt.
simout = simout.'; plot(20*log10(abs(simout(:))))

The resulting figure is below.

Binary Symmetric Channel

Binary error channels process binary signals by adding noise modulo 2. This
library contains the Binary Symmetric Channel block, which either preserves
or perturbs each vector element independently. It requires a probability that
applies independently to each noise element. An example using the Binary
Symmetric Channel block is in the section “Example: A Rate 2/3 Feedforward
Convolutional Encoder” on page 2-42.

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 Channels

Selected Bibliography for Channels

[1] Fechtel, Stefan A. “A Novel Approach to Modeling and Efficient Simulation
of Frequency-Selective Fading Radio Channels.” IEEE Journal on Selected
Areas in Communications, vol. 11, April 1993. 422-431.
[2] Jakes, William C., ed. Microwave Mobile Communications. New York: IEEE
Press, 1974.
[3] Lee, William C. Y. Mobile Communications Design Fundamentals, 2nd ed.
New York: Wiley, 1993.
[4] Proakis, John G. Digital Communications, 3rd ed. New York: McGraw-Hill,
1995.

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2 Using the Communications Blockset

Synchronization
In order to interpret information correctly, a communication receiver must be
synchronized with the corresponding transmitter. A phase-locked loop, or PLL,
can help accomplish this synchronization when used in conjunction with other
components. A PLL is an automatic control system that adjusts the phase of a
local signal to match the phase of the received signal. The PLL design works
best for narrowband signals.

Synchronization Features of the Blockset

This blockset contains four phase-locked loop blocks in its Synchronization
library. You can open the Synchronization library by double-clicking on its icon
in the main Communications Blockset library (commlib), or by typing
commsync2

at the MATLAB prompt.

The table below indicates which block in the Synchronization library
implements each supported type of PLL.

Table 2-6: Supported PLLs in Synchronization Library

Type of PLL Block

Analog passband PLL Phase-Locked Loop

Analog baseband PLL Baseband PLL

Linearized analog baseband PLL Linearized Baseband PLL

Digital PLL using a charge pump Charge Pump PLL

This section discusses these topics:

• “Overview of PLL Simulation” on page 2-91

• “Implementing an Analog Baseband PLL” on page 2-91
• “Implementing a Digital PLL” on page 2-92

For details about phase-locked loops, see the works listed in “Selected
Bibliography for Synchronization” on page 2-92.

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 Synchronization

Overview of PLL Simulation

A simple PLL consists of a phase detector, a loop filter, and a voltage-controlled
oscillator (VCO). For example, the figure below shows how these components
are arranged for an analog passband PLL. In this case, the phase detector is
just a multiplier. The signal e(t) is often called the error signal.

s(t) e(t)
Filter

S(t)
VCO

Different PLLs use different phase detectors, filters, and VCO characteristics.
Some of these attributes are built into the PLL blocks in this blockset, while
others depend on parameters that you set in the block mask:

• You specify the filter’s transfer function in the block mask using the
Lowpass filter numerator and Lowpass filter denominator parameters.
Each of these parameters is a vector that lists the coefficients of the
respective polynomial in order of descending exponents of the variable s. To
design a filter, you can use functions such as butter, cheby1, and cheby2 in
the Signal Processing Toolbox.
• You specify the key VCO characteristics in the block mask. All four PLL
blocks use a VCO input sensitivity parameter. Some blocks also use VCO
quiescent frequency, VCO initial phase, and VCO output amplitude
parameters.
• The phase detector for each of the PLL blocks is a feature that you cannot
change from the block mask.

Implementing an Analog Baseband PLL

Unlike passband models for a phase-locked loop, a baseband model does not
depend on a carrier frequency. This allows you to use a lower sampling rate in
the simulation. These two blocks implement analog baseband PLLs:

• Baseband PLL
• Linearized Baseband PLL

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2 Using the Communications Blockset

The linearized model and the nonlinearized model differ in that the linearized
model uses the approximation

sin ( ∆θ ( t ) ) ≅ ∆θ ( t )

to simplify the computations. This approximation is close when ∆θ ( t ) is near

zero. Thus, instead of using the input signal and the VCO output signal
directly, the linearized PLL model uses only their phases.

Implementing a Digital PLL

The charge pump PLL is a classical digital PLL. Unlike the analog PLLs
mentioned above, the charge pump PLL uses a sequential logic phase detector,
which is also known as a digital phase detector or a phase/frequency detector.

Selected Bibliography for Synchronization

[1] Gardner, F. M. “Charge-pump Phase-lock Loops.” IEEE Trans. on
Communications, vol. 28, November 1980. 1849-1858.
[2] Gardner, F. M. “Phase Accuracy of Charge Pump PLLs.” IEEE Trans. on
Communications, vol. 30, October 1982. 2362-2363.
[3] Gupta, S. C. “Phase Locked Loops.” Proceedings of the IEEE, vol. 63.
February 1975. 291-306.
[4] Lindsay, W. C. and C. M. Chie. “A Survey on Digital Phase-Locked Loops.”
Proceedings of the IEEE, vol. 69, April 1981. 410-431.
[5] Meyr, Heinrich and Ascheid, Gerd. Synchronization in Digital
Communications, vol. 1. New York: John Wiley & Sons, 1990.

2-92
 3

Function Reference
3 Function Reference

Alphabetical List of Functions

comm_links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
commlib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4

3-2
 comm_links

Purpose 3comm_links
Display library link information for Communications Blockset blocks

Syntax comm_links
comm_links(sys)
comm_links(sys,mode)

Description comm_links displays library link information for blocks in the current model
that are linked to the Communications Blockset. For each block in the current
model, comm_links replaces the block name with the full pathname to the
block’s library link in the Communications Blockset. Blocks linked to the
current Communications Blockset libraries are highlighted in blue. Blocks
linked to older versions of the Simulink portion of the Communications Toolbox
are highlighted in red. Blocks at all levels of the model are analyzed.
A summary report indicating the number of blocks linked to each blockset
version is also displayed in the MATLAB command window. The highlighting
and link display are disabled when the model is executed or saved, or when
comm_links is executed a second time from the MATLAB command line.

comm_links(sys) toggles the display of block links in system sys. If sys is the
current model (gcs), this is the same as the earlier comm_links syntax.

comm_links(sys,mode) directly sets the link display state, where mode can be
'on', 'off', or 'toggle'. The default is 'toggle'.

See Also liblinks (DSP Blockset)

3-3
commlib

Purpose 3commlib
Open the main Communications Blockset library

Syntax commlib
commlib(n)
commlib n

Description commlib opens the current version of the main Communications Blockset
library.

commlib(n) opens version number n of the main Communications Blockset

library, where n can be either 1.3, 1.5, or 2.0. Version 2.0 refers to the Release
12 Communications Blockset. Version 1.5 refers to the Simulink portion of the
Communications Toolbox 1.5 (Release 11.1). Version 1.3 refers to the Simulink
portion of the Communications Toolbox 1.3 (Release 10).

commlib n is the same as commlib(n).

See Also simulink3 (Simulink), dsplib (DSP Blockset)

3-4
 4

Block Reference
Communications Sources . . . . . . . . . . . . . . 4-3

Communications Sinks . . . . . . . . . . . . . . . 4-5

Source Coding . . . . . . . . . . . . . . . . . . . 4-7

Channel Coding . . . . . . . . . . . . . . . . . . 4-9

Block Coding . . . . . . . . . . . . . . . . . . . . 4-9
Convolutional Coding . . . . . . . . . . . . . . . . . 4-11

Interleaving . . . . . . . . . . . . . . . . . . . . 4-13
Block Interleaving . . . . . . . . . . . . . . . . . . 4-13
Convolutional Interleaving . . . . . . . . . . . . . . . 4-15

Modulation . . . . . . . . . . . . . . . . . . . . 4-18
Digital Baseband Modulation . . . . . . . . . . . . . . 4-18
Analog Baseband Modulation . . . . . . . . . . . . . 4-24
Digital Passband Modulation . . . . . . . . . . . . . . 4-26
Analog Passband Modulation . . . . . . . . . . . . . . 4-31

Channels . . . . . . . . . . . . . . . . . . . . . 4-34

Synchronization . . . . . . . . . . . . . . . . . . 4-36

Basic Communications Functions . . . . . . . . . . 4-37

Integrators . . . . . . . . . . . . . . . . . . . . . 4-37
Sequence Operations . . . . . . . . . . . . . . . . . 4-38

Utility Functions . . . . . . . . . . . . . . . . . . 4-41

4 Block Reference

This chapter contains detailed descriptions of all Communications Blockset

blocks. It first shows the libraries and lists their contents, and then presents
the block reference entries in alphabetical order. More detailed discussions of
the core libraries’ capabilities are in the previous chapter.
Below is the Communications Blockset. You can open it by typing commlib at
the MATLAB prompt. Each yellow icon in this window represents a library. In
Simulink, double-clicking on a library icon opens the library. In this document,
clicking on one of the yellow icons below jumps to an overview of that library.

To access an older version of the library (for example, if you are modifying one
of your legacy models), then you should use one of these alternative syntaxes
of the commlib command.
commlib 1.3 % To open version 1.3
commlib 1.5 % To open version 1.5

4-2
 Communications Sources

Communications Sources
Every communication system contains one or more sources. You can open the
Comm Sources library by double-clicking on its icon in the main
Communications Blockset library (commlib), or by typing commsource2 at the
MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

The table below lists and describes the blocks in the Comm Sources library. For
information about a specific block, see the reference pages that follow; for a

4-3
4 Block Reference

discussion of this library’s capabilities, see “Communications Sources” on page

2-6.

Block Name Purpose

Bernoulli Random Binary Generate Bernoulli-distributed random

Generator binary numbers

Binary Vector Noise Generator Generate a binary vector while

controlling the number of 1s

Discrete-Time VCO Implement a voltage-controlled

oscillator in discrete time

Gaussian Noise Generator Generate Gaussian distributed noise

with given mean and variance values

PN Sequence Generator Generate pseudonoise sequence

Poisson Int Generator Generate Poisson-distributed random

integers

Random-Integer Generator Generate integers randomly distributed

in the range [0, M-1]

Rayleigh Noise Generator Generate Rayleigh distributed noise

Rician Noise Generator Generate Rician distributed noise

Triggered Read From File Read from a file, refreshing the output
at rising edges of an input signal

Uniform Noise Generator Generate uniformly distributed noise

between the upper and lower bounds

Voltage-Controlled Oscillator Implement a voltage-controlled

oscillator

4-4
 Communications Sinks

Communications Sinks
The Comm Sinks library provides sinks and display devices that facilitate
analysis of communication system performance. You can open the Comm Sinks
library by double-clicking on its icon in the main Communications Blockset
library (commlib), or by typing commsink2 at the MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

The table below lists and describes the blocks in the Comm Sinks library. For
information about a specific block, see the reference pages that follow; for a
discussion of this library’s capabilities, see “Communications Sinks” on page
2-12.

Block Name Purpose

Error Rate Calculation Compute the bit error rate or symbol error
rate of input data

Continuous-Time Eye and Produce eye diagram, scatter, or x-y plots,

Scatter Diagrams using trigger to set decision timing

4-5
4 Block Reference

Block Name (Continued) Purpose (Continued)

Discrete-Time Eye and Produce an eye diagram and/or scatter

Scatter Diagrams diagram

Triggered Write to File Write to a file at each rising edge of an input

signal

4-6
 Source Coding

Source Coding
This blockset supports companders, scalar quantization and predictive
quantization. You can open the Source Coding library by double-clicking on its
icon in the main Communications Blockset library (commlib), or by typing
commsrccod2 at the MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-7
4 Block Reference

The table below lists and describes the blocks in the Source Coding library. For
information about a specific block, see the reference pages that follow; for a
discussion of this library’s capabilities, see “Source Coding” on page 2-16.

Block Name Purpose

A-Law Compressor Implement A-law compressor for source

coding

A-Law Expander Implement A-law expander for source

coding

Differential Decoder Decode a binary signal using differential

coding technique.

Differential Encoder Encode a binary signal using differential

coding technique.

DPCM Decoder Decode differential pulse code modulation

DPCM Encoder Encode using differential pulse code

modulation

Mu-Law Compressor Implement m-law compressor for source

coding

Mu-Law Expander Implement m-law expander for source

coding

Quantizer Decode Decode quantization index according to

codebook

Sampled Quantizer Encode Quantize a signal, indicating quantization

index, coded signal, and distortion
Enabled Quantizer Encode Quantize a signal, using trigger to control
processing

4-8
 Channel Coding

Channel Coding
The Channel Coding library contains two sublibraries:

• Block, which contains blocks that implement the encoding and decoding of
linear, cyclic, BCH, Hamming, and Reed-Solomon codes
• Convolutional, which contains blocks that implement convolutional encoding
and decoding

The main Channel Coding library appears below. You can open it by
double-clicking on its icon in the main Communications Blockset library
(commlib), or by typing commfeccod2 at the MATLAB prompt. Each icon in the
Channel Coding window represents a sublibrary. In Simulink, double-clicking
on one of these icons opens the sublibrary. In this document, clicking on one of
the icons below jumps to an overview of that sublibrary.

Block Coding
You can open the Block sublibrary by double-clicking on the Block icon in the
main Channel Coding library, or by typing commblkcod2 at the MATLAB
prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-9
4 Block Reference

The table below lists and describes the blocks in the Block sublibrary of the
Channel Coding library. For information about a specific block, see the
reference pages that follow; for a discussion of this library’s capabilities, see
“Block Coding” on page 2-27.

Block Name Purpose

BCH Decoder Decode a BCH code to recover binary

vector data

BCH Encoder Create a BCH code from binary vector

data

Binary Cyclic Decoder Decode a systematic cyclic code to

recover binary vector data
Binary Cyclic Encoder Create a systematic cyclic code from
binary vector data

4-10
 Channel Coding

Block Name (Continued) Purpose (Continued)

Binary-Output RS Decoder Decode a Reed-Solomon code to

recover binary vector data

Binary-Input RS Encoder Create a Reed-Solomon code from

binary vector data

Binary Linear Decoder Decode a linear block code to recover

binary vector data

Binary Linear Encoder Create a linear block code from binary

vector data

Hamming Decoder Decode a Hamming code to recover

binary vector data

Hamming Encoder Create a Hamming code from binary

vector data
Integer-Output RS Decoder Decode a Reed-Solomon code to
recover integer vector data
Integer-Input RS Encoder Create a Reed-Solomon code from
integer vector data

Convolutional Coding
You can open the Convolutional sublibrary by double-clicking on the
Convolutional icon in the main Channel Coding library, or by typing
commcnvcod2 at the MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-11
4 Block Reference

The table below lists and describes the blocks in the Convolutional sublibrary
of the Channel Coding library. For information about a specific block, see the
reference pages that follow; for a discussion of this library’s capabilities, see
“Convolutional Coding” on page 2-40.

Block Name Purpose

APP Decoder Decode a convolutional code using the a

posteriori probability (APP) method

Convolutional Encoder Create a convolutional code from binary data

Viterbi Decoder Decode convolutionally encoded data using the
Viterbi algorithm

4-12
 Interleaving

Interleaving
The Interleaving library contains two sublibraries:

• Block
• Convolutional

The main Interleaving library appears below. You can open it by

double-clicking on its icon in the main Communications Blockset library
(commlib), or by typing comminterleave2 at the MATLAB prompt. Each icon in
the Interleaving window represents a sublibrary. In Simulink, double-clicking
on one of these icons opens the sublibrary. In this document, clicking on one of
the icons below jumps to an overview of that sublibrary.

Block Interleaving
You can open the Block sublibrary by double-clicking on the Block icon in the
main Interleaving library, or by typing commblkintrlv2 at the MATLAB
prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-13
4 Block Reference

The table below lists and describes the blocks in the Block sublibrary of the
Interleaving library. For information about a specific block, see the reference
pages that follow; for a discussion of this library’s capabilities, see “Block
Interleavers” on page 2-46.

Block Name Purpose

Algebraic Deinterleaver Restore ordering of the input symbols

using algebraically derived
permutation

Algebraic Interleaver Reorder the input symbols using

algebraically derived permutation
table

4-14
 Interleaving

Block Name (Continued) Purpose (Continued)

General Block Deinterleaver Restore ordering of the symbols in the

input vector
General Block Interleaver Reorder the symbols in the input
vector

Matrix Deinterleaver Permute input symbols by filling a

matrix by columns and emptying it by
rows

Matrix Helical Scan Restore ordering of input symbols by

Deinterleaver filling a matrix along diagonals

Matrix Helical Scan Interleaver Permute input symbols by selecting

matrix elements along diagonals

Matrix Interleaver Permute input symbols by filling a

matrix by rows and emptying it by
columns

Random Deinterleaver Restore ordering of the input symbols

using a random permutation

Random Interleaver Reorder the input symbols using a

random permutation

Convolutional Interleaving
You can open the Convolutional sublibrary by double-clicking on the
Convolutional icon in the main Interleaving library, or by typing
commcnvintrlv2 at the MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-15
4 Block Reference

The table below lists and describes the blocks in the Convolutional sublibrary
of the Interleaving library. For information about a specific block, see the
reference pages that follow; for a discussion of this library’s capabilities, see
“Convolutional Interleavers” on page 2-47.

Block Name Purpose

Convolutional Deinterleaver Restore ordering of symbols that were

permuted using shift registers

Convolutional Interleaver Permute input symbols using a set of

shift registers

General Multiplexed Restore ordering of symbols using

Deinterleaver specified-delay shift registers

General Multiplexed Interleaver Permute input symbols using a set of

shift registers with specified delays

4-16
 Interleaving

Block Name (Continued) Purpose (Continued)

Helical Deinterleaver Restore ordering of symbols permuted

by a helical interleaver

Helical Interleaver Permute input symbols using a helical

array

4-17
4 Block Reference

Modulation
The Modulation library contains four sublibraries, each of which addresses a
category of modulation:

• Digital Baseband Modulation

• Analog Baseband Modulation
• Digital Passband Modulation
• Analog Passband Modulation

The main Modulation library appears below. You can open it by double-clicking
on its icon in the main Communications Blockset library (commlib), or by
typing commmod2 at the MATLAB prompt. Each icon in the Modulation window
represents a sublibrary. In Simulink, double-clicking on one of these icons
opens the sublibrary. In this document, clicking on one of the icons below jumps
to an overview of that sublibrary.

The first column shows the sublibraries for baseband simulation; the second
column shows the sublibraries for passband simulation. The first row shows
the sublibraries for digital modulation and demodulation. The second row
shows the sublibraries for analog modulation and demodulation.

Digital Baseband Modulation

You can open the Digital Baseband sublibrary of Modulation by double-clicking
on the Digital Baseband icon in the main Modulation library, or by typing

4-18
 Modulation

commdigbbnd2 at the MATLAB prompt. clicking on one of the icons below jumps
to an overview of that sublibrary.

Digital Baseband is further divided into sublibraries according to specific

modulation techniques:
• Amplitude modulation (PAM, QAM)
• Phase modulation (PSK, DPSK)
• Frequency modulation (FSK)
• Continuous phase modulation (MSK, GMSK)

The figures and tables below show and list the blocks in the method-specific
sublibraries. For information about a specific block, see the reference pages
that follow; for a discussion of digital baseband modulation capabilities, see
“Digital Modulation” on page 2-64.

4-19
4 Block Reference

AM Sublibrary

Block Name Purpose

General QAM Demodulator Demodulate QAM-modulated data

Baseband

General QAM Modulator Modulate using quadrature amplitude

Baseband modulation

M-PAM Demodulator Baseband Demodulate PAM-modulated data

M-PAM Modulator Baseband Modulate using M-ary pulse amplitude

modulation

Rectangular QAM Demodulator Demodulate QAM-modulated data

Baseband

Rectangular QAM Modulator Modulate using M-ary quadrature

Baseband amplitude modulation

4-20
 Modulation

PM Sublibrary

Block Name Purpose

BPSK Demodulator Baseband Demodulate BPSK-modulated data

BPSK Modulator Baseband Modulate using the binary phase shift

keying method

DBPSK Demodulator Baseband Demodulate DBPSK-modulated data

DBPSK Modulator Baseband Modulate using the differential binary

phase shift keying method

DQPSK Demodulator Baseband Demodulate DQPSK-modulated data

DQPSK Modulator Baseband Modulate using the differential

quaternary phase shift keying method

4-21
4 Block Reference

Block Name (Continued) Purpose (Continued)

M-DPSK Demodulator Demodulate DPSK-modulated data

Baseband

M-DPSK Modulator Baseband Modulate using the M-ary differential

phase shift keying method

M-PSK Demodulator Baseband Demodulate PSK-modulated data

M-PSK Modulator Baseband Modulate using the M-ary phase shift

keying method

OQPSK Demodulator Baseband Demodulate OQPSK-modulated data

OQPSK Modulator Baseband Modulate using the offset quadrature

phase shift keying method

QPSK Demodulator Baseband Demodulate QPSK-modulated data

QPSK Modulator Baseband Modulate using the quaternary phase

shift keying method

FM Sublibrary

Block Name Purpose

M-FSK Demodulator Baseband Demodulate FSK-modulated data

M-FSK Modulator Baseband Modulate using the M-ary frequency
shift keying method

4-22
 Modulation

CPM Sublibrary

Block Name Purpose

CPFSK Demodulator Baseband Demodulate CPFSK-modulated data

CPFSK Modulator Baseband Modulate using the continuous phase
frequency shift keying method
CPM Demodulator Baseband Demodulate CPM-modulated data

CPM Modulator Baseband Modulate using continuous phase

modulation

GMSK Demodulator Baseband Demodulate GMSK-modulated data

4-23
4 Block Reference

Block Name (Continued) Purpose (Continued)

GMSK Modulator Baseband Modulate using the Gaussian

minimum shift keying method
MSK Demodulator Baseband Demodulate MSK-modulated data

MSK Modulator Baseband Modulate using the minimum shift

keying method

Analog Baseband Modulation

You can open the Analog Baseband sublibrary of Modulation by double-clicking
on the Analog Baseband icon in the main Modulation library, or by typing
commanabbnd2 at the MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-24
 Modulation

The table below lists and describes the blocks in the Analog Baseband
sublibrary of the Modulation library. For information about a specific block, see
the reference pages that follow; for a discussion of this library’s capabilities, see
“Analog Modulation” on page 2-53.

Block Name Purpose

DSB AM Demodulator Demodulate DSB-AM-modulated data

Baseband

DSB AM Modulator Modulate using double-sideband

Baseband amplitude modulation

DSBSC AM Demodulator Demodulate DSBSC-AM-modulated data

Baseband

4-25
4 Block Reference

Block Name (Continued) Purpose (Continued)

DSBSC AM Modulator Modulate using double-sideband

Baseband suppressed-carrier amplitude modulation
FM Demodulator Baseband Demodulate FM-modulated data

FM Modulator Baseband Modulate using frequency modulation

PM Demodulator Baseband Demodulate PM-modulated data

PM Modulator Baseband Modulate using phase modulation

SSB AM Demodulator Demodulate SSB-AM-modulated data

Baseband

SSB AM Modulator Modulate using single-sideband

Baseband amplitude modulation

Digital Passband Modulation

You can open the Digital Passband sublibrary of Modulation by double-clicking
on the Digital Passband icon in the main Modulation library, or by typing
commdigpbnd2 at the MATLAB prompt. clicking on one of the icons below jumps
to an overview of that sublibrary.

Digital Passband is further divided into sublibraries according to specific

modulation techniques:
• Amplitude modulation (PAM, QAM)
• Phase modulation (PSK, DPSK)

4-26
 Modulation

• Frequency modulation (FSK)

• Continuous phase modulation (MSK, GMSK)

The figures and tables below show and list the blocks in the method-specific
sublibraries. For information about a specific block, see the reference pages
that follow.

AM Sublibrary

Block Name Purpose

General QAM Demodulator Demodulate QAM-modulated data

Passband
General QAM Modulator Modulate using the pulse amplitude
Passband modulation phase shift keying method
M-PAM Demodulator Passband Demodulate PAM-modulated data

M-PAM Modulator Passband Modulate using M-ary pulse amplitude

modulation

4-27
4 Block Reference

Block Name (Continued) Purpose (Continued)

Rectangular QAM Demodulator Demodulate QAM-modulated data

Passband

Rectangular QAM Modulator Modulate using M-ary quadrature

Passband amplitude modulation

PM Sublibrary

Block Name Purpose

M-DPSK Demodulator Passband Demodulate DPSK-modulated data

M-DPSK Modulator Passband Modulate using the M-ary differential
phase shift keying method

M-PSK Demodulator Passband Demodulate PSK-modulated data

M-PSK Modulator Passband Modulate using the M-ary phase shift

keying method

4-28
 Modulation

Block Name (Continued) Purpose (Continued)

OQPSK Demodulator Passband Demodulate OQPSK-modulated data

OQPSK Modulator Passband Modulate using the offset quadrature

phase shift keying method

FM Sublibrary

Block Name Purpose

M-FSK Demodulator Passband Modulate using the M-ary frequency

shift keying method

M-FSK Modulator Passband Modulate using the M-ary frequency

shift keying method

4-29
4 Block Reference

CPM Sublibrary

Block Name Purpose

CPFSK Demodulator Passband Demodulate CPFSK-modulated data

CPFSK Modulator Passband Modulate using the continuous phase

frequency shift keying method
CPM Demodulator Passband Demodulate CPM-modulated data

CPM Modulator Passband Modulate using continuous phase

modulation

GMSK Demodulator Passband Demodulate GMSK-modulated data

GMSK Modulator Passband Modulate using the Gaussian
minimum shift keying method

4-30
 Modulation

Block Name (Continued) Purpose (Continued)

MSK Demodulator Passband Demodulate MSK-modulated data

MSK Modulator Passband Modulate using the minimum shift

keying method

Analog Passband Modulation

You can open the Analog Passband sublibrary of Modulation by double-clicking
on the Analog Passband icon in the main Modulation library, or by typing
commanapbnd2 at the MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-31
4 Block Reference

The table below lists and describes the blocks in the Analog Passband
sublibrary of the Modulation library. For information about a specific block, see
the reference pages that follow; for a discussion of this library’s capabilities, see
“Analog Modulation” on page 2-53.

Block Name Purpose

DSB AM Demodulator Demodulate DSB-AM-modulated data

Passband

DSB AM Modulator Modulate using double-sideband amplitude

Passband modulation

DSBSC AM Demodulator Demodulate DSBSC-AM-modulated data

Passband

4-32
 Modulation

Block Name (Continued) Purpose (Continued)

DSBSC AM Modulator Modulate using double-sideband

Passband suppressed-carrier amplitude modulation

FM Demodulator Passband Demodulate FM-modulated data

FM Modulator Passband Modulate using frequency modulation

PM Demodulator Passband Demodulate PM-modulated data

PM Modulator Passband Modulate using phase modulation

SSB AM Demodulator Demodulate SSB-AM-modulated data

Passband

SSB AM Modulator Modulate using single-sideband amplitude

Passband modulation

4-33
4 Block Reference

Channels
The Channels library provides passband and baseband channels. You can open
the Channels library by double-clicking on its icon in the main
Communications Blockset library (commlib), or by typing commchan2 at the
MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

The table below lists and describes the blocks in the Channels library. For
information about a specific block, see the reference pages that follow; for a
discussion of this library’s capabilities, see “Channels” on page 2-84.

Block Name Purpose

AWGN Channel Add white Gaussian noise to the input signal

Binary Symmetric Introduce binary errors

Channel

4-34
 Channels

Block Name (Continued) Purpose (Continued)

Multipath Rayleigh Fading Simulate a multipath Rayleigh fading

Channel propagation channel

Rician Fading Channel Simulate a Rician fading propagation

channel

4-35
4 Block Reference

Synchronization
The Synchronization library provides four phase-locked loop models. You can
open the Synchronization library by double-clicking on its icon in the main
Communications Blockset library (commlib), or by typing commsync2 at the
MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

The table below lists and describes the blocks in the Synchronization library.
For information about a specific block, see the reference pages that follow; for
a discussion of this library’s capabilities, see “Synchronization” on page 2-90.

Block Name Purpose

Baseband PLL Implement a baseband phase-locked loop

Charge Pump PLL Implement a charge pump phase-locked loop

using a digital phase detector

Linearized Baseband PLL Implement a linearized version of a

baseband phase-locked loop

Phase-Locked Loop Implement a phase-locked loop to recover the

phase of the input signal

4-36
 Basic Communications Functions

Basic Communications Functions

The Basic Comm Functions library contains these sublibraries:

• Integrators
• Sequence Operations

The main Basic Comm Functions library appears below. You can open it by
double-clicking on its icon in the main Communications Blockset library
(commlib), or by typing commbasic2 at the MATLAB prompt. Each icon in the
Basic Comm Functions window represents a sublibrary. In Simulink,
double-clicking on one of these icons opens the sublibrary. In this document,
clicking on one of the icons below jumps to an overview of that sublibrary.

Integrators
You can open the Integrators sublibrary by double-clicking on the Integrators
icon in the main Basic Comm Functions library, or by typing comminteg2 at the
MATLAB prompt.

Tip In this document, you can jump to a block’s reference page by clicking on
its icon below.

4-37
4 Block Reference

The table below lists and describes the blocks in the Integrators library. For
information about a specific block, see the reference pages that follow.

Block Name Purpose

Discrete Modulo Integrator Integrate in discrete time and reduce by a

modulus

Integrate and Dump Integrate, resetting to zero periodically and

reducing by a modulus

Modulo Integrator Integrate in continuous time and reduce by a

modulus

Windowed Integrator Integrate over a time window of fixed length

Sequence Operations
You can open the Sequence Operations sublibrary by double-clicking on the
Sequence Operations icon in the main Basic Comm Functions library, or by
typing commsequence2 at the MATLAB prompt.

Tip In this document, you can jump to a Communications Blockset block’s

reference page by clicking on its icon below. (The Repeat block is in the DSP
Blockset, not the Communications Blockset; the icon in the Sequence
Operations sublibrary is merely a link to the DSP Blockset.)

4-38
 Basic Communications Functions

The table below lists and describes the blocks in the Sequence Operations
library. For information about a specific block, see the reference pages that
follow.

Block Name Purpose

Complex Output the phase difference between the two complex

Phase input signals
Difference

Complex Shift the phase of the complex input signal by the second
Phase Shift input value

Deinterlacer Distribute elements of input vector alternately between

two output vectors
Derepeat Reduce sampling rate by averaging consecutive samples

Descrambler Descramble the input signal

4-39
4 Block Reference

Block Name Purpose (Continued)

Insert Zero Distribute input elements in output vector

Interlacer Alternately select elements from two input vectors to

generate output vector

Puncture Output the elements which correspond to 1s in the binary

Puncture vector

Repeat Repeat input samples N times

Scrambler Scramble the input signal

4-40
 Utility Functions

Utility Functions
You can open the Utility Functions library by double-clicking on its icon in the
main Communications Blockset library (commlib), or by typing commutil2 at
the MATLAB prompt.

Tip In this document, you can jump to a Communications Blockset block’s

reference page by clicking on its icon below. (The dB Conversion block is in the
DSP Blockset, not the Communications Blockset; the icon in the Utility
Functions library is merely a link to the DSP Blockset.)

The table below lists and describes the blocks in the Utility Functions library.
For information about a specific block, see the reference pages that follow.

Block Name Purpose

Bit to Integer Converter Map a vector of bits to a corresponding vector of

integers

dB Conversion Convert input of Watts or Volts to decibels

Data Mapper Map integer symbols from one coding scheme to

another

Integer to Bit Converter Map a vector of integers to a vector of bits

4-41
4

Alphabetical List of Blocks 4

A-Law Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-47

A-Law Expander . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-49
Algebraic Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-51
Algebraic Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-53
APP Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-56
AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-60
Baseband PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64
BCH Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-66
BCH Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-68
Bernoulli Random Binary Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-70
Binary Cyclic Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-73
Binary Cyclic Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-75
Binary-Input RS Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-77
Binary Linear Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-79
Binary Linear Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-81
Binary-Output RS Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-82
Binary Symmetric Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-84
Binary Vector Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-86
Bit to Integer Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-89
BPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-90
BPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-92
Charge Pump PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-94
Complex Phase Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-97
Complex Phase Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-98
Continuous-Time Eye and Scatter Diagrams . . . . . . . . . . . . . . . . . . . . . . 4-99
Convolutional Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-103
Convolutional Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-105
Convolutional Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-107
CPFSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-109
CPFSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-112
CPFSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-115
CPFSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-118
CPM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-121
CPM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-125
CPM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-130

4-42
 Alphabetical List of Blocks

CPM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-134

Data Mapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-139
DBPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-142
DBPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-144
Deinterlacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-146
Derepeat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-147
Descrambler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-150
Differential Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-152
Differential Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-153
Discrete Modulo Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-154
Discrete-Time Eye and Scatter Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 4-156
Discrete-Time VCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-159
DPCM Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-161
DPCM Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-163
DQPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-165
DQPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
DSB AM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-171
DSB AM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-173
DSB AM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-175
DSB AM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-176
DSBSC AM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-178
DSBSC AM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-180
DSBSC AM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-182
DSBSC AM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-183
Enabled Quantizer Encode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-185
Error Rate Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
FM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-194
FM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-196
FM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-198
FM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-200
Gaussian Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-202
General Block Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-205
General Block Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
General Multiplexed Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-208
General Multiplexed Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-210
General QAM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-212
General QAM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-214

4-43
4

General QAM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-217

General QAM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-219
GMSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-222
GMSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-225
GMSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-228
GMSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-231
Hamming Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-234
Hamming Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-236
Helical Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-238
Helical Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-241
Insert Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-244
Integer-Input RS Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-246
Integer-Output RS Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-248
Integer to Bit Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-250
Integrate and Dump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-251
Interlacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-253
Linearized Baseband PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-254
Matrix Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-256
Matrix Helical Scan Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-257
Matrix Helical Scan Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-259
Matrix Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-262
M-DPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-264
M-DPSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-267
M-DPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-270
M-DPSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-274
M-FSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-277
M-FSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-280
M-FSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-283
M-FSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-286
Modulo Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-289
M-PAM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-290
M-PAM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-293
M-PAM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-297
M-PAM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-301
M-PSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-305
M-PSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-308
M-PSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-311

4-44
 Alphabetical List of Blocks

M-PSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-316

MSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-319
MSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-321
MSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-324
MSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-326
Mu-Law Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-329
Mu-Law Expander . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-330
Multipath Rayleigh Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-331
OQPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-334
OQPSK Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-336
OQPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-339
OQPSK Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-342
Phase-Locked Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-345
PM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-348
PM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-350
PM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-352
PM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-353
PN Sequence Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-355
Poisson Int Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-358
Puncture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-360
QPSK Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-362
QPSK Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-364
Quantizer Decode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-367
Random Deinterleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-368
Random-Integer Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-369
Random Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-372
Rayleigh Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-373
Rectangular QAM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . 4-376
Rectangular QAM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . 4-379
Rectangular QAM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . 4-383
Rectangular QAM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . 4-387
Rician Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-391
Rician Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-394
Sampled Quantizer Encode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-397
Scrambler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-399
SSB AM Demodulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-401
SSB AM Demodulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-403

4-45
4

SSB AM Modulator Baseband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-405

SSB AM Modulator Passband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-408
Triggered Read From File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-411
Triggered Write to File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-414
Uniform Noise Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-416
Viterbi Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-419
Voltage-Controlled Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-424
Windowed Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-426

4-46
 A-Law Compressor

Purpose 4A-Law Compressor

Implement A-law compressor for source coding

Library Source Coding

Description The A-Law Compressor block implements an A-law compressor for the input
signal. The formula for the A-law compressor is


 Ax
---------------------- sgn ( x )
V
for 0 ≤ x ≤ ----
 1 + log A A
y = 
 V ( 1 + log ( A x ⁄ V ) ) V
 --------------------------------------------------- sgn ( x ) for ---- < x ≤ V
1 + log A A
î

where A is the A-law parameter of the compressor, V is the peak signal

magnitude for x, log is the natural logarithm, and sgn is the signum function
(sign in MATLAB).
The most commonly used A value is 87.6.
The input can have any shape or frame status. This block processes each vector
element independently.

Dialog Box

A value
The A-law parameter of the compressor.

4-47
A-Law Compressor

Peak signal magnitude

The peak value of the input signal. This is also the peak value of the output
signal.

Pair Block A-Law Expander

See Also Mu-Law Compressor

References [1] Sklar, Bernard. Digital Communications: Fundamentals and Applications.

Englewood Cliffs, N.J.: Prentice-Hall, 1988.

4-48
 A-Law Expander

Purpose 4A-Law Expander

Implement A-law expander for source coding

Library Source Coding

Description The A-Law Expander block recovers data that the A-Law Compressor block
compressed. The formula for the A-law expander, shown below, is the inverse
of the compressor function.


 y ( 1 + log A ) V

------------------------------ for 0 ≤ y ≤ ----------------------
A 1 + log A
x = 
 y ( 1 + log A ) ⁄ V – 1 V V
---- sgn ( y ) for ---------------------- < y ≤ V
 e A 1 + log A
î

The input can have any shape or frame status. This block processes each vector
element independently.

Dialog Box

A value
The A-law parameter of the compressor.
Peak signal magnitude
The peak value of the input signal. This is also the peak value of the output
signal.
Match these parameters to the ones in the corresponding A-Law Compressor
block.

4-49
A-Law Expander

Pair Block A-Law Compressor

See Also Mu-Law Expander

References [1] Sklar, Bernard. Digital Communications: Fundamentals and Applications.

Englewood Cliffs, N.J.: Prentice-Hall, 1988.

4-50
 Algebraic Deinterleaver

Purpose 4Algebraic Deinterleaver

Restore ordering of the input symbols using algebraically derived permutation

Library Block sublibrary of Interleaving

Description The Algebraic Deinterleaver block restores the original ordering of a sequence
that was interleaved using the Algebraic Interleaver block. In typical usage,
the parameters in the two blocks have the same values.
The Number of elements parameter, N, indicates how many numbers are in
the input vector.If the input is frame-based, then it must be a column vector.
The Type parameter indicates the algebraic method that the block uses to
generate the appropriate permutation table. Choices are Takeshita-Costello
and Welch-Costas. Each of these methods has parameters and restrictions
that are specific to it; these are described on the reference page for the
Algebraic Interleaver block.

Dialog Box

Type
The type of permutation table that the block uses for deinterleaving.
Choices are Takeshita-Costello and Welch-Costas.

4-51
Algebraic Deinterleaver

Number of elements
The number of elements, N, in the input vector.
Multiplicative factor
The factor used to compute the corresponding interleaver’s cycle vector.
This field appears only if Type is set to Takeshita-Costello.
Cyclic shift
The amount by which the block shifts indices when creating the
corresponding interleaver’s permutation table. This field appears only if
Type is set to Takeshita-Costello.

Primitive element
An element of order N in the finite field GF(N+1). This field appears only
if Type is set to Welch-Costas.

Pair Block Algebraic Interleaver

See Also General Block Deinterleaver

References [1] Heegard, Chris and Stephen B. Wicker. Turbo Coding. Boston: Kluwer
Academic Publishers, 1999.
[2] Takeshita, O. Y. and D. J. Costello, Jr. “New Classes Of Algebraic
Interleavers for Turbo-Codes.” Proc. 1998 IEEE International Symposium on
Information Theory, Boston, Aug. 16-21, 1998. 419.

4-52
 Algebraic Interleaver

Purpose 4Algebraic Interleaver

Reorder the input symbols using algebraically derived permutation table

Library Block sublibrary of Interleaving

Description The Algebraic Interleaver block rearranges the elements of its input vector
using a permutation that is algebraically derived. The Number of elements
parameter, N, indicates how many numbers are in the input vector.If the input
is frame-based, then it must be a column vector.
The Type parameter indicates the algebraic method that the block uses to
generate the appropriate permutation table. Choices are Takeshita-Costello
and Welch-Costas. Each of these methods has parameters and restrictions
that are specific to it:

• If Type is set to Welch-Costas, then N+1 must be prime. The Primitive

element parameter is an integer, A, between 1 and N that represents a
primitive element of the finite field GF(N+1). This means that every nonzero
element of GF(N+1) can be expressed as A raised to some integer power.
In a Welch-Costas interleaver, the permutation maps the integer k to
mod(Ak,N+1) - 1.

• If Type is set to Takeshita-Costello, then N must be 2m for some integer m.

The Multiplicative factor parameter, h, must be an odd integer less than N.
The Cyclic shift parameter, k, must be a nonnegative integer less than N.
A Takeshita-Costello interleaver uses a length-N cycle vector whose nth
element is
mod(k*(n-1)*n/2, N)
for integers n between 1 and N. The block creates a permutation vector by
listing, for each element of the cycle vector in ascending order, one plus the
element’s successor. The interleaver’s actual permutation table is the result
of shifting the elements of the permutation vector left by the Cyclic shift
parameter. (The block performs all computations on numbers and indices
modulo N.)

4-53
Algebraic Interleaver

Dialog Box

Type
The type of permutation table that the block uses for interleaving.
Number of elements
The number of elements, N, in the input vector.
Multiplicative factor
The factor used to compute the interleaver’s cycle vector. This field appears
only if Type is set to Takeshita-Costello.
Cyclic shift
The amount by which the block shifts indices when creating the
permutation table. This field appears only if Type is set to
Takeshita-Costello.

Primitive element
An element of order N in the finite field GF(N+1). This field appears only
if Type is set to Welch-Costas.

Pair Block Algebraic Deinterleaver

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 Algebraic Interleaver

See Also General Block Interleaver

References [1] Heegard, Chris and Stephen B. Wicker. Turbo Coding. Boston: Kluwer
Academic Publishers, 1999.
[2] Takeshita, O. Y. and D. J. Costello, Jr. “New Classes Of Algebraic
Interleavers for Turbo-Codes.” Proc. 1998 IEEE International Symposium on
Information Theory, Boston, Aug. 16-21, 1998. 419.

4-55
APP Decoder

Purpose 4APP Decoder

Decode a convolutional code using the a posteriori probability (APP) method

Library Convolutional sublibrary of Channel Coding

Description The APP Decoder block performs a posteriori probability (APP) decoding of a
convolutional code. You can use this block to build a turbo decoder.

Inputs and Outputs

The input L(u) represents the sequence of log-likelihoods of encoder input bits,
while the input L(c) represents the sequence of log-likelihoods of code bits. The
outputs L(u) and L(c) are updated versions of these sequences, based on
information about the encoder.
If the convolutional code uses an alphabet of 2n possible symbols, then this
block’s L(c) vectors have length Q*n for some positive integer Q. Similarly, if
the decoded data uses an alphabet of 2k possible output symbols, then this
block’s L(u) vectors have length Q*k. The integer Q is the number of frames
that the block processes in each step.
The inputs can be either:

• Sample-based vectors having the same dimension and orientation, with

Q=1
• Frame-based column vectors with any positive integer for Q

If you only need the input L(c) and output L(u), then you can attach a Simulink
Ground block to the input L(u) and a Simulink Terminator block to the output
L(c).

Specifying the Encoder

To define the convolutional encoder that produced the coded input, use the
Trellis structure parameter. This parameter is a MATLAB structure whose
format is described in the section, “Trellis Description of a Convolutional
Encoder,” in the Communications Toolbox User’s Guide. You can use this
parameter field in two ways:

• If you have a variable in the MATLAB workspace that contains the trellis
structure, then enter its name as the Trellis structure parameter. This way
is preferable because it causes Simulink to spend less time updating the

4-56
 APP Decoder

diagram at the beginning of each simulation, compared to the usage in the

next bulleted item.
• If you want to specify the encoder using its constraint length, generator
polynomials, and possibly feedback connection polynomials, then use a
poly2trellis command within the Trellis structure field. For example, to
use an encoder with a constraint length of 7, code generator polynomials of
171 and 133 (in octal numbers), and a feedback connection of 171 (in octal),
set the Trellis structure parameter to
poly2trellis(7,[171 133],171)

To indicate how the encoder treats the trellis at the beginning and end of each
frame, set the Termination method parameter to either Truncated or
Terminated. The Truncated option indicates that the encoder resets to the
all-zeros state at the beginning of each frame, while the Terminated option
indicates that the encoder forces the trellis to end each frame in the all-zeros
state. If you use the Convolutional Encoder block with the Reset parameter set
to On each frame, then use the Truncated option in this block.

Specifying Details of the Algorithm

You can control part of the decoding algorithm using the Algorithm
parameter. The True APP option implements a posteriori probability. To gain
speed, both the Max* and Max options approximate expressions like

log å exp ai
i
by other quantities. The Max option uses max{ai} as the approximation, while
the Max* option uses max{ai} plus a correction term.
The Max* option enables the Scaling bits parameter in the mask. This
parameter is the number of bits by which the block scales the data it processes
internally. You can use this parameter to avoid losing precision during the
computations. It is especially appropriate if your implementation uses
fixed-point components. For more information about the Max* option, see the
article by Viterbi in the “References” section below.

4-57
APP Decoder

Dialog Box

Trellis structure
MATLAB structure that contains the trellis description of the
convolutional encoder.
Termination method
Either Truncated or Terminated. This parameter indicates how the
convolutional encoder treats the trellis at the beginning and end of frames.
Algorithm
Either True APP, Max*, or Max.
Number of scaling bits
An integer between 0 and 8 that indicates by how many bits the decoder
scales data in order to avoid losing precision. This field is active only when
Algorithm is set to Max*.

See Also Viterbi Decoder, Convolutional Encoder; poly2trellis (Communications

Toolbox)

References [1] Benedetto, Sergio and Guido Montorsi. “Performance of Continuous and
Blockwise Decoded Turbo Codes.” IEEE Communications Letters, vol. 1, May
1997. 77-79.
[2] Benedetto, S., G. Montorsi, D. Divsalar, and F. Pollara. “A Soft-Input
Soft-Output Maximum A Posterior (MAP) Module to Decode Parallel and

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 APP Decoder

Serial Concatenated Codes.” JPL TMO Progress Report, vol. 42-127, November
1996. [This electronic journal is available at
http://tmo.jpl.nasa.gov/tmo/progress_report/index.html.]

[3] Viterbi, Andrew J. “An Intuitive Justification and a Simplified

Implementation of the MAP Decoder for Convolutional Codes.” IEEE Journal
on Selected Areas in Communications, vol. 16, February 1998. 260-264.

4-59
AWGN Channel

Purpose 4AWGN Channel

Add white Gaussian noise to the input signal

Library Channels

Description The AWGN Channel block adds white Gaussian noise to a real or complex
input signal. When the input signal is real, this block adds real Gaussian noise
and produces a real output signal. When the input signal is complex, this block
adds complex Gaussian noise and produces a complex output signal. This block
inherits its sample time from the input signal.
This block uses the DSP Blockset’s Random Source block to generate the noise.
The Initial seed parameter in this block initializes the noise generator. Initial
seed can be either a scalar or a vector whose length matches the number of
channels in the input signal. For details on Initial seed, see the Random
Source block reference page in the DSP Blockset User’s Guide.

Frame-Based Processing and Input Dimensions

This block can process multichannel signals that are frame-based or
sample-based. The guidelines below indicate how the block interprets your
data, depending on the data’s shape and frame status:

• If your input is a sample-based scalar, then the block adds scalar Gaussian
noise to your signal.
• If your input is a sample-based vector or a frame-based row vector, then the
block adds independent Gaussian noise to each channel.
• If your input is a frame-based column vector, then the block adds a frame of
Gaussian noise to your single-channel signal.
• If your input is a frame-based m-by-n matrix, then the block adds a length-m
frame of Gaussian noise independently to each of the n channels.

The input cannot be a sample-based m-by-n matrix if both m and n are greater
than 1.

Specifying the Variance Directly or Indirectly

You can specify the variance of the noise generated by the AWGN Channel
block using one of four modes:

• Signal to noise ratio (Es/No), where the block calculates the variance from
these quantities that you specify in the block mask:

4-60
 AWGN Channel

- Es/No, the ratio of signal energy to noise power spectral density

- Input signal power, the power of the input symbols
- Symbol period
• Signal to noise ratio (SNR), where the block calculates the variance from
these quantities that you specify in the block mask:
- SNR, the ratio of signal power to noise power
- Input signal power, the power of the input samples
• Variance from mask, where you specify the variance in the block mask. The
value must be positive.
• Variance from port, where you provide the variance as an input to the
block. The variance input must be positive, and its sampling rate must equal
that of the input signal. If the first input signal is sample-based, then the
variance input must be sample-based. If the first input signal is frame-based,
then the variance input can be either frame-based with exactly one row, or
sample-based.

In both Variance from mask mode and Variance from port mode, these rules
describe how the block interprets the variance:

• If the variance is a scalar, then all signal channels are uncorrelated but
share the same variance.
• If the variance is a vector whose length is the number of channels in the
input signal, then each element represents the variance of the corresponding
signal channel.

Note If you apply complex input signals to the AWGN Channel block, then it
adds complex zero-mean Gaussian noise with the calculated or specified
variance. The variance of each of the quadrature components of the complex
noise is half of the calculated or specified value.

4-61
AWGN Channel

Dialog Box

Initial seed
The seed for the Gaussian noise generator.
Mode
The mode by which you specify the noise variance: Signal to noise
ratio (Es/No), Signal to noise ratio (SNR), Variance from mask, or
Variance from port.

Es/No (dB)
The ratio of signal energy per symbol to noise power spectral density, in
decibels. This field appears only if Mode is set to Es/No.
SNR (dB)
The ratio of signal power to noise power, in decibels. This field appears only
if Mode is set to SNR.
Input signal power (watts)
The root mean square power of the input symbols (if Mode is Es/No) or
input samples (if Mode is SNR), in watts. This field appears only if Mode
is set to either Es/No or SNR.

4-62
 AWGN Channel

Symbol period (s)

The duration of a channel symbol, in seconds. This field appears only if
Mode is set to Es/No.

Variance
The variance of the white Gaussian noise. This field appears only if Mode
is set to Variance from mask.

See Also Random Source (DSP Blockset)

4-63
Baseband PLL

Purpose 4Baseband PLL

Implement a baseband phase-locked loop

Library Synchronization

Description The Baseband PLL (phase-locked loop) block is a feedback control system that
automatically adjusts the phase of a locally generated signal to match the
phase of an input signal. Unlike the Phase-Locked Loop block, this block uses
a baseband method and does not depend on a carrier frequency.
This PLL has these three components:

• An integrator used as a phase detector.

• A filter. You specify the filter’s transfer function using the Lowpass filter
numerator and Lowpass filter denominator mask parameters. Each is a
vector that gives the respective polynomial’s coefficients in order of
descending powers of s.
To design a filter, you can use functions such as butter, cheby1, and cheby2
in the Signal Processing Toolbox. The default filter is a Chebyshev type II
filter whose transfer function arises from the command below.
[num, den] = cheby2(3,40,100,'s')

• A voltage-controlled oscillator (VCO). You specify the sensitivity of the VCO

signal to its input using the VCO input sensitivity parameter. This
parameter, measured in Hertz per volt, is a scale factor that determines how
much the VCO shifts from its quiescent frequency.

The input signal represents the received signal. The input must be a
sample-based scalar signal. The three output ports produce:

• The output of the filter

• The output of the phase detector
• The output of the VCO

This model is nonlinear; for a linearized version, use the Linearized Baseband
PLL block.

4-64
 Baseband PLL

Dialog Box

Lowpass filter numerator

The numerator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
VCO input sensitivity (Hz/V)
This value scales the input to the VCO and, consequently, the shift from
the VCO’s quiescent frequency.

See Also Linearized Baseband PLL, Phase-Locked Loop

References For more information about phase-locked loops, see the works listed in
“Selected Bibliography for Synchronization” on page 2-92.

4-65
BCH Decoder

Purpose 4BCH Decoder

Decode a BCH code to recover binary vector data

Library Block sublibrary of Channel Coding

Description The BCH Decoder block recovers a binary message vector from a binary BCH
codeword vector. For proper decoding, the first two parameter values in this
block should match the parameters in the corresponding BCH Encoder block.
The input is the binary codeword vector and the first output is the
corresponding binary message vector. If the BCH code has message length K
and codeword length N, then the input has length N and the first output has
length K. If the input is frame-based, then it must be a column vector.
The number N must have the form 2M-1, where M is an integer greater than or
equal to 3. For a given codeword length N, only specific message lengths K are
valid for a BCH code. To see which values of K are valid, use the bchpoly
function in the Communications Toolbox. No known analytic formula describes
the relationship among the codeword length, message length, and
error-correction capability.
The second output is the number of errors detected during decoding of the
codeword. A negative integer indicates that the block detected more errors
than it could correct using the coding scheme.
The sample times of all input and output signals are equal.
The Error-correction capability T parameter either:

• Indicates the error-correction capability of the code as a positive integer, or

• Tells the block to compute the error-correction capability, if you enter zero

The block runs faster in the first case above. You can use the bchpoly function
in the Communications Toolbox to calculate the error-correction capability.

4-66
 BCH Decoder

Dialog Box

Codeword length N
The codeword length, which is also the vector length of the first input.
Message length K
The message length, which is also the vector length of the first output.
Error-correction capability T
Either the error-correction capability of the code, or zero. A zero forces the
block to calculate the error-control capability when initializing.

Pair Block BCH Encoder

See Also bchpoly (Communications Toolbox)

4-67
BCH Encoder

Purpose 4BCH Encoder

Create a BCH code from binary vector data

Library Block sublibrary of Channel Coding

Description The BCH Encoder block creates a BCH code with message length K and
codeword length N. You specify both N and K directly in the block mask.
The input must contain exactly K elements. If it is frame-based, then it must
be a column vector. The output is a vector of length N.
N must have the form 2M-1, where M is an integer greater than or equal to 3.
For a given codeword length N, only specific message lengths K are valid for a
BCH code. To see which values of K are valid, use the bchpoly function in the
Communications Toolbox. For example, in the output below, the second column
lists all possible message lengths that correspond to a codeword length of 15.
The third column lists the corresponding error-correction capabilities.
params = bchpoly(15)

params =

15 11 1
15 7 2
15 5 3

No known analytic formula describes the relationship among the codeword

length, message length, and error-correction capability.

Dialog Box

4-68
 BCH Encoder

Codeword length N
The codeword length, which is also the output vector length.
Message length K
The message length, which is also the input vector length.

Pair Block BCH Decoder

See Also bchpoly (Communications Toolbox)

4-69
Bernoulli Random Binary Generator

Purpose 4Bernoulli Random Binary Generator

Generate Bernoulli-distributed random binary numbers

Library Comm Sources

Description The Bernoulli Random Binary Generator block generates random binary
numbers using a Bernoulli distribution. The Bernoulli distribution with
parameter p produces zero with probability p and one with probability 1-p. The
Bernoulli distribution has mean value 1-p and variance p(1-p). The
Probability of a zero parameter specifies p, and can be any real number
between zero and one.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret
vector parameters as 1-D parameters. See “Signal Attribute Parameters for
Random Sources” on page 2-7 for more details.
The number of elements in the Initial seed and Probability of a zero
parameters becomes the number of columns in a frame-based output or the
number of elements in a sample-based vector output. Also, the shape (row or
column) of the Initial seed and Probability of a zero parameters becomes the
shape of a sample-based two-dimensional output signal.

4-70
 Bernoulli Random Binary Generator

Dialog Box

Probability of a zero
The probability with which a zero output occurs.
Initial seed
The initial seed value for the random number generator. The seed can be
either a vector of the same length as the Probability of a zero parameter,
or a scalar.
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.
Samples per frame
The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.

4-71
Bernoulli Random Binary Generator

Interpret vector parameters as 1-D

If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

See Also Binary Vector Noise Generator, Random-Integer Generator, Binary

Symmetric Channel; randint (Communications Toolbox), rand (built-in
MATLAB function)

4-72
 Binary Cyclic Decoder

Purpose 4Binary Cyclic Decoder

Decode a systematic cyclic code to recover binary vector data

Library Block sublibrary of Channel Coding

Description The Binary Cyclic Decoder block recovers a message vector from a codeword
vector of a binary systematic cyclic code. For proper decoding, the parameter
values in this block should match those in the corresponding Binary Cyclic
Encoder block.
If the cyclic code has message length K and codeword length N, then N must
have the form 2M-1 for some integer M greater than or equal to 3.
The input must contain exactly N elements. If it is frame-based, then it must
be a column vector. The output is a vector of length K.
You can determine the systematic cyclic coding scheme in one of two ways:

• To create an [N,K] code, enter N and K as the first and second mask
parameters, respectively. The block computes an appropriate generator
polynomial, namely, cyclpoly(N,K,'min').
• To create a code with codeword length N and a particular degree-(N-K)
binary generator polynomial, enter N as the first parameter and a binary
vector as the second parameter. The vector represents the generator
polynomial by listing its coefficients in order of ascending exponents. You can
create cyclic generator polynomials using the cyclpoly function in the
Communications Toolbox.

Dialog Box

4-73
Binary Cyclic Decoder

Codeword length N
The codeword length N, which is also the input vector length.
Message length K, or generator polynomial
Either the message length, which is also the output vector length; or a
binary vector that represents the generator polynomial for the code.

Pair Block Binary Cyclic Encoder

See Also cyclpoly (Communications Toolbox)

4-74
 Binary Cyclic Encoder

Purpose 4Binary Cyclic Encoder

Create a systematic cyclic code from binary vector data

Library Block sublibrary of Channel Coding

Description The Binary Cyclic Encoder block creates a systematic cyclic code with message
length K and codeword length N. The number N must have the form 2M-1,
where M is an integer greater than or equal to 3.
The input must contain exactly K elements. If it is frame-based, then it must
be a column vector. The output is a vector of length N.
You can determine the systematic cyclic coding scheme in one of two ways:

• To create an [N,K] code, enter N and K as the first and second mask
parameters, respectively. The block computes an appropriate generator
polynomial, namely, cyclpoly(N,K,'min').
• To create a code with codeword length N and a particular degree-(N-K)
binary generator polynomial, enter N as the first parameter and a binary
vector as the second parameter. The vector represents the generator
polynomial by listing its coefficients in order of ascending exponents. You can
create cyclic generator polynomials using the cyclpoly function in the
Communications Toolbox.

Dialog Box

Codeword length N
The codeword length, which is also the output vector length.

4-75
Binary Cyclic Encoder

Message length K, or generator polynomial

Either the message length, which is also the input vector length; or a
binary vector that represents the generator polynomial for the code.

Pair Block Binary Cyclic Decoder

See Also cyclpoly (Communications Toolbox)

4-76
 Binary-Input RS Encoder

Purpose 4Binary-Input RS Encoder

Create a Reed-Solomon code from binary vector data

Library Block sublibrary of Channel Coding

Description The Binary-Input RS Encoder block creates a Reed-Solomon code with message
length K and codeword length N. You specify both N and K directly in the block
mask. N must have the form 2M-1, where M is an integer greater than or equal
to 3. The code is more efficient if N-K is an even integer.
The input and output are binary-valued signals that represent messages and
codewords, respectively. The input must contain exactly M*K elements. If it is
frame-based, then it must be a column vector. The output is a vector of length
M*N.
The M*K input bits represent K integers between 0 and 2M-1, where more
significant bits are to the right. Similarly, the M*N output bits represent N
integers between 0 and 2M-1. These integers in turn represent elements of the
finite field GF(2M).
An (N,K) Reed-Solomon code can correct up to floor((N-K)/2) symbol errors
(not bit errors) in each codeword.

Examples Suppose M = 3, N = 23-1 = 7, and K = 5. Then a message is a binary vector of

length 15 that represents 5 three-bit integers. A corresponding codeword is a
binary vector of length 21 that represents 7 three-bit integers. The figure below
shows the codeword that would result from a particular message word. The
integer format equivalents illustrate that the highest-order bit is at the right.

Message input: [0 1 1 1 1 1 0 0 1 0 0 0 0 0 1] [6 7 4 0 4]
in integer format
Binary-Input RS Encoder
with N = 7, K = 5

Code output: [1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1] [3 2 6 7 4 0 4]
in integer format

4-77
Binary-Input RS Encoder

Dialog Box

Codeword length N
The codeword length. The output has vector length M*N.
Message length K
The message length. The input has vector length M*K.

Pair Block Binary-Output RS Decoder

See Also Integer-Input RS Encoder

4-78
 Binary Linear Decoder

Purpose 4Binary Linear Decoder

Decode a linear block code to recover binary vector data

Library Block sublibrary of Channel Coding

Description The Binary Linear Decoder block recovers a binary message vector from a
binary codeword vector of a linear block code.
The Generator matrix parameter is the generator matrix for the block code.
For proper decoding, this should match the Generator matrix parameter in
the corresponding Binary Linear Encoder block. If N is the codeword length of
the code, then Generator matrix must have N columns. If K is the message
length of the code, then the Generator matrix parameter must have K rows.
The input must contain exactly N elements. If it is frame-based, then it must
be a column vector. The output is a vector of length K.
The decoder tries to correct errors, using the Decoding table parameter. If
Decoding table is the scalar 0, then the block defaults to the table produced by
the Communications Toolbox function syndtable. Otherwise, Decoding table
must be a 2N-K-by-N binary matrix. The rth row of this matrix is the correction
vector for a received binary codeword whose syndrome has decimal integer
value r-1. The syndrome of a received codeword is its product with the
transpose of the parity-check matrix.

Dialog Box

4-79
Binary Linear Decoder

Generator matrix
Generator matrix for the code; same as in Binary Linear Encoder block.
Decoding table
Either a 2N-K-by-N matrix that lists correction vectors for each codeword’s
syndrome; or the scalar 0, in which case the block defaults to the table
corresponding to the Generator matrix parameter.

Pair Block Binary Linear Encoder

4-80
 Binary Linear Encoder

Purpose 4Binary Linear Encoder

Create a linear block code from binary vector data

Library Block sublibrary of Channel Coding

Description The Binary Linear Encoder block creates a binary linear block code using a
generator matrix that you provide in the parameter mask. If K is the message
length of the code, then the Generator matrix parameter must have K rows.
If N is the codeword length of the code, then Generator matrix must have N
columns.
The input must contain exactly K elements. If it is frame-based, then it must
be a column vector. The output is a vector of length N.

Dialog Box

Generator matrix
A K-by-N matrix, where K is the message length and N is the codeword
length.

Pair Block Binary Linear Decoder

4-81
Binary-Output RS Decoder

Purpose 4Binary-Output RS Decoder

Decode a Reed-Solomon code to recover binary vector data

Library Block sublibrary of Channel Coding

Description The Binary-Output RS Decoder block recovers a binary message vector from a
binary Reed-Solomon codeword vector. For proper decoding, the parameter
values in this block should match those in the corresponding Binary-Input RS
Encoder block.
If the Reed-Solomon code has message length K and codeword length N, then
N must have the form 2M-1 for some integer M greater than or equal to 3. The
code is more efficient if N-K is an even integer.
The input and first output are binary-valued signals that represent codewords
and messages, respectively. The input must contain exactly M*N elements. If
it is frame-based, then it must be a column vector. The first output is a vector
of length M*K.
The M*N input bits represent N integers between 0 and 2M-1, where more
significant bits are to the right. Similarly, M*K output bits represent K
integers between 0 and 2M-1. These integers in turn represent elements of the
finite field GF(2M).
The second output is the number of errors detected during decoding of the
codeword. A negative integer indicates that the block detected more errors
than it could correct using the coding scheme. An (N,K) Reed-Solomon code can
correct up to floor((N-K)/2) symbol errors (not bit errors) in each codeword.

4-82
 Binary-Output RS Decoder

Dialog Box

Codeword length N
The codeword length. The input has vector length M*N.
Message length K
The message length. The first output has vector length M*K.

Pair Block Binary-Input RS Encoder

See Also Integer-Output RS Decoder

4-83
Binary Symmetric Channel

Purpose 4Binary Symmetric Channel

Introduce binary errors

Library Channels

Description The Binary Symmetric Channel block introduces binary errors to the signal
transmitted through this channel.
The input port is the transmitted binary signal. The input can be either a
scalar, a sample-based vector, or a frame-based row vector. This block
processes each vector element independently, and introduces an error in a
given spot with probability Error probability.
The first output port is the binary signal that has passed through the channel.
The second output port is the vector of errors that were introduced.

Dialog Box

Error probability
The probability that a binary error will occur. The value of this parameter
must be between zero and one.
Input vector length
Length of the input vector signal. This is the same as the vector length of
the signal at the first output port.

4-84
 Binary Symmetric Channel

Initial seed
The initial seed value for the random number generator.
Sample time
The block’s sample time.

See Also Bernoulli Random Binary Generator

4-85
Binary Vector Noise Generator

Purpose 4Binary Vector Noise Generator

Generate a binary vector while controlling the number of 1s

Library Comm Sources

Description The Binary Vector Noise Generator outputs a random binary vector whose
length is the Binary vector length parameter. The Probabilities parameter
helps determine how many 1s appear in each output vector. Once the number
of 1s is determined, their placement is determined according to a uniform
distribution.
If p1, p2,...pm are the entries in the Probabilities parameter, then p1 is the
probability that the output vector will have a single 1, p2 is the probability that
the output vector will have exactly two 1s, and so on. Note that Probabilities
must have sum less than or equal to one, and length less than or equal to the
Binary vector length. Also, the probability of a zero vector is one minus the
sum of Probabilities.
This block is useful in testing error-control coding algorithms.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret
vector parameters as 1-D parameters. See “Signal Attribute Parameters for
Random Sources” on page 2-7 for more details.
The Binary vector length parameter becomes the number of columns in a
frame-based output or the number of elements in a sample-based vector
output. Also, the shape (row or column) of the Probabilities parameter
becomes the shape of a sample-based two-dimensional output signal.

4-86
 Binary Vector Noise Generator

Dialog Box

Binary vector length

The output vector length.
Probabilities
A vector whose kth entry indicates the probability that the output vector
has exactly k 1s.
Initial seed
The initial seed value for the random number generator. This must be a
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.

4-87
Binary Vector Noise Generator

Samples per frame

The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.
Interpret vector parameters as 1-D
If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

See Also Bernoulli Random Binary Generator; randerr (Communications Toolbox)

4-88
 Bit to Integer Converter

Purpose 4Bit to Integer Converter

Map a vector of bits to a corresponding vector of integers

Library Utility Functions

Description The Bit to Integer Converter block maps groups of bits in the input vector to
integers in the output vector. If M is the Number of bits per integer
parameter, then the block maps each group of M bits to an integer between 0
and 2M-1. As a result, the output vector length is 1/M times the input vector
length.
If the input is sample-based input, then it must be a vector whose length equals
the Number of bits per integer parameter. If the input is frame-based, then
it must be a column vector whose length is an integer multiple of Number of
bits per integer.

The block interprets the first bit in each group as the most significant bit.

Dialog Box

Number of bits per integer

The number of input bits that the block maps to each integer of the output.
This parameter must be an integer between 1 and 31.

Examples If the input is [0; 1; 1; 1; 1; 1; 0; 1] and the Number of bits per integer
parameter is 4, then the output is [7; 13]. The block maps the first group of four
bits (0, 1, 1, 1) to 7 and the second group of four bits (1, 1, 0, 1) to 13. Notice that
the output length is one-fourth of the output length.
Pair Block Integer to Bit Converter

4-89
BPSK Demodulator Baseband

Purpose 4BPSK Demodulator Baseband

Demodulate BPSK-modulated data

Library PM, in Digital Baseband sublibrary of Modulation

Description The BPSK Demodulator Baseband block demodulates a signal that was
modulated using the binary phase shift keying method. The input is a
baseband representation of the modulated signal. The input can be either a
scalar or a frame-based column vector.
The input must be a discrete-time complex signal. The block maps the points
exp(jθ) and -exp(jθ) to 0 and 1, respectively, where θ is the Phase offset
parameter.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

Phase offset (rad)

The phase of the zeroth point of the signal constellation.
Samples per symbol
The number of input samples that represent each modulated symbol.

4-90
 BPSK Demodulator Baseband

Pair Block BPSK Modulator Baseband

See Also M-PSK Demodulator Baseband, QPSK Demodulator Baseband, DBPSK

Demodulator Baseband

4-91
BPSK Modulator Baseband

Purpose 4BPSK Modulator Baseband

Modulate using the binary phase shift keying method

Library PM, in Digital Baseband sublibrary of Modulation

Description The BPSK Modulator Baseband block modulates using the binary phase shift
keying method. The output is a baseband representation of the modulated
signal.
The input must be a discrete-time binary-valued signal. If the input bit is 0 or
1, respectively, then the modulated symbol is exp(jθ) or -exp(jθ) respectively,
where θ is the Phase offset parameter.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

Phase offset (rad)

The phase of the zeroth point of the signal constellation.
Samples per symbol
The number of output samples that the block produces for each input bit.

4-92
 BPSK Modulator Baseband

Pair Block BPSK Demodulator Baseband

See Also M-PSK Modulator Baseband, QPSK Modulator Baseband, DBPSK Modulator
Baseband

4-93
Charge Pump PLL

Purpose 4Charge Pump PLL

Implement a charge pump phase-locked loop using a digital phase detector

Library Synchronization

Description The Charge Pump PLL (phase-locked loop) block automatically adjusts the
phase of a locally generated signal to match the phase of an input signal. It is
suitable for use with digital signals.
This PLL has these three components:

• A sequential logic phase detector, also called a digital phase detector or a

phase/frequency detector.
• A filter. You specify the filter’s transfer function using the Lowpass filter
numerator and Lowpass filter denominator mask parameters. Each is a
vector that gives the respective polynomial’s coefficients in order of
descending powers of s.
To design a filter, you can use functions such as butter, cheby1, and cheby2
in the Signal Processing Toolbox. The default filter is a Chebyshev type II
filter whose transfer function arises from the command below.
[num, den] = cheby2(3,40,100,'s')

• A voltage-controlled oscillator (VCO). You specify characteristics of the VCO

using the VCO input sensitivity, VCO quiescent frequency, VCO initial
phase, and VCO output amplitude parameters.

The input signal represents the received signal. The input must be a
sample-based scalar signal. The three output ports produce:

• The output of the filter

• The output of the phase detector
• The output of the VCO

A sequential logic phase detector operates on the zero crossings of the signal
waveform. The equilibrium point of the phase difference between the input
signal and the VCO signal equals π. The sequential logic detector can
compensate for any frequency difference that might exist between a VCO and
an incoming signal frequency. Hence, the sequential logic phase detector acts
as a frequency detector.

4-94
 Charge Pump PLL

Dialog Box

Lowpass filter numerator

The numerator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
VCO input sensitivity (Hz/V)
This value scales the input to the VCO and, consequently, the shift from
the VCO quiescent frequency value. The units of VCO input sensitivity
are Hertz per volt.
VCO quiescent frequency (Hz)
The frequency of the VCO signal when the voltage applied to it is zero. This
should match the frequency of the input signal.
VCO initial phase (rad)
The initial phase of the VCO signal.

4-95
Charge Pump PLL

VCO output amplitude

The amplitude of the VCO signal.

See Also Phase-Locked Loop

References For more information about digital phase-locked loops, see the works listed in
“Selected Bibliography for Synchronization” on page 2-92.

4-96
 Complex Phase Difference

Purpose 4Complex Phase Difference

Output the phase difference between the two complex input signals

Library Sequence Operations, in Basic Comm Functions

Description The Complex Phase Difference block accepts two complex input signals that
have the same size and frame status. The output is the phase difference from
the second to the first, measured in radians. The elements of the output are
between -π and π.
The input signals can have any size or frame status. This block processes each
pair of elements independently.

Dialog Box

See Also Complex Phase Shift

4-97
Complex Phase Shift

Purpose 4Complex Phase Shift

Shift the phase of the complex input signal by the second input value

Library Sequence Operations, in Basic Comm Functions

Description The Complex Phase Shift block accepts a complex signal at the port labeled In.
The output is the result of shifting this signal’s phase by an amount specified
by the real signal at the input port labeled Ph. The Ph input is measured in
radians, and must have the same size and frame status as the In input.
The input signals can have any size or frame status. This block processes each
pair of corresponding elements independently.

Dialog Box

See Also Complex Phase Difference

4-98
 Continuous-Time Eye and Scatter Diagrams

Purpose 4Continuous-Time Eye and Scatter Diagrams

Produce eye diagram, scatter, or x-y plots, using trigger to set decision timing

Library Comm Sinks

Description The Continuous-Time Eye and Scatter Diagrams block plots eye diagrams,
scatter diagrams, and X-Y diagrams from a continuous-time input signal. The
Diagram type parameter determines which plots the block produces. The
block draws the diagrams in a single window, as in the case of the eye diagram
and scatter diagram below.

The first input is a complex message signal. It must be a sample-based scalar

signal. The eye diagram and the X-Y diagram both record the trajectories of the
message signal in continuous time.
The second input is a scalar trigger signal that determines the decision timing
for the scatter diagram. At each rising edge of the trigger signal, the block plots
a vertical line in the eye diagram and adds a new point to the scatter plot.

4-99
Continuous-Time Eye and Scatter Diagrams

The Trace period parameter is the number of seconds represented by the

horizontal axis in the eye diagram. The Trace offset parameter is the time
value at the left edge of the horizontal axis of the eye diagram.

Tip This block works better if the model’s simulation step size is suitable for
your data. From the model window’s Simulation menu, choose Simulation
parameters and then choose a value for the Max step size parameter. Try
multiplying this block’s Trace period parameter by 1/8 or 1/16.

To specify the plotting color as well as the line type and/or marker type, use the
Line type parameters that appear after you select a value for the Diagram
type parameter. In the Line type for eye diagram parameter, use a slash (/)
to separate the specifications for the real and imaginary components of the
input signal. Choices for the color, marker, and line types are in the table
below.

Color Characters Marker-Type Characters Line-Type Characters

y Yellow . Point - Solid

m Magenta o Circle : Dotted
c Cyan x Cross -. Dash-dot
r Red + Plus sign -- Dashed
g Green * Asterisk
b Blue s Square
w White d Diamond
k Black v Triangle (down)
^ Triangle (up)
< Triangle (left)
> Triangle (right)

4-100
 Continuous-Time Eye and Scatter Diagrams

Color Characters Marker-Type Characters Line-Type Characters

p Five-pointed star
h Six-pointed star

Dialog Box

Trace period
The duration of the horizontal axis of the eye diagram, in seconds.
Trace offset
The time at the leftmost edge of the horizontal axis of the eye diagram.
Lower and upper bounds of diagram
A two-element vector containing the minimum and maximum signal
values in the diagrams.
Number of saved traces
The number of curves in the eye diagram, or points in the scatter plot, that
are visible after you resize or restore the figure window.
Diagram type
The diagram(s) that the block produces.

4-101
Continuous-Time Eye and Scatter Diagrams

Line type for eye diagram

A string that specifies the color and the line type for the eye diagram. This
field appears only when the Diagram type parameter is set to an option
that includes an eye diagram.
Line type for scatter diagram
A string that specifies the color and the marker type for the scatter
diagram. This field appears only when the Diagram type parameter is set
to an option that includes an scatter diagram.
Line type for X-Y diagram
A string that specifies the color and the line type for the X-Y diagram. This
field appears only when the Diagram type parameter is set to an option
that includes an X-Y diagram.

Limitations Since this block uses an M-file, you cannot generate C code for it using the
Real-Time Workshop.

See Also Discrete-Time Eye and Scatter Diagrams

4-102
 Convolutional Deinterleaver

Purpose 4Convolutional Deinterleaver

Restore ordering of symbols that were permuted using shift registers

Library Convolutional sublibrary of Interleaving

Description The Convolutional Deinterleaver block recovers a signal that was interleaved
using the Convolutional Interleaver block. The parameters in the two blocks
should have the same values.
The input can be either a scalar or a frame-based column vector. It can be real
or complex. The sample times of the input and output signals are the same.

Dialog Box

Rows of shift registers

The number of shift registers that the block uses internally.
Register length step
The difference in symbol capacity of each successive shift register, where
the last register holds zero symbols.
Initial conditions
The values that fill each shift register when the simulation begins.

Pair Block Convolutional Interleaver

See Also General Multiplexed Deinterleaver, Helical Deinterleaver

4-103
Convolutional Deinterleaver

References [1] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[2] Forney, G., D., Jr. “Burst-Correcting Codes for the Classic Bursty Channel.”
IEEE Transactions on Communications, vol. COM-19, October 1971. 772-781.
[3] Ramsey, J. L. “Realization of Optimum Interleavers.” IEEE Transactions on
Information Theory, IT-16 (3), May 1970. 338-345.

4-104
 Convolutional Encoder

Purpose 4Convolutional Encoder

Create a convolutional code from binary data

Library Convolutional sublibrary of Channel Coding

Description The Convolutional Encoder block encodes a sequence of binary input vectors to
produce a sequence of binary output vectors. This block can process multiple
symbols at a time.

Input and Output Sizes

If the encoder takes k input bit streams (that is, can receive 2k possible input
symbols), then this block’s input vector length is L*k for some positive integer
L. Similarly, if the encoder produces n output bit streams (that is, can produce
2n possible output symbols), then this block’s output vector length is L*n.
The input can be a sample-based vector with L = 1, or a frame-based column
vector with any positive integer for L.

Specifying the Encoder

To define the convolutional encoder, use the Trellis structure parameter. This
parameter is a MATLAB structure whose format is described in the section,
“Trellis Description of a Convolutional Encoder,” in the Communications
Toolbox User’s Guide. You can use this parameter field in two ways:

• If you have a variable in the MATLAB workspace that contains the trellis
structure, then enter its name as the Trellis structure parameter. This way
is preferable because it causes Simulink to spend less time updating the
diagram at the beginning of each simulation, compared to the usage in the
next bulleted item.
• If you want to specify the encoder using its constraint length, generator
polynomials, and possibly feedback connection polynomials, then use a
poly2trellis command within the Trellis structure field. For example, to
use an encoder with a constraint length of 7, code generator polynomials of
171 and 133 (in octal numbers), and a feedback connection of 171 (in octal),
set the Trellis structure parameter to
poly2trellis(7,[171 133],171)

The encoder registers begin in the all-zeros state. You can configure the
encoder so that it resets its registers to the all-zeros state during the course of
the simulation. To do this, use one of these values of the Reset parameter:

4-105
Convolutional Encoder

• The value None indicates that the encoder never resets.

• The value On each frame indicates that the encoder resets at the beginning
of each frame, before processing the next frame of input data
• The value On nonzero Rst input causes the block to have a second input
port, labeled Rst. The signal at the Rst port is a scalar signal. When it is
nonzero, the encoder resets before processing the data at the first input port.

Dialog Box

Trellis structure
MATLAB structure that contains the trellis description of the
convolutional encoder.
Reset
Determines whether and under what circumstances the encoder resets to
the all-zeros state before processing the input data. Choices are None, On
each frame, and On nonzero Rst input. The last option causes the block
to have a second input port, labeled Rst.

See Also Viterbi Decoder, APP Decoder

References [1] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[2] Gitlin, Richard D., Jeremiah F. Hayes, and Stephen B. Weinstein. Data
Communications Principles. New York: Plenum, 1992.

4-106
 Convolutional Interleaver

Purpose 4Convolutional Interleaver

Permute input symbols using a set of shift registers

Library Convolutional sublibrary of Interleaving

Description The Convolutional Interleaver block permutes the symbols in the input signal.
Internally, it uses a set of shift registers. The delay value of the kth shift
register is (k-1) times the Register length step parameter. The number of shift
registers is the value of the Rows of shift registers parameter.
The Initial conditions parameter indicates the values that fill each shift
register at the beginning of the simulation (except for the first shift register,
which has zero delay). If Initial conditions is a scalar, then its value fills all
shift registers except the first; if Initial conditions is a column vector whose
length is the Rows of shift registers parameter, then each entry fills the
corresponding shift register. The value of the first element of the Initial
conditions parameter is unimportant, since the first shift register has zero
delay.
The input can be either a scalar or a frame-based column vector. It can be real
or complex. The sample times of the input and output signals are the same.

Dialog Box

Rows of shift registers

The number of shift registers that the block uses internally.

4-107
Convolutional Interleaver

Register length step

The number of additional symbols that fit in each successive shift register,
where the first register holds zero symbols.
Initial conditions
The values that fill each shift register when the simulation begins.

Pair Block Convolutional Deinterleaver

See Also General Multiplexed Interleaver, Helical Interleaver

References [1] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[2] Forney, G., D., Jr. “Burst-Correcting Codes for the Classic Bursty Channel.”
IEEE Transactions on Communications, vol. COM-19, October 1971. 772-781.
[3] Ramsey, J. L. “Realization of Optimum Interleavers.” IEEE Transactions on
Information Theory, IT-16 (3), May 1970. 338-345.

4-108
 CPFSK Demodulator Baseband

Purpose 4CPFSK Demodulator Baseband

Demodulate CPFSK-modulated data

Library CPM, in Digital Baseband sublibrary of Modulation

Description The CPFSK Demodulator Baseband block demodulates a signal that was
modulated using the continuous phase frequency shift keying method. The
input is a baseband representation of the modulated signal. The M-ary
number parameter, M, is the size of the input alphabet. M must have the form
2K for some positive integer K.
The Modulation index parameter times π radians is the phase shift in the
modulated signal due to the latest symbol, when that symbol is the integer 1.
The Phase offset parameter is the initial phase of the modulated waveform.

Traceback Length and Output Delays

Internally, this block creates a trellis description of the modulation scheme and
uses the Viterbi algorithm. The Traceback length parameter, D, in this block
is the number of trellis branches used to construct each traceback path. D
influences the output delay, which is the number of zero symbols that precede
the first meaningful demodulated value in the output.

• If the input signal is sample-based, then the delay consists of D+1 zero
symbols.
• If the input signal is frame-based, then the delay consists of D zero symbols.

Outputs and Symbol Sets

If the Output type parameter is set to Integer, then the block produces odd
integers between -(M-1) and M-1.
If the Output type parameter is set to Bit, then the block produces groupings
of K bits. Each grouping is called a binary word.
In binary output mode, the block first maps each input symbol to an
intermediate value as in the integer output mode. The block then maps the odd
integer k to the nonnegative integer (k+M-1)/2. Finally, the block maps each
nonnegative integer to a binary word, using a mapping that depends on
whether the Symbol set ordering parameter is set to Binary or Gray. For
more information about Gray and binary coding, see “Binary-Valued and
Integer-Valued Signals” on page 2-68.

4-109
CPFSK Demodulator Baseband

The input can be either a scalar or a frame-based column vector.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

M-ary number
The size of the alphabet.
Output type
Determines whether the output consists of integers or groups of bits.

4-110
 CPFSK Demodulator Baseband

Symbol set ordering

Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Modulation index
The number of half-revolutions of phase shift in the modulated signal after
modulating the latest symbol of 1.
Phase offset (rad)
The initial phase of the modulated waveform.
Samples per symbol
The number of input samples that represent each modulated symbol.
Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.

Pair Block CPFSK Modulator Baseband

See Also CPM Demodulator Baseband, Viterbi Decoder, M-FSK Demodulator Baseband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-111
CPFSK Demodulator Passband

Purpose 4CPFSK Demodulator Passband

Demodulate CPFSK-modulated data

Library CPM, in Digital Passband sublibrary of Modulation

Description The CPFSK Demodulator Passband block demodulates a signal that was
modulated using the continuous phase frequency shift keying method. The
input is a passband representation of the modulated signal. The M-ary
number parameter, M, is the size of the input alphabet. M must have the form
2K for some positive integer K.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, CPFSK Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• M-ary number
• Output type
• Signal set ordering
• Modulation index
• Traceback length
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1

4-112
 CPFSK Demodulator Passband

• Input sample time = K*Symbol period*Baseband samples per symbol for

some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

Dialog Box

M-ary number
The size of the alphabet.
Output type
Determines whether the output consists of integers or groups of bits.

4-113
CPFSK Demodulator Passband

Symbol set ordering

Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Modulation index
The number of half-revolutions of phase shift in the modulated signal after
modulating the latest symbol of 1.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.
Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.

Pair Block CPFSK Modulator Passband

See Also CPFSK Demodulator Baseband, Viterbi Decoder, M-FSK Demodulator

Passband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-114
 CPFSK Modulator Baseband

Purpose 4CPFSK Modulator Baseband

Modulate using the continuous phase frequency shift keying method

Library CPM, in Digital Baseband sublibrary of Modulation

Description The CPFSK Modulator Baseband block modulates using the continuous phase
frequency shift keying method. The output is a baseband representation of the
modulated signal. The M-ary number parameter, M, is the size of the input
alphabet. M must have the form 2K for some positive integer K.
The Modulation index parameter times π radians is the phase shift due to the
latest symbol when that symbol is the integer 1. The Phase offset parameter
is the initial phase of the output waveform, measured in radians.
For the exact definitions of the rectangular pulse shape that this block uses, see
the work by Anderson, Aulin, and Sundberg listed in “References” on page
4-117.

Inputs and Symbol Sets

If the Input type parameter is set to Integer, then the block accepts odd
integers between -(M-1) and M-1.
If the Input type parameter is set to Bit, then the block accepts groupings of
K bits. Each grouping is called a binary word. The input vector length must be
an integer multiple of K.
In binary input mode, the block maps each binary word to an integer between
0 and M-1, using a mapping that depends on whether the Symbol set ordering
parameter is set to Binary or Gray. The block then maps the integer k to the
intermediate value 2k-(M-1) and proceeds as in the integer input mode. For
more information, see “Binary-Valued and Integer-Valued Signals” on page
2-68.
The input can be either a scalar or a frame-based column vector. If Input type
is Bit, then the input can also be a vector of length K.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-115
CPFSK Modulator Baseband

Dialog Box

M-ary number
The size of the alphabet.
Input type
Indicates whether the input consists of integers or groups of bits.
Symbol set ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Modulation index
The number of half-revolutions of phase shift due to the latest symbol when
that symbol is the integer 1.

4-116
 CPFSK Modulator Baseband

Phase offset (rad)

The initial phase of the output waveform.
Samples per symbol
The number of output samples that the block produces for each integer or
binary word in the input.

Pair Block CPFSK Demodulator Baseband

See Also CPM Modulator Baseband, M-FSK Modulator Baseband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-117
CPFSK Modulator Passband

Purpose 4CPFSK Modulator Passband

Modulate using the continuous phase frequency shift keying method

Library CPM, in Digital Passband sublibrary of Modulation

Description The CPFSK Modulator Passand block modulates using the continuous phase
frequency shift keying method. The output is a passband representation of the
modulated signal. The M-ary number parameter, M, is the size of the input
alphabet. M must have the form 2K for some positive integer K.
This block uses the baseband equivalent block, CPFSK Modulator Baseband,
for internal computations and converts the resulting baseband signal to a
passband representation. The following parameters in this block are the same
as those of the baseband equivalent block:
• M-ary number
• Input type
• Symbol set ordering
• Modulation index

The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.
The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1

4-118
 CPFSK Modulator Passband

• Symbol period = K*Output sample time*Baseband samples per symbol

for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

M-ary number
The size of the alphabet.
Input type
Indicates whether the input consists of integers or groups of bits.
Symbol set ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.

4-119
CPFSK Modulator Passband

Modulation index
The number of half-revolutions of phase shift due to the latest symbol when
that symbol is the integer 1.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block CPFSK Demodulator Passband

See Also CPFSK Modulator Baseband, M-FSK Modulator Passband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-120
 CPM Demodulator Baseband

Purpose 4CPM Demodulator Baseband

Demodulate CPM-modulated data

Library CPM, in Digital Baseband sublibrary of Modulation

Description The CPM Demodulator Baseband block demodulates a signal that was
modulated using continuous phase modulation. The input is a baseband
representation of the modulated signal. The M-ary number parameter, M, is
the size of the input alphabet. M must have the form 2K for some positive
integer K.
The input can be either a scalar or a frame-based column vector.
The Modulation index, Frequency pulse shape, Rolloff, BT product, Pulse
length, Symbol prehistory, and Phase offset parameters are as described on
the reference page for the CPM Modulator Baseband block.

Traceback Length and Output Delays

Internally, this block creates a trellis description of the modulation scheme and
uses the Viterbi algorithm. The Traceback length parameter, D, in this block
is the number of trellis branches used to construct each traceback path. D
influences the output delay, which is the number of zero symbols that precede
the first meaningful demodulated value in the output.

• If the input signal is sample-based, then the delay consists of D+1 zero
symbols.
• If the input signal is frame-based, then the delay consists of D zero symbols.

Outputs and Symbol Sets

If the Output type parameter is set to Integer, then the block produces odd
integers between -(M-1) and M-1.
If the Output type parameter is set to Bit, then the block produces groupings
of K bits. Each grouping is called a binary word.
In binary output mode, the block first maps each input symbol to an
intermediate value as in the integer output mode. The block then maps the odd
integer k to the nonnegative integer (k+M-1)/2. Finally, the block maps each
nonnegative integer to a binary word, using a mapping that depends on
whether the Symbol set ordering parameter is set to Binary or Gray. For

4-121
CPM Demodulator Baseband

more information about Gray and binary coding, see “Binary-Valued and
Integer-Valued Signals” on page 2-68.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-122
 CPM Demodulator Baseband

Dialog Box

M-ary number
The size of the alphabet.
Output type
Determines whether the output consists of integers or groups of bits.

4-123
CPM Demodulator Baseband

Symbol set ordering

Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Modulation index
The number of half-revolutions of phase shift in the modulated signal after
modulating the latest symbol of 1.
Frequency pulse shape
The type of pulse shaping that the corresponding modulator uses to smooth
the phase transitions of the modulated signal.
Rolloff
The rolloff factor of the raised cosine filter. This field appears only when
Frequency pulse shape is set to Spectral Raised Cosine.

BT product
The product of bandwidth and time. This field appears only when
Frequency pulse shape is set to Gaussian.

Pulse length (symbol intervals)

The length of the frequency pulse shape.
Symbol prehistory
The data symbols used by the modulator before the start of the simulation.
Phase offset (rad)
The initial phase of the modulated waveform.
Samples per symbol
The number of input samples that represent each modulated symbol.
Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.
Pair Block CPM Modulator Baseband
See Also CPFSK Demodulator Baseband, GMSK Demodulator Baseband, MSK
Demodulator Baseband, Viterbi Decoder
References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-124
 CPM Demodulator Passband

Purpose 4CPM Demodulator Passband

Demodulate CPM-modulated data

Library CPM, in Digital Passband sublibrary of Modulation

Description The CPM Demodulator Passband block demodulates a signal that was
modulated using continuous phase modulation. The input is a passband
representation of the modulated signal. The M-ary number parameter, M, is
the size of the input alphabet. M must have the form 2K for some positive
integer K.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, CPM Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• M-ary number
• Output type
• Symbol set ordering
• Modulation index
• Frequency pulse shape
• Rolloff
• BT product
• Pulse length
• Symbol prehistory
• Traceback length
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.

4-125
CPM Demodulator Passband

The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1
• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

4-126
 CPM Demodulator Passband

Dialog Box

M-ary number
The size of the alphabet.
Output type
Determines whether the output consists of integers or groups of bits.

4-127
CPM Demodulator Passband

Symbol set ordering

Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Modulation index
The number of half-revolutions of phase shift in the modulated signal after
modulating the latest symbol of 1.
Frequency pulse shape
The type of pulse shaping that the corresponding modulator uses to smooth
the phase transitions of the modulated signal.
Rolloff
The rolloff factor of the raised cosine filter. This field appears only when
Frequency pulse shape is set to Spectral Raised Cosine.

BT product
The product of bandwidth and time. This field appears only when
Frequency pulse shape is set to Gaussian.

Pulse length (symbol intervals)

The length of the frequency pulse shape.
Symbol prehistory
The data symbols used by the modulator before the start of the simulation.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.

4-128
 CPM Demodulator Passband

Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.

Pair Block CPM Modulator Passband

See Also CPM Demodulator Baseband, Viterbi Decoder

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-129
CPM Modulator Baseband

Purpose 4CPM Modulator Baseband

Modulate using continuous phase modulation

Library CPM, in Digital Baseband sublibrary of Modulation

Description The CPM Modulator Baseband block modulates using continuous phase
modulation. The output is a baseband representation of the modulated signal.
The M-ary number parameter, M, is the size of the input alphabet. M must
have the form 2K for some positive integer K.
Continuous phase modulation uses pulse shaping to smooth the phase
transitions of the modulated signal. Using the Frequency pulse shape
parameter, you can choose these types of pulse shapes:
• Rectangular
• Raised Cosine
• Spectral Raised Cosine
This option requires an additional parameter, Rolloff. The Rolloff
parameter, which affects the spectrum of the pulse, is a scalar between zero
and one.
• Gaussian
This option requires an additional parameter, BT product. The BT product
parameter, which represents bandwidth multipled by time, is a nonnegative
scalar. It is used to reduce the bandwidth at the expense of increased
intersymbol interference.
• Tamed FM (tamed frequency modulation)

For the exact definitions of these pulse shapes, see the work by Anderson,
Aulin, and Sundberg listed in “References” on page 4-133. Each pulse shape
has a correponding pulse duration. The Pulse length parameter measures this
quantity in symbol intervals.
The Modulation index parameter times π radians is the phase shift due to the
latest symbol when that symbol is the integer 1. The Phase offset parameter
is the initial phase of the output waveform, measured in radians.
The Symbol prehistory parameter is a scalar or vector that specifies the data
symbols used before the start of the simulation, in reverse chronological order.
If it is a vector, then its length must be one less than the Pulse length
parameter.

4-130
 CPM Modulator Baseband

Inputs and Symbol Sets

If the Input type parameter is set to Integer, then the block accepts odd
integers between -(M-1) and M-1.
If the Input type parameter is set to Bit, then the block accepts groupings of
K bits. Each grouping is called a binary word. The input vector length must be
an integer multiple of K.
In binary input mode, the block maps each binary word to an integer between
0 and M-1, using a mapping that depends on whether the Symbol set ordering
parameter is set to Binary or Gray. The block then maps the integer k to the
intermediate value 2k-(M-1) and proceeds as in the integer input mode. For
more information, see “Binary-Valued and Integer-Valued Signals” on page
2-68.
The input can be either a scalar or a frame-based column vector. If Input type
is Bit, then the input can also be a vector of length K.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-131
CPM Modulator Baseband

Dialog Box

M-ary number
The size of the alphabet.
Input type
Indicates whether the input consists of integers or groups of bits.

4-132
 CPM Modulator Baseband

Symbol set ordering

Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Modulation index
The number of half-revolutions of phase shift due to the latest symbol when
that symbol is the integer 1.
Frequency pulse shape
The type of pulse shaping that the block uses to smooth the phase
transitions of the modulated signal.
Rolloff
The rolloff factor of the raised cosine filter. This field appears only when
Frequency pulse shape is set to Spectral Raised Cosine.

BT product
The product of bandwidth and time. This field appears only when
Frequency pulse shape is set to Gaussian.

Pulse length (symbol intervals)

The length of the frequency pulse shape.
Symbol prehistory
The data symbols used before the start of the simulation, in reverse
chronological order.
Phase offset (rad)
The initial phase of the output waveform.
Samples per symbol
The number of output samples that the block produces for each integer or
binary word in the input.

Pair Block CPM Demodulator Baseband

See Also CPFSK Modulator Baseband, GMSK Modulator Baseband, MSK Modulator
Baseband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-133
CPM Modulator Passband

Purpose 4CPM Modulator Passband

Modulate using continuous phase modulation

Library CPM, in Digital Passband sublibrary of Modulation

Description The CPM Modulator Passband block modulates using continuous phase
modulation. The output is a passband representation of the modulated signal.
The M-ary number parameter, M, is the size of the input alphabet. M must
have the form 2K for some positive integer K.
This block uses the baseband equivalent block, CPM Modulator Baseband, for
internal computations and converts the resulting baseband signal to a
passband representation. The following parameters in this block are the same
as those of the baseband equivalent block:
• M-ary number
• Input type
• Symbol set ordering
• Modulation index
• Frequency pulse shape
• Rolloff
• BT product
• Pulse length
• Symbol prehistory
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each

4-134
 CPM Modulator Passband

integer or binary word in the input, before the block converts them to a
passband output.
The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1
• Symbol period = K*Output sample time*Baseband samples per symbol
for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

4-135
CPM Modulator Passband

Dialog Box

M-ary number
The size of the alphabet.
Input type
Indicates whether the input consists of integers or groups of bits.
Symbol set ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.

4-136
 CPM Modulator Passband

Modulation index
The number of half-revolutions of phase shift due to the latest symbol when
that symbol is the integer 1.
Frequency pulse shape
The type of pulse shaping that the block uses to smooth the phase
transitions of the modulated signal.
Rolloff
The rolloff factor of the raised cosine filter. This field appears only when
Frequency pulse shape is set to Spectral Raised Cosine.

BT product
The product of bandwidth and time. This field appears only when
Frequency pulse shape is set to Gaussian.

Pulse length (symbol intervals)

The length of the frequency pulse shape.
Symbol prehistory
The data symbols used before the start of the simulation, in reverse
chronological order.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block CPM Demodulator Passband

4-137
CPM Modulator Passband

See Also CPM Modulator Baseband

References [2] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-138
 Data Mapper

Purpose 4Data Mapper

Map integer symbols from one coding scheme to another

Library Utility Functions

Description The Data Mapper block accepts integer inputs and produces integer outputs.
You can select one of four mapping modes: Binary to Gray, Gray to Binary,
User Defined, or Straight Through.

The input can be either a scalar, a sample-based vector, or a frame-based

column vector.
Gray coding is an ordering of binary numbers such that all adjacent numbers
differ by only one bit. However, the inputs and outputs of this block are
integers, not binary vectors. As a result, the first two mapping modes perform
code conversions as follows:

• In the Binary to Gray mode, the output from this block is the integer
equivalent of the Gray code bit representation for the input integer.
• In the Gray to Binary mode, the output from this block is the integer
position of the binary equivalent of the input integer in a Gray code ordering.

As an example, the table below shows both the Binary to Gray and Gray to
Binary mappings for integers in the range 0 to 7. In the Binary to Gray Mode
Output column, notice that binary representations in successive rows differ by
exactly one bit. In the Gray to Binary Mode columns, notice that sorting the
rows by Output value creates a Gray code ordering of Input binary
representations.

Binary to Gray Mode Gray to Binary Mode

Input Output Input Output

0 0 (000) 0 (000) 0

1 1 (001) 1 (001) 1

2 3 (011) 2 (010) 3

3 2 (010) 3 (011) 2

4 6 (110) 4 (100) 7

4-139
Data Mapper

Binary to Gray Mode Gray to Binary Mode

Input Output Input Output

5 7 (111) 5 (101) 6

6 5 (101) 6 (110) 4
7 4 (100) 7 (111) 5

When you select the User Defined mode, you can use any arbitrary mapping
by providing a vector to specify the output ordering. For example, the vector
[1,5,0,4,2,3] defines the following mapping:

• 0→1
• 1→5
• 2→0
• 3→4
• 4→2
• 5→3

When you select the Straight Through mode, the output equals the input.

Dialog Box

Mapping mode
The type of data mapping that the block performs.

4-140
 Data Mapper

Symbol set size

Symbol set size of M restricts this block’s inputs and outputs to integers in
the range 0 to M-1.
Mapping vector
A vector of length M that contains the integers from 0 to M-1. The order of
the elements of this vector specifies the mapping of inputs to outputs. This
field is active only when Mapping mode is set to User Defined.

4-141
DBPSK Demodulator Baseband

Purpose 4DBPSK Demodulator Baseband

Demodulate DBPSK-modulated data

Library PM, in Digital Baseband sublibrary of Modulation

Description The DBPSK Demodulator Baseband block demodulates a signal that was
modulated using the differential binary phase shift keying method. The input
is a baseband representation of the modulated signal.
The input must be a discrete-time complex signal. The block compares the
current symbol to the previous symbol. It maps phase differences of θ and π+θ,
respectively, to outputs of 0 and 1, respectively, where θ is the Phase offset
parameter. The first element of the block’s output is the initial condition of zero
because there is no previous symbol with which to compare the first symbol.
The input can be either a scalar or a frame-based column vector.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

4-142
 DBPSK Demodulator Baseband

Phase offset (rad)

This phase difference between the current and previous modulated
symbols results in an output of zero.
Samples per symbol
The number of input samples that represent each modulated symbol.

Pair Block DBPSK Modulator Baseband

See Also M-DPSK Demodulator Baseband, DQPSK Demodulator Baseband, BPSK

Demodulator Baseband

4-143
DBPSK Modulator Baseband

Purpose 4DBPSK Modulator Baseband

Modulate using the differential binary phase shift keying method

Library PM, in Digital Baseband sublibrary of Modulation

Description The DBPSK Modulator Baseband block modulates using the differential
binary phase shift keying method. The output is a baseband representation of
the modulated signal.
The input must be a discrete-time binary-valued signal. The input can be
either a scalar or a frame-based column vector. These rules govern this
modulation method when the Phase offset parameter is θ:

• If the first input bit is 0 or 1, respectively, then the first modulated symbol
is exp(jθ) or -exp(jθ), respectively.
• If a successive input bit is 0 or 1, respectively, then the modulated symbol is
the previous modulated symbol multiplied by exp(jθ) or -exp(jθ), respectively.

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

4-144
 DBPSK Modulator Baseband

Phase offset (rad)

The phase difference between the previous and current modulated symbols
when the input is zero.
Samples per symbol
The number of output samples that the block produces for each input bit.

Pair Block DBPSK Demodulator Baseband

See Also M-DPSK Modulator Passband, DQPSK Modulator Baseband, BPSK

Modulator Baseband

4-145
Deinterlacer

Purpose 4Deinterlacer
Distribute elements of input vector alternately between two output vectors

Library Sequence Operations, in Basic Comm Functions

Description The Deinterlacer block accepts an input vector that has an even number of
elements. The block alternately places the elements in each of two output
vectors. As a result, each output vector size is half the input vector size. The
output vectors have the same complexity and sample time of the input.
The input can be either a sample-based vector of length two, or a frame-based
column vector whose length is any even integer.
This block can be useful for separating in-phase and quadrature information
from a single vector into separate vectors.

Dialog Box

Examples If the input vector is frame-based with value [1; 5; 2; 6; 3; 7; 4; 8], then the two
output vectors are [1; 2; 3; 4] and [5; 6; 7; 8]. Notice that this is the inverse of
the example on the reference page for the Interlacer block.
If the input vector is frame-based with value [1; 2; 3; 4; 5; 6], then the two
output vectors are [1; 3; 5] and [2; 4; 6].

Pair Block Interlacer

See Also Demux (Simulink)

4-146
 Derepeat

Purpose 4Derepeat
Reduce sampling rate by averaging consecutive samples

Library Sequence Operations, in Basic Comm Functions

Description The Derepeat block resamples the discrete input at a rate 1/N times the input
sample rate by averaging N consecutive samples. This is one possible inverse
of the Repeat block (DSP Blockset). The positive integer N is the Derepeat
factor parameter in the Derepeat mask.

The Initial condition parameter prescribes elements of the output when it is

still too early for the input data to show up in the output. If the dimensions of
the Initial condition parameter match the output dimensions, then the
parameter represents the initial output value. If Initial condition is a scalar,
then it represents the initial value of each element in the output.
The input can have any shape or frame status.

Sample-Based Operation
If the input is sample-based, then the block assumes that the input is a vector
or matrix whose elements represent samples from independent channels. The
block averages samples from each channel independently over time. The
output period is N times the input period, and the input and output sizes are
identical.

Frame-Based Operation
If the input is frame-based, then the block derepeats each frame, treating
distinct channels independently. Each element of the output is the average of
N consecutive elements along a column of the input matrix. The Derepeat
factor must be less than the frame size.

The Framing parameter determines how the block adjusts the rate at the
output to accommodate the reduced number of samples. The two options are:

• Maintain input frame size

The block reduces the sampling rate by using a proportionally longer frame
period at the output port than at the input port. For derepetition by a factor

4-147
Derepeat

of N, the output frame period is N times the input frame period, but the input
and output frame sizes are equal.

For example, if a single-channel input with a frame period of 1 second is

derepeated by a factor of 4, then the output has a frame period of 4 seconds.
The input and output frame sizes are equal.

• Maintain input frame rate

The block reduces the sampling rate by using a proportionally smaller frame
size than the input. For derepetition by a factor of N, the output frame size
is 1/N times the input frame size, but the input and output frame rates are
equal. The Initial condition parameter does not apply to this option because
the input data immediately shows up in the output.
For example, if a single-channel input with 64 elements is derepeated by a
factor of 4, then the output contains 16 elements. The input and output frame
periods are equal.

Dialog Box

Derepeat factor, N
The number of consecutive input samples to average in order to produce
each output sample.
Initial condition
The value with which to initialize the block.

4-148
 Derepeat

Framing
For frame-based operation, the method by which to reduce the amount of
data. One method decreases the frame rate while maintaining frame size,
while the other decreases the frame size while maintaining frame rate.

See Also Repeat (DSP Blockset), Downsample (DSP Blockset)

4-149
Descrambler

Purpose 4Descrambler
Descramble the input signal

Library Sequence Operations, in Basic Comm Functions

Description The Descrambler block descrambles the scalar input signal. The Descrambler
block is the inverse of the Scrambler block. If you use the Scrambler block in
the transmitter, then you should use the Descrambler block in the receiver.
Below is a schematic of the descrambler. All adders perform addition modulo
N, where N is the Calculation base parameter. The input values must be
integers between 0 and N-1.

Input data
1 2 M-1 M

+ + + +

Descrambled data

At each time step, the input causes the contents of the registers to shift
sequentially. Each switch in the descrambler is on or off as defined by the
Scramble polynomial parameter. To make the Descrambler block reverse the
operation of the Scrambler block, use the same Scramble polynomial
parameters in both blocks. The Initial states can be different in the two blocks,
considering the transmitting and receiving filter delay. See the reference page
for the Scrambler block for more information about these parameters.

4-150
 Descrambler

Dialog Box

Calculation base
The calculation base N. The input and output of this block are integers in
the range [0, N-1].
Scramble polynomial
A polynomial that defines the connections in the scrambler.
Initial states
The states of the scrambler’s registers when the simulation starts.

Pair Block Scrambler

4-151
Differential Decoder

Purpose 4Differential Decoder

Decode a binary signal using differential coding technique.

Library Source Coding

Description The Differential Decoder block decodes the binary input signal. The output of
the Differential Decoder block is the decoded binary signal.
The block’s input m and output d are related by
d(t0) = m(t0) + 1 mod 2

d(tk) = m(tk-1) + m(tk) + 1 mod 2

where tk is the kth time step.

The input can be either a scalar, a sample-based vector, or a frame-based row
vector. This block processes each vector element independently.

Dialog Box

Symbol interval (s)

The sample time of the input symbol.

Pair Block Differential Encoder

4-152
 Differential Encoder

Purpose 4Differential Encoder

Encode a binary signal using differential coding technique.

Library Source Coding

Description The Differential Encoder block encodes and outputs the binary input signal.
The input m and output d are related by
d(t0) = m(t0) +1 mod 2

d(tk) = d(tk-1) + m(tk) +1 mod 2

where tk is the kth time step.

The input can be either a scalar, a sample-based vector, or a frame-based row
vector. This block processes each vector element independently.

Dialog Box

Symbol interval (s)

The sample time of the input symbol.

Pair Block Differential Decoder

4-153
Discrete Modulo Integrator

Purpose 4Discrete Modulo Integrator

Integrate in discrete time and reduce by a modulus

Library Integrators, in Basic Comm Functions

Description The Discrete Modulo Integrator block integrates its input signal in discrete
time and then reduces modulo the Absolute value bound parameter. If the
Absolute value bound parameter is K, then the block output is strictly
between -K and K.
The input can be either a scalar, a sample-based vector, or a frame-based row
vector. The block processes each vector element independently.
This block’s functionality is useful for monotonically increasing or decreasing
functions, but works with any integrable function. This block uses the Forward
Euler integration method.

Dialog Box

Absolute value bound

The modulus by which the integration result is reduced. This parameter
must be nonzero.
Initial condition
The initial condition for integration.

4-154
 Discrete Modulo Integrator

Sample time
The integration sample time.

See Also Modulo Integrator, Windowed Integrator, Integrate and Dump, Discrete-Time
Integrator (Simulink); rem (MATLAB)

4-155
Discrete-Time Eye and Scatter Diagrams

Purpose 4Discrete-Time Eye and Scatter Diagrams

Produce an eye diagram and/or scatter diagram

Library Comm Sinks

Description The Discrete-Time Eye and Scatter Diagrams block plots eye diagrams and
scatter diagrams from a discrete-time complex input signal. The input can be
either a scalar or a frame-based column vector.
The Diagram type parameter determines which plots the block produces. The
block draws the diagrams in a single window.
The Trace period parameter is the number of seconds represented by the
horizontal axis in the eye diagram. The Trace offset parameter is the time
value at the left edge of the horizontal axis of the eye diagram. This parameter
must be between zero and the Trace period parameter.
Whenever the simulation time modulo the Trace period value equals the
Decision point parameter, the block plots a new point in the scatter diagram
and a vertical line in the eye diagram. The Decision point parameter must be
greater than or equal to the Trace offset parameter, and less than or equal to
the sum of Trace period and Trace offset. Furthermore, if the block plots a
scatter diagram, then the Decision point parameter must be an integer
multiple of the Sample time for plot update parameter.
The two-element Lower and upper bound of incoming signal vector
parameter determines the vertical axis in the eye diagram and both axes in the
scatter plot.
To specify the plotting color, as well as the line type or marker type, use the
Line type parameters that appear after you select a value for the Diagram
type parameter. In the Line type for eye diagram parameter, use a slash (/)
to separate the specifications for the in-phase and quadrature components of
the input signal. Choices for the color, marker, and line types are in the table
on the reference page for the Continuous-Time Eye and Scatter Diagrams
block.
The Sample time for plot update parameter determines which of the input
data the block uses for creating plots. If the parameter matches the sample
time of the input signal, then the block uses all available data. If the parameter
is an integer multiple of the sample time of the input signal, then the block uses
a decimated version of the input data.

4-156
 Discrete-Time Eye and Scatter Diagrams

Dialog Box

Trace period
The duration of the horizontal axis of the eye diagram, in seconds.
Trace offset
The time at the leftmost edge of the horizontal axis of the eye diagram.
Decision point
The time at which the first point in the scatter plot and the vertical line in
the eye diagram are plotted.
Lower and upper bounds of diagram
A two-element vector containing the minimum and maximum signal
values in the diagrams.
Number of saved traces
The number of curves in the eye diagram, or points in the scatter plot, that
are visible after you resize or restore the figure window.

4-157
Discrete-Time Eye and Scatter Diagrams

Diagram type
The diagram(s) that the block produces.
Line type for eye diagram
A string that specifies the color and the line type for the eye diagram. This
field appears only when the Diagram type parameter is set to an option
that includes an eye diagram.
Line type for scatter diagram
A string that specifies the color and the marker type for the scatter
diagram. This field appears only when the Diagram type parameter is set
to an option that includes an scatter diagram.
Sample time for plot update
The time interval between successive input values that the block includes
in the plot(s).

Limitations Since this block uses an M-file, you cannot generate C code for it using the
Real-Time Workshop.

See Also Continuous-Time Eye and Scatter Diagrams

4-158
 Discrete-Time VCO

Purpose 4Discrete-Time VCO

Implement a voltage-controlled oscillator in discrete time

Library Comm Sources

Description The Discrete-Time VCO (voltage-controlled oscillator) block generates a signal

whose frequency shift from the Oscillation frequency parameter is
proportional to the input signal. The input signal is interpreted as a voltage. If
the input signal is u(t), then the output signal is
t
y ( t ) = A c cos ( 2πf c t + 2πk c ò0 u ( τ )dτ + ϕ )
where Ac is the Output amplitude, fc is the Oscillation frequency, kc is the
Input sensitivity, and ϕ is the Initial phase

This block uses a discrete-time integrator to interpret the equation above.

The input and output signals are both scalars.

Dialog Box

Output amplitude
The amplitude of the output.
Oscillation frequency (Hz)
The frequency of the oscillator output when the input signal is zero.

4-159
Discrete-Time VCO

Input sensitivity
This value scales the input voltage and, consequently, the shift from the
Oscillation frequency value. The units of Input sensitivity are Hertz per
volt.
Initial phase (rad)
The initial phase of the oscillator in radians.
Sample time
The calculation sample time.

See Also Voltage-Controlled Oscillator

4-160
 DPCM Decoder

Purpose 4DPCM Decoder

Decode differential pulse code modulation

Library Source Coding

Description The DPCM Decoder block recovers a message from a quantized signal using
differential pulse code demodulation. The input represents a DPCM-encoded
quantization index. The input must be a scalar signal. Its two outputs are the
recovered signal and the quantized predictive error.
The description of the Sampled Quantizer Encode block gives more detailed
information about quantization indices and quantization-encoded signals. The
description of the DPCM Encoder block and the section “Implementing
Differential Pulse Code Modulation” on page 2-21 give more information about
implementing DPCM.

Dialog Box

Predictor numerator
The vector of coefficients of the numerator of the predictor transfer
function, in order of ascending powers of z-1. The first entry must be zero.
Predictor denominator
The vector of coefficients of the denominator of the predictor transfer
function, in order of ascending powers of z-1. Usually this parameter is 1.

4-161
DPCM Decoder

Quantization codebook
The vector of output values that the quantizer assigns to each partition.
Sample time
The block’s sample time.
Match these parameters to the ones in the corresponding DPCM Encoder block.

Pair Block DPCM Encoder

References [1] Kondoz, A. M. Digital Speech. Chichester, England: John Wiley & Sons,
1994.

4-162
 DPCM Encoder

Purpose 4DPCM Encoder

Encode using differential pulse code modulation

Library Source Coding

Description The DPCM Encoder block quantizes the input signal using differential pulse
code modulation. The input must be a scalar signal. Its two outputs are the
quantization index and the quantization-encoded signal.
This block uses the Sampled Quantizer Encode block. The description of that
block gives more detailed information about quantization indices and
quantization-encoded signals.
Quantization partition is a vector whose entries give the endpoints of the
partition intervals. Quantization codebook, a vector whose length exceeds
the length of Quantization partition by one, prescribes a value for each
partition in the quantization. The first element of Quantization codebook is
the value for the interval between negative infinity and the first element of
Quantization partition.

You can think of the predictor as a transfer function for an IIR filter, hence a
rational function of z-1. Specify the predictor’s numerator and denominator by
listing their coefficients in the vectors Predictor numerator and Predictor
denominator, respectively. List the coefficients in order of increasing powers
of z-1.

Note The first entry of Predictor numerator must be zero. A nonzero entry
there would fail to make sense conceptually, and would create an algebraic
loop in the implementation.

You can use the function dpcmopt in the Communications Toolbox to train the
Predictor numerator, Predictor denominator, Quantization partition, and
Quantization codebook parameters. The output of dpcmopt omits the
denominator of the predictor, assuming that it will be 1. In most DPCM
applications, the denominator of the predictor transfer function is 1.
If Predictor numerator has the form [0, x] and Predictor denominator is 1,
then the modulation is called delta modulation.

4-163
DPCM Encoder

Dialog Box

Predictor numerator
The vector of coefficients of the numerator of the predictor transfer
function, in order of ascending powers of z-1. The first entry must be zero.
Predictor denominator
The vector of coefficients of the denominator of the predictor transfer
function, in order of ascending powers of z-1. Usually this parameter is 1.
Quantization partition
The vector of endpoints of the partition intervals. The elements must be in
strictly ascending order.
Quantization codebook
The vector of output values that the quantizer assigns to each partition.
Sample time
The block’s sample time.

Pair Block DPCM Decoder

References [1] Kondoz, A. M. Digital Speech. Chichester, England: John Wiley & Sons,
1994.

4-164
 DQPSK Demodulator Baseband

Purpose 4DQPSK Demodulator Baseband

Demodulate DQPSK-modulated data

Library PM, in Digital Baseband sublibrary of Modulation

Description The DQPSK Demodulator Baseband block demodulates a signal that was
modulated using the differential quaternary phase shift keying method. The
input is a baseband representation of the modulated signal.
The input must be a discrete-time complex signal. The output depends on the
phase difference between the current symbol and the previous symbol. The
first integer (or binary pair, if the Output type parameter is set to Bit) in the
block’s output is the initial condition of zero because there is no previous
symbol.
The input can be either a scalar or a frame-based column vector.

Outputs and Constellation Types

If the Output type parameter is set to Integer, then the block maps a phase
difference of
θ + πm/2
to m, where θ is the Phase offset parameter and m is 0, 1, 2, or 3.
If the Output type parameter is set to Bit, then the output contains pairs of
binary values. The reference page for the DQPSK Modulator Baseband block
shows which phase differences map to each binary pair, for the cases when the
Constellation ordering parameter is either Binary or Gray.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-165
DQPSK Demodulator Baseband

Dialog Box

Output type
Determines whether the output consists of integers or pairs of bits.
Constellation ordering
Determines how the block maps each integer to a pair of output bits. This
field is active only when Output type is set to Bit.
Phase offset (rad)
This phase difference between the current and previous modulated
symbols results in an output of zero.
Samples per symbol
The number of input samples that represent each modulated symbol.

Pair Block DQPSK Modulator Baseband

See Also M-DPSK Demodulator Baseband, DBPSK Demodulator Baseband, QPSK

Demodulator Baseband

4-166
 DQPSK Modulator Baseband

Purpose 4DQPSK Modulator Baseband

Modulate using the differential quaternary phase shift keying method

Library PM, in Digital Baseband sublibrary of Modulation

Description The DQPSK Modulator Baseband block modulates using the differential
quaternary phase shift keying method. The output is a baseband
representation of the modulated signal.
The input must be a discrete-time signal.

Inputs and Constellation Types

If the Input type parameter is set to Integer, then valid input values are 0, 1,
2, and 3. In this case, the input can be either a scalar or a frame-based column
vector. If the first input is m, then the modulated symbol is
exp(jθ + jπm/2)
where θ is the Phase offset parameter. If a successive input is m, then the
modulated symbol is the previous modulated symbol multiplied by
exp(jθ + jπm/2).
If the Input type parameter is set to Bit, then the input contains pairs of
binary values. The input can be either a vector of length two or a frame-based
column vector whose length is an even integer. The figure below shows the
complex numbers by which the block multiples the previous symbol to compute
the current symbol, depending on whether the Constellation ordering
parameter is set to Binary or Gray. The figure assumes that the Phase offset
parameter is set to pi/4; in other cases, the two schematics would be rotated
accordingly.

4-167
DQPSK Modulator Baseband

Binary Gray

01 00 01 00

10 11 11 10

The figure below shows the signal constellation for the DQPSK modulation
method when the Phase offset parameter is π/4. The arrows indicate the four
possible transitions from each symbol to the next symbol. The Binary and
Gray options determine which transition is associated with each pair of input
values.

Constellation point
Transition to next point

More generally, if the Phase offset parameter has the form π/k for some
integer k, then the signal constellation has 2k points.

4-168
 DQPSK Modulator Baseband

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

Input type
Indicates whether the input consists of integers or pairs of bits.
Constellation ordering
Determines how the block maps each pair of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Phase offset (rad)
The phase difference between the previous and current modulated symbols
when the input is zero.

4-169
DQPSK Modulator Baseband

Samples per symbol

The number of output samples that the block produces for each integer or
pair of bits in the input.

Pair Block DQPSK Demodulator Baseband

See Also M-DPSK Modulator Passband, DBPSK Modulator Baseband, QPSK

Modulator Baseband

4-170
 DSB AM Demodulator Baseband

Purpose 4DSB AM Demodulator Baseband

Demodulate DSB-AM-modulated data

Library Analog Baseband Modulation, in Modulation

Description The DSB AM Demodulator Baseband block demodulates a signal that was
modulated using double-sideband amplitude modulation. The input is a
baseband representation of the modulated signal. The input is complex, while
the output is real. The input must be a sample-based scalar signal.
In the course of demodulating, this block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Box

Output signal offset

The same as the Input signal offset parameter in the corresponding DSB
AM Modulator Baseband block.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.

4-171
DSB AM Demodulator Baseband

Lowpass filter denominator

The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
Initial phase (rad)
The initial phase in the corresponding DSB AM Modulator Baseband block.
Sample time
The sample time of the output signal.

Pair Block DSB AM Modulator Baseband

4-172
 DSB AM Demodulator Passband

Purpose 4DSB AM Demodulator Passband

Demodulate DSB-AM-modulated data

Library Analog Passband Modulation, in Modulation

Description The DSB AM Demodulator Passband block demodulates a signal that was
modulated using double-sideband amplitude modulation. The block uses the
envelope detection method. The input is a passband representation of the
modulated signal. Both the input and output signals are real sample-based
scalar signals.
In the course of demodulating, this block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Block

Offset factor
The same as the Input signal offset parameter in the corresponding AM
with Carrier block.
Carrier frequency (Hz)
The frequency of the carrier in the corresponding AM with Carrier block.

4-173
DSB AM Demodulator Passband

Initial phase (rad)

The initial phase of the carrier in radians.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
Sample time
The sample time of the output signal.

Pair Block DSB AM Modulator Passband

See Also DSB AM Demodulator Baseband

4-174
 DSB AM Modulator Baseband

Purpose 4DSB AM Modulator Baseband

Modulate using double-sideband amplitude modulation

Library Analog Baseband Modulation, in Modulation

Description The DSB AM Modulator Baseband block modulates using double-sideband

amplitude modulation. The output is a baseband representation of the
modulated signal. The input signal is real, while the output signal is complex.
The input must be a sample-based scalar signal.
If the input is u(t) as a function of time t, then the output is
jθ
( u ( t ) + k )e
where:

• θ is the Initial phase parameter.

• k is the Input signal offset parameter.

Dialog Box

Input signal offset

The offset factor k. This value should be greater than or equal to the
absolute value of the minimum of the input signal.
Initial phase (rad)
The phase of the modulated signal.

Pair Block DSB AM Demodulator Baseband

See Also DSBSC AM Modulator Baseband, SSB AM Modulator Baseband

4-175
DSB AM Modulator Passband

Purpose 4DSB AM Modulator Passband

Modulate using double-sideband amplitude modulation

Library Analog Passband Modulation, in Modulation

Description The DSB AM Modulator Passband block modulates using double-sideband

amplitude modulation. The output is a passband representation of the
modulated signal. Both the input and output signals are real sample-based
scalar signals.
If the input is u(t) as a function of time t, then the output is
(u(t)+k) cos(2πfct+θ)

where:

• k is the Input signal offset parameter.

• fc is the Carrier frequency parameter.
• θ is the Initial phase parameter.

It is common to set the value of k to the maximum absolute value of the

negative part of the input signal u(t).
Typically, an appropriate Carrier frequency value is much higher than the
highest frequency of the input signal. To avoid having to use a high carrier
frequency and consequently a high sampling rate, you can use baseband
simulation instead of passband simulation.

Dialog Box

4-176
 DSB AM Modulator Passband

Input signal offset

The offset factor k. This value should be greater than or equal to the
absolute value of the minimum of the input signal.
Carrier frequency (Hz)
The frequency of the carrier.
Initial phase (rad)
The initial phase of the carrier.

Pair Block DSB AM Demodulator Passband

See Also DSB AM Modulator Baseband, DSBSC AM Modulator Passband, SSB AM

Modulator Passband

4-177
DSBSC AM Demodulator Baseband

Purpose 4DSBSC AM Demodulator Baseband

Demodulate DSBSC-AM-modulated data

Library Analog Baseband Modulation, in Modulation

Description The DSBSC AM Demodulator Baseband block demodulates a signal that was
modulated using double-sideband suppressed-carrier amplitude modulation.
The input is a baseband representation of the modulated signal. The input is
complex, while the output is real. The input must be a sample-based scalar
signal.
In the course of demodulating, this block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Box

Lowpass filter numerator

The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.

4-178
 DSBSC AM Demodulator Baseband

Initial phase (rad)

The initial phase in the corresponding DSBSC AM Modulator Baseband
block.
Sample time
The sample time of the output signal.

Pair Block DSBSC AM Modulator Baseband

See Also DSB AM Demodulator Baseband, SSB AM Demodulator Baseband

4-179
DSBSC AM Demodulator Passband

Purpose 4DSBSC AM Demodulator Passband

Demodulate DSBSC-AM-modulated data

Library Analog Passband Modulation, in Modulation

Description The DSBSC AM Demodulator Passband block demodulates a signal that was
modulated using double-sideband suppressed-carrier amplitude modulation.
The input is a passband representation of the modulated signal. Both the input
and output signals are real sample-based scalar signals.
In the course of demodulating, this block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Box

Carrier frequency (Hz)

The carrier frequency in the corresponding DSBSC AM Modulator
Passband block.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.

4-180
 DSBSC AM Demodulator Passband

Lowpass filter denominator

The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
Initial phase (rad)
The initial phase of the carrier in radians.
Sample time
The sample time of the output signal.

Pair Block DSBSC AM Modulator Passband

See Also DSBSC AM Demodulator Baseband, DSB AM Demodulator Passband, SSB

AM Demodulator Passband

4-181
DSBSC AM Modulator Baseband

Purpose 4DSBSC AM Modulator Baseband

Modulate using double-sideband suppressed-carrier amplitude modulation

Library Analog Baseband Modulation, in Modulation

Description The DSBSC AM Modulator Baseband block modulates using double-sideband

suppressed-carrier amplitude modulation. The output is a baseband
representation of the modulated signal. The block accepts a real input signal
and produces a complex output signal. The input may be continuous-time or
discrete-time; the output sample time matches the input sample time. The
input must be a sample-based scalar signal.
If the input is u(t) as a function of time t, then the output is
jθ
u ( t )e
where θ is the Initial phase parameter.

Dialog Box

Initial phase (rad)

The phase of the modulated signal in radians.

Pair Block DSBSC AM Demodulator Baseband

See Also DSB AM Modulator Baseband, SSB AM Modulator Baseband

4-182
 DSBSC AM Modulator Passband

Purpose 4DSBSC AM Modulator Passband

Modulate using double-sideband suppressed-carrier amplitude modulation

Library Analog Passband Modulation, in Modulation

Description The DSBSC AM Modulator Passband block modulates using double-sideband

suppressed-carrier amplitude modulation. The output is a passband
representation of the modulated signal. Both the input and output signals are
real sample-based scalar signals.
If the input is u(t) as a function of time t, then the output is
u(t) cos(2πfct+θ)

where fc is the Carrier frequency parameter and θ is the Initial phase

parameter.
Typically, an appropriate Carrier frequency value is much higher than the
highest frequency of the input signal. To avoid having to use a high carrier
frequency and consequently a high sampling rate, you can use baseband
simulation (DSBSC AM Modulator Baseband block) instead of passband
simulation.

Dialog Box

Carrier frequency (Hz)

The frequency of the carrier.
Initial phase (rad)
The initial phase of the carrier in radians.

Pair Block DSBSC AM Demodulator Passband

4-183
DSBSC AM Modulator Passband

See Also DSBSC AM Modulator Baseband, DSB AM Modulator Passband, SSB AM

Modulator Passband

4-184
 Enabled Quantizer Encode

Purpose 4Enabled Quantizer Encode

Quantize a signal, using trigger to control processing

Library Source Coding

Description The Enabled Quantizer Encode block performs quantization when a trigger
signal occurs. This block is similar to the Sampled Quantizer Encode block,
except that a trigger signal at the second input port controls the quantization
processing. This block renews its output when the scalar trigger signal is
nonzero. For more about quantization, see the reference page for the Sampled
Quantizer Encode block.
This block has two input ports and three output ports. The first input signal is
the data to be quantized, while the second is the trigger signal that controls the
timing of quantization. The three output signals represent the quantization
index, quantization value, and mean square distortion, respectively.
The first input can be either a scalar, a sample-based vector, or a frame-based
row vector. This block processes each vector element independently. Each
output signal is a vector of the same length as the first input signal. The trigger
input must be a scalar.

Dialog Box

4-185
Enabled Quantizer Encode

Quantization partition
The vector of endpoints of the partition intervals. The elements must be in
strictly ascending order.
Quantization codebook
The vector of output values assigned to each partition.
Input signal vector length
The length of the input signal.

Pair Block Quantizer Decode

See Also Sampled Quantizer Encode

4-186
 Error Rate Calculation

Purpose 4Error Rate Calculation

Compute the bit error rate or symbol error rate of input data

Library Comm Sinks

Description The Error Rate Calculation block compares input data from a transmitter with
input data from a receiver. It calculates the error rate as a running statistic, by
dividing the total number of unequal pairs of data elements by the total
number of input data elements from one source.
You can use this block to compute either symbol or bit error rate, because it
does not consider the magnitude of the difference between input data elements.
If the inputs are bits, then the block computes the bit error rate. If the inputs
are symbols, then it computes the symbol error rate.
This block inherits the sample time of its inputs.

Input Data
This block has between two and four input ports, depending on how you set the
mask parameters. The inports marked Tx and Rx accept transmitted and
received signals, respectively. The Tx and Rx signals must share the same
sampling rate.
The Tx and Rx inputs can be either scalars or frame-based column vectors. If Tx
is a scalar and Rx is a vector, or vice-versa, then the block compares the scalar
with each element of the vector. (Overall, the block behaves as if you had
preprocessed the scalar signal with the DSP Blockset’s Repeat block using the
Maintain input frame rate option.)

If you check the Reset port box in the mask, then an additional inport appears,
labeled Rst. The Rst input must be a sample-based scalar signal and must have
the same sampling rate as the Tx and Rx signals. When the Rst input is
nonzero, the block clears its error statistics and then computes them anew.
If you set the Computation mode mask parameter to Select samples from
port, then an additional inport appears, labeled Sel. The Sel input indicates
which elements of a frame are relevant for the computation; this is explained
further, in the last subbullet below. The Sel input can be either a sample-based
column vector or a one-dimensional vector.

4-187
Error Rate Calculation

The guidelines below indicate how you should configure the inputs and the
mask parameters depending on how you want this block to interpret your Tx
and Rx data.

• If both data signals are scalar, then this block compares the Tx scalar signal
with the Rx scalar signal. You should leave the Computation mode
parameter at its default value, Entire frame.
• If both data signals are vectors, then this block compares some or all of the
Tx and Rx data:
- If you set the Computation mode parameter to Entire frame, then the
block compares all of the Tx frame with all of the Rx frame.
- If you set the Computation mode parameter to Select samples from
mask, then the Selected samples from frame field appears in the mask.
This parameter field accepts a vector that lists the indices of those
elements of the Rx frame that you want the block to consider. For example,
to consider only the first and last elements of a length-six receiver frame,
set the Selected samples from frame parameter to [1 6]. If the Selected
samples from frame vector includes zeros, then the block ignores them.
- If you set the Computation mode parameter to Select samples from
port, then an additional input port, labeled Sel, appears on the block icon.
The data at this input port must have the same format as that of the
Selected samples from frame mask parameter described above.
• If one data signal is a scalar and the other is a vector, then this block
compares the scalar with each entry of the vector. The three subbullets above
are still valid for this mode, except that if Rx is a scalar, then the phrase “Rx
frame” above refers to the vector expansion of Rx.

Note Simulink requires that input signals have constant length throughout
a simulation. If you choose the Select samples from port option and want the
number of elements in the subframe to vary during the simulation, then you
should pad the Sel signal with zeros. (See the Zero Pad block in the DSP
Blockset.) The Error Rate Calculation block ignores zeros in the Sel signal.

4-188
 Error Rate Calculation

Output Data
This block produces a vector of length three, whose entries correspond to:

• The error rate

• The total number of errors, that is, comparisons between unequal elements
• The total number of comparisons that the block made

The block sends this output data to the workspace or to an output port,
depending on how you set the Output data parameter in the mask:

• If you set the Output data parameter to Workspace and fill in the Variable
name parameter, then that variable contains the current value when the
simulation ends. Pausing the simulation does not cause the block to write
interim data to the variable.
If you plan to use this block along with the Real-Time Workshop, then you
should not use the Workspace option; instead, use the Port option below and
connect the output port to a Simulink To Workspace block.
• If you set the Output data parameter to Port, then an output port appears.
This output port contains the running error statistics.

Delays
The Receive delay and Computation delay parameters implement two
different types of delays for this block. One is useful when part of your model
causes a lag in the received data, and the other is useful when you want to
ignore the transient behavior of both input signals:

• The Receive delay parameter is the number of samples by which the

received data lags behind the transmitted data. This parameter tells the
block which samples “correspond” to each other and should be compared. The
receive delay persists throughout the simulation.
• The Computation delay parameter tells the block to ignore the specified
number of samples at the beginning of the comparison.

4-189
Error Rate Calculation

Note The Version 1.4 Error Rate Calculation block considers a vector input
to be a sample, whereas the current block considers a vector input to be a
frame of multiple samples. For vector inputs of length n, a Receive delay of k
in the Version 1.4 block is equivalent to a Receive delay of k*n in the current
block.

If you use the Select samples from mask or Select samples from port option,
then each delay parameter refers to the number of samples that the block
receives, whether the block ultimately ignores some of them or not.

Examples The figure below shows how the block compares pairs of elements and counts
the number of error events. This example assumes that the sample time of each
input signal is 1 second and that the block’s parameters are as follows:

• Receive delay = 2
• Computation delay = 0
• Computation mode = Entire frame

The input signals are both frame-based column vectors of length three.
However, the schematic arranges each column vector horizontally and aligns
pairs of vectors so as to reflect a receive delay of two samples. At each time step,
the block compares elements of the Rx signal with those of the Tx signal that
appear directly above them in the schematic. For instance, at time 1, the block
compares 2, 4, and 1 from the Rx signal with 2, 3, and 1 from the Tx signal.
The values of the first two elements of Rx appear as asterisks because they do
not influence the output. Similarly, the 6 and 5 in the Tx signal do not influence
the output up to time 3, though they would influence the output at time 4.
In the error rates on the right side of the figure, each numerator at time t
reflects the number of errors when considering the elements of Rx up through
time t.

4-190
 Error Rate Calculation

t=0 t=1
Tx Error rates as fractions
1 2 3 1 2 3 1 7 7 1 6 5
0/1 1/4 2/7 4/10
* * 1 2 4 1 2 3 3 3 2 1
Rx t=0 t=1
t=0 t=1
time time

Note: Tx and Rx inputs are frame-based column vectors.

If the block’s Reset port box had been checked and a reset had occurred at
time = 3 seconds, then the last error rate would have been 2/3 instead of 4/10.
This value 2/3 would reflect the comparison of 3, 2, and 1 from the Rx signal
with 7, 7, and 1 from the Tx signal. The figure below illustrates this scenario.

t=0 t=1
Tx 1 2 3 1 2 3 1 7 7 1 6 5 Error rates as fractions
Rx * * 1 2 4 1 2 3 3 3 2 1 0/1 1/4 2/7 2/3
0 0 0 1 t=0 t=1

t=0 t=1
time time

Note: Tx and Rx inputs are frame-based column vectors.

4-191
Error Rate Calculation

Dialog Box

Receive delay
Number of samples by which the received data lags behind the transmitted
data. (If Tx or Rx is a vector, then each entry represents a sample.)
Computation delay
Number of samples that the block should ignore at the beginning of the
comparison.
Computation mode
Either Entire frame, Select samples from mask, or Select samples from
port, depending on whether the block should consider all or only part of the
input frames.
Selected samples from frame
A vector that lists the indices of the elements of the Rx frame vector that
the block should consider when making comparisons. This field appears
only if Computation mode is set to Select samples from mask.

4-192
 Error Rate Calculation

Output data
Either Workspace or Port, depending on where you want to send the
output data.
Variable name
Name of workspace variable for the output data vector. This field appears
only if Output data is set to Workspace.
Reset port
If you check this box, then an additional input port appears, labeled Rst.

4-193
FM Demodulator Baseband

Purpose 4FM Demodulator Baseband

Demodulate FM-modulated data

Library Analog Baseband Modulation, in Modulation

Description The FM Demodulator Baseband block demodulates a signal that was

modulated using frequency modulation. The input is a baseband
representation of the modulated signal. The input is complex, while the output
is real. The input must be a sample-based scalar signal.
In the course of demodulating, this block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Box

Initial phase (rad)

The initial phase in the corresponding FM Modulator Baseband block.
Modulation constant (Hertz per volt)
The modulation constant in the corresponding FM Modulator Baseband
block.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.

4-194
 FM Demodulator Baseband

Lowpass filter denominator

The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
Sample time
The sample time of the output signal.

Pair Block FM Modulator Baseband

4-195
FM Demodulator Passband

Purpose 4FM Demodulator Passband

Demodulate FM-modulated data

Library Analog Passband Modulation, in Modulation

Description The FM Demodulator Passband block demodulates a signal that was

modulated using frequency modulation. The input is a passband
representation of the modulated signal. Both the input and output signals are
real sample-based scalar signals.
In the course of demodulating, the block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

The block uses a voltage-controlled oscillator (VCO) in the demodulation. The

Initial phase parameter gives the initial phase of the VCO.

Dialog Box

Carrier frequency (Hz)

The carrier frequency in the corresponding FM Modulator Passband block.
Initial phase (rad)
The initial phase of the VCO in radians.

4-196
 FM Demodulator Passband

Modulation constant (Hertz per volt)

The modulation constant in the corresponding FM Modulator Passband
block.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
Sample time
The sample time in the corresponding FM Modulator Passband block.

Pair Block FM Modulator Passband

See Also FM Demodulator Baseband

4-197
FM Modulator Baseband

Purpose 4FM Modulator Baseband

Modulate using frequency modulation

Library Analog Baseband Modulation, in Modulation

Description The FM Modulator Baseband block modulates using frequency modulation.

The output is a baseband representation of the modulated signal. The input
signal is real, while the output signal is complex. The input must be a
sample-based scalar signal. In the frequency modulation technique, the
frequency of the modulated signal varies according to the amplitude of the
input signal.
If the input is u(t) as a function of time t, then the output is

 t
ò
exp jθ + 2πjKc u ( τ ) dτ

where θ is the Initial phase parameter and Kc is the Modulation constant

parameter.

Dialog Box

Initial phase (rad)

The initial phase of the modulated signal in radians.

4-198
 FM Modulator Baseband

Modulation constant (Hertz per volt)

The modulation constant Kc.
Sample time
The sample time of the output signal. It must be a positive number.
Symbol interval (s)
Inf by default. To use this block to model FSK, set this parameter to the
length of time required to transmit a single information bit.

Pair Block FM Demodulator Baseband

4-199
FM Modulator Passband

Purpose 4FM Modulator Passband

Modulate using frequency modulation

Library Analog Passband Modulation, in Modulation

Description The FM Modulator Passband block modulates using frequency modulation.

The output is a passband representation of the modulated signal. The output
signal’s frequency varies with the input signal’s amplitude. Both the input and
output signals are real sample-based scalar signals.
If the input is u(t) as a function of time t, then the output is

 t
ò
cos 2πf c t + 2πK c u ( τ ) dτ + θ

where:

• fc is the Carrier frequency parameter.

• θ is the Initial phase parameter.
• Kc is the Modulation constant parameter.

Typically, an appropriate Carrier frequency value is much higher than the

highest frequency of the input signal. To avoid having to use a high carrier
frequency and consequently a high sampling rate, you can use baseband
simulation (FM Modulator Baseband block) instead of passband simulation.
By the Nyquist sampling theorem, the reciprocal of the Sample time
parameter must exceed twice the Carrier frequency parameter.

4-200
 FM Modulator Passband

Dialog Box

Carrier frequency (Hz)

The frequency of the carrier.
Initial phase (rad)
The initial phase of the carrier in radians.
Modulation constant (Hertz per volt)
The modulation constant Kc.
Sample time
The sample time of the output signal. It must be a positive number.
Symbol interval
Inf by default. To use this block to model FSK, set this parameter to the
length of time required to transmit a single information bit.

Pair Block FM Demodulator Passband

See Also FM Modulator Baseband

4-201
Gaussian Noise Generator

Purpose 4Gaussian Noise Generator

Generate Gaussian distributed noise with given mean and variance values

Library Comm Sources

Description The Gaussian Noise Generator block generates discrete-time white Gaussian
noise. You must specify the Initial seed vector in the simulation.
The Mean Value and the Variance can be either scalars or vectors. If either of
these is a scalar, then the block applies the same value to each element of a
sample-based output or each column of a frame-based output. Individual
elements or columns, respectively, are uncorrelated with each other.
When the Variance is a vector, its length must be the same as that of the
Initial seed vector. In this case, the covariance matrix is a diagonal matrix
whose diagonal elements come from the Variance vector. Since the
off-diagonal elements are zero, the output Gaussian random variables are
uncorrelated.
When the Variance is a square matrix, it represents the covariance matrix. Its
off-diagonal elements are the correlations between pairs of output Gaussian
random variables. In this case, the Variance matrix must be positive definite,
and it must be N-by-N, where N is the length of the Initial seed.
The probability density function of n-dimensional Gaussian noise is
1
– ---
n 2 T –1
f ( x ) = ( ( 2π ) det K ) exp ( – ( x – µ ) K ( x – µ ) ⁄ 2 )
where x is a length-n vector, K is the n-by-n covariance matrix, µ is the mean
value vector, and the superscript T indicates matrix transpose.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret
vector parameters as 1-D parameters. See “Signal Attribute Parameters for
Random Sources” on page 2-7 for more details.
If the Initial seed parameter is a vector, then its length becomes the number
of columns in a frame-based output or the number of elements in a
sample-based vector output. In this case, the shape (row or column) of the

4-202
 Gaussian Noise Generator

Initial seed parameter becomes the shape of a sample-based two-dimensional

output signal. If the Initial seed parameter is a scalar but either the Mean
value or Variance parameter is a vector, then the vector length determines the
output attributes mentioned above.

Dialog Box

Mean value
The mean value of the random variable output.
Variance
The covariance among the output random variables.
Initial seed
The initial seed value for the random number generator.
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.

4-203
Gaussian Noise Generator

Samples per frame

The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.
Interpret vector parameters as 1-D
If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

See Also Random Source (DSP Blockset), AWGN Channel; rand (built-in MATLAB
function)

4-204
 General Block Deinterleaver

Purpose 4General Block Deinterleaver

Restore ordering of the symbols in the input vector

Library Block sublibrary of Interleaving

Description The General Block Deinterleaver block rearranges the elements of its input
vector without repeating or omitting any elements. The input can be real or
complex. If the input contains N elements, then the Elements parameter is a
vector of length N that indicates the indices, in order, of the output elements
that came from the input vector. That is, for each integer k between 1 and N,
Output(Elements(k)) = Input(k)
The Elements parameter must contain unique integers between 1 and N.
If the input is frame-based, then both it and the Elements parameter must be
column vectors.
To use this block as an inverse of the General Block Interleaver block, use the
same Elements parameter in both blocks. In that case, the two blocks are
inverses in the sense that applying the General Block Interleaver block
followed by the General Block Deinterleaver block leaves data unchanged.

Dialog Box

Elements
A vector of length N that lists the indices of the output elements that came
from the input vector.

Examples This example reverses the operation in the example on the General Block
Interleaver block reference page. If Elements is [4,1,3,2] and the input to the
General Block Deinterleaver block is [1;40;59;32], then the output of the
General Block Deinterleaver block is [40;32;59;1].

4-205
General Block Deinterleaver

Pair Block General Block Interleaver

See Also perms (MATLAB function)

4-206
 General Block Interleaver

Purpose 4General Block Interleaver

Reorder the symbols in the input vector

Library Block sublibrary of Interleaving

Description The General Block Interleaver block rearranges the elements of its input vector
without repeating or omitting any elements. The input can be real or complex.
If the input contains N elements, then the Elements parameter is a vector of
length N that indicates the indices, in order, of the input elements that form
the length-N output vector; that is,
Output(k) = Input(Elements(k))
for each integer k between 1 and N. The contents of Elements must be integers
between 1 and N, and must have no repetitions.
If the input is frame-based, then both it and the Elements parameter must be
column vectors.

Dialog Box

Elements
A vector of length N that lists the indices of the input elements that form
the output vector.

Examples If Elements is [4,1,3,2] and the input vector is [40;32;59;1], then the
output vector is [1;40;59;32]. Notice that all of these vectors have the same
length and that the vector Elements is a permutation of the vector [1:4].

Pair Block General Block Deinterleaver

See Also perms (MATLAB function)

4-207
General Multiplexed Deinterleaver

Purpose 4General Multiplexed Deinterleaver

Restore ordering of symbols using specified-delay shift registers

Library Convolutional sublibrary of Interleaving

Description The General Multiplexed Deinterleaver block restores the original ordering of
a sequence that was interleaved using the General Multiplexed Interleaver
block.
In typical usage, the parameters in the two blocks have the same values. As a
result, the Interleaver delay parameter, V, specifies the delays for each shift
register in the corresponding interleaver, so that the delays of the
deinterleaver’s shift registers are actually max(V)-V.
The input can be either a scalar or a frame-based column vector. It can be real
or complex. The input and output signals share the same sample time.

Dialog Box

Interleaver delay (samples)

A vector that lists the number of symbols that fit in each shift register of
the corresponding interleaver. The length of this vector is the number of
shift registers.
Initial conditions
The values that fill each shift register when the simulation begins.

4-208
 General Multiplexed Deinterleaver

Pair Block General Multiplexed Interleaver

See Also Convolutional Deinterleaver, Helical Deinterleaver

References [1] Heegard, Chris and Stephen B. Wicker. Turbo Coding. Boston: Kluwer
Academic Publishers, 1999.

4-209
General Multiplexed Interleaver

Purpose 4General Multiplexed Interleaver

Permute input symbols using a set of shift registers with specified delays

Library Convolutional sublibrary of Interleaving

Description The General Multiplexed Interleaver block permutes the symbols in the input
signal. Internally, it uses a set of shift registers, each with its own delay value.
The input can be either a scalar or a frame-based column vector. It can be real
or complex. The input and output signals share the same sample time.
The Interleaver delay parameter is a column vector whose entries indicate
how many symbols can fit into each shift register. The length of the vector is
the number of shift registers. (In sample-based mode, it can also be a row
vector.)
The Initial conditions parameter indicates the values that fill each shift
register at the beginning of the simulation. If Initial conditions is a scalar,
then its value fills all shift registers; if Initial conditions is a column vector,
then each entry fills the corresponding shift register. (In sample-based mode,
Initial conditions can also be a row vector.) If a given shift register has zero
delay, then the value of the corresponding entry in the Initial conditions
vector is unimportant.

Dialog Box

Interleaver delay (samples)

A vector that lists the number of symbols that fit in each shift register. The
length of this vector is the number of shift registers.

4-210
 General Multiplexed Interleaver

Initial conditions
The values that fill each shift register when the simulation begins.

Pair Block General Multiplexed Deinterleaver

See Also Convolutional Interleaver, Helical Interleaver

References [1] Heegard, Chris and Stephen B. Wicker. Turbo Coding. Boston: Kluwer
Academic Publishers, 1999.

4-211
General QAM Demodulator Baseband

Purpose 4General QAM Demodulator Baseband

Demodulate QAM-modulated data

Library AM, in Digital Baseband sublibrary of Modulation

Description The General QAM Demodulator Baseband block demodulates a signal that was
modulated using quadrature amplitude modulation. The input is a baseband
representation of the modulated signal.
The input must be a discrete-time complex signal. The Signal constellation
parameter defines the constellation by listing its points in a vector of complex
numbers. The block maps the mth point in the Signal constellation vector to
the integer m-1.
The input can be either a scalar or a frame-based column vector.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

Signal constellation
A real or complex vector that lists the constellation points.

4-212
 General QAM Demodulator Baseband

Samples per symbol

The number of input samples that represent each modulated symbol.

Pair Block General QAM Modulator Baseband

See Also Rectangular QAM Demodulator Baseband

4-213
General QAM Demodulator Passband

Purpose 4General QAM Demodulator Passband

Demodulate QAM-modulated data

Library AM, in Digital Passband sublibrary of Modulation

Description The General QAM Demodulator Passband block demodulates a signal that was
modulated using the pulse amplitude phase shift keying method. The input is
a passband representation of the modulated signal.
The input must be a sample-based scalar. Furthermore, it must be a
discrete-time complex signal.
The Signal constellation parameter defines the constellation by listing its
points in a vector of complex numbers.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1
• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

4-214
 General QAM Demodulator Passband

Dialog Box

Signal constellation
A real or complex vector that lists the constellation points.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.

4-215
General QAM Demodulator Passband

Pair Block General QAM Modulator Passband

See Also General QAM Demodulator Baseband

4-216
 General QAM Modulator Baseband

Purpose 4General QAM Modulator Baseband

Modulate using quadrature amplitude modulation

Library AM, in Digital Baseband sublibrary of Modulation

Description The General QAM Modulator Baseband block modulates using quadrature
amplitude modulation. The output is a baseband representation of the
modulated signal.
The Signal constellation parameter defines the constellation by listing its
points in a length-M vector of complex numbers. The input signal values must
be integers between 0 and M-1. The block maps an input integer m to the
(m-1)st value in the Signal constellation vector.
The input can be either a scalar or a frame-based column vector.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

Signal constellation
A real or complex vector that lists the constellation points.

4-217
General QAM Modulator Baseband

Samples per symbol

The number of output samples that the block produces for each input
integer.

Pair Block General QAM Demodulator Baseband

See Also Rectangular QAM Modulator Baseband

4-218
 General QAM Modulator Passband

Purpose 4General QAM Modulator Passband

Modulate using the pulse amplitude modulation phase shift keying method

Library AM, in Digital Passband sublibrary of Modulation

Description The General QAM Modulator Passband block modulates using the pulse
amplitude modulation phase shift keying method. The output is a passband
representation of the modulated signal.
The Signal constellation parameter defines the constellation by listing its
points in a length-M vector of complex numbers. The input signal values must
be integers between 0 and M-1. The block maps an input integer m to the
(m-1)st value in the Signal constellation vector, and then converts these
mapped values to a passband output signal.
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.
The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1
• Symbol period = K*Output sample time*Baseband samples per symbol
for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

4-219
General QAM Modulator Passband

Dialog Box

Signal constellation
A real or complex vector that lists the constellation points.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

4-220
 General QAM Modulator Passband

Pair Block General QAM Demodulator Passband

See Also General QAM Modulator Baseband

4-221
GMSK Demodulator Baseband

Purpose 4GMSK Demodulator Baseband

Demodulate GMSK-modulated data

Library CPM, in Digital Baseband sublibrary of Modulation

Description The GMSK Demodulator Baseband block demodulates a signal that was
modulated using the Gaussian minimum shift keying method. The input is a
baseband representation of the modulated signal.
The BT product, Pulse length, Symbol prehistory, and Phase offset
parameters are as described on the reference page for the GMSK Modulator
Baseband block.

Traceback Length and Output Delays

Internally, this block creates a trellis description of the modulation scheme and
uses the Viterbi algorithm. The Traceback length parameter, D, in this block
is the number of trellis branches used to construct each traceback path. D
influences the output delay, which is the number of zero symbols that precede
the first meaningful demodulated value in the output.

• If the input signal is sample-based, then the delay consists of D+1 zero
symbols.
• If the input signal is frame-based, then the delay consists of D zero symbols.

Inputs and Outputs

The input can be either a scalar or a frame-based column vector. If the Output
type parameter is set to Integer, then the block produces values of 1 and -1. If
the Output type parameter is set to Bit, then the block produces values of 0
and 1.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-222
 GMSK Demodulator Baseband

Dialog Box

Output type
Determines whether the output consists of bipolar or binary values.
BT product
The product of bandwidth and time.
Pulse length (symbol intervals)
The length of the frequency pulse shape.
Symbol prehistory
The data symbols used by the modulator before the start of the simulation.
Phase offset (rad)
The initial phase of the modulated waveform.

4-223
GMSK Demodulator Baseband

Samples per symbol

The number of input samples that represent each modulated symbol.
Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.

Pair Block GMSK Modulator Baseband

See Also CPM Demodulator Baseband, Viterbi Decoder

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-224
 GMSK Demodulator Passband

Purpose 4GMSK Demodulator Passband

Demodulate GMSK-modulated data

Library CPM, in Digital Passband sublibrary of Modulation

Description The GMSK Demodulator Passband block demodulates a signal that was
modulated using the Gaussian minimum shift keying method. The input is a
passband representation of the modulated signal.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, GMSK Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• Output type
• BT product
• Pulse length
• Symbol prehistory
• Traceback length
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1
• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

4-225
GMSK Demodulator Passband

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

Dialog Box

Output type
Determines whether the output consists of bipolar or binary values.
BT product
The product of bandwidth and time.

4-226
 GMSK Demodulator Passband

Pulse length (symbol intervals)

The length of the frequency pulse shape.
Symbol prehistory
The data symbols used by the modulator before the start of the simulation.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.
Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.

Pair Block GMSK Modulator Passband

See Also GMSK Demodulator Baseband, Viterbi Decoder

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-227
GMSK Modulator Baseband

Purpose 4GMSK Modulator Baseband

Modulate using the Gaussian minimum shift keying method

Library CPM, in Digital Baseband sublibrary of Modulation

Description The GMSK Modulator Baseband block modulates using the Gaussian
minimum shift keying method. The output is a baseband representation of the
modulated signal.
The BT product parameter represents bandwidth multipled by time. This
parameter is a nonnegative scalar. It is used to reduce the bandwidth at the
expense of increased intersymbol interference. The Pulse length parameter
measures the length of the Gaussian pulse shape, in symbol intervals. For the
exact definitions of the pulse shape, see the work by Anderson, Aulin, and
Sundberg listed in “References” on page 4-230.
The Symbol prehistory parameter is a scalar or vector that specifies the data
symbols used before the start of the simulation, in reverse chronological order.
If it is a vector, then its length must be one less than the Pulse length
parameter.
In this block, a symbol of 1 causes a phase shift of π/2 radians. The Phase offset
parameter is the initial phase of the output waveform, measured in radians.

Input Attributes
The input can be either a scalar or a frame-based column vector. If the Input
type parameter is set to Integer, then the block accepts values of 1 and -1. If
the Input type parameter is set to Bit, then the block accepts values of 0 and 1.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-228
 GMSK Modulator Baseband

Dialog Box

Input type
Indicates whether the input consists of bipolar or binary values.
BT product
The product of bandwidth and time.
Pulse length (symbol intervals)
The length of the frequency pulse shape.
Symbol prehistory
The data symbols used before the start of the simulation, in reverse
chronological order.
Phase offset (rad)
The initial phase of the output waveform.

4-229
GMSK Modulator Baseband

Samples per symbol

The number of output samples that the block produces for each integer or
bit in the input.

Pair Block GMSK Demodulator Baseband

See Also CPM Modulator Baseband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-230
 GMSK Modulator Passband

Purpose 4GMSK Modulator Passband

Modulate using the Gaussian minimum shift keying method

Library CPM, in Digital Passband sublibrary of Modulation

Description The GMSK Modulator Passband block modulates using the Gaussian
minimum shift keying method. The output is a passband representation of the
modulated signal.
This block uses the baseband equivalent block, GMSK Modulator Baseband,
for internal computations and converts the resulting baseband signal to a
passband representation. The following parameters in this block are the same
as those of the baseband equivalent block:

• Input type
• BT product
• Pulse length
• Symbol prehistory
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.
The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1

4-231
GMSK Modulator Passband

• Symbol period = K*Output sample time*Baseband samples per symbol

for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

Input type
Indicates whether the input consists of bipolar or binary values.
BT product
The product of bandwidth and time.
Pulse length (symbol intervals)
The length of the frequency pulse shape.

4-232
 GMSK Modulator Passband

Symbol prehistory
The data symbols used before the start of the simulation, in reverse
chronological order.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block GMSK Demodulator Passband

See Also GMSK Modulator Baseband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-233
Hamming Decoder

Purpose 4Hamming Decoder

Decode a Hamming code to recover binary vector data

Library Block sublibrary of Channel Coding

Description The Hamming Decoder block recovers a binary message vector from a binary
Hamming codeword vector. For proper decoding, the parameter values in this
block should match those in the corresponding Hamming Encoder block.
If the Hamming code has message length K and codeword length N, then N
must have the form 2M-1 for some integer M greater than or equal to 3. Also, K
must equal N-M.
The input must contain exactly N elements. If it is frame-based, then it must
be a column vector. The output is a vector of length K.
The coding scheme uses elements of the finite field GF(2M). You can either
specify the primitive polynomial that the algorithm should use, or you can rely
on the default setting:

• To use the default primitive polynomial, simply enter N and K as the first
and second mask parameters, respectively. The algorithm uses gfprimdf(M)
as the primitive polynomial for GF(2M).
• To specify the primitive polynomial, enter N as the first parameter and a
binary vector as the second parameter. The vector represents the primitive
polynomial by listing its coefficients in order of ascending exponents. You can
create primitive polynomials using the gfprimfd function in the
Communications Toolbox.

4-234
 Hamming Decoder

Dialog Box

Codeword length N
The codeword length N, which is also the input vector length.
Message length K, or M-degree primitive polynomial
Either the message length, which is also the output vector length; or a
binary vector that represents a primitive polynomial for GF(2M).

Pair Block Hamming Encoder

See Also hammgen (Communications Toolbox)

4-235
Hamming Encoder

Purpose 4Hamming Encoder

Create a Hamming code from binary vector data

Library Block sublibrary of Channel Coding

Description The Hamming Encoder block creates a Hamming code with message length K
and codeword length N. The number N must have the form 2M-1, where M is
an integer greater than or equal to 3. Then K equals N-M.
The input must contain exactly K elements. If it is frame-based, then it must
be a column vector. The output is a vector of length N.
The coding scheme uses elements of the finite field GF(2M). You can either
specify the primitive polynomial that the algorithm should use, or you can rely
on the default setting:

• To use the default primitive polynomial, simply enter N and K as the first
and second mask parameters, respectively. The algorithm uses gfprimdf(M)
as the primitive polynomial for GF(2M).
• To specify the primitive polynomial, enter N as the first parameter and a
binary vector as the second parameter. The vector represents the primitive
polynomial by listing its coefficients in order of ascending exponents. You can
create primitive polynomials using the gfprimfd function in the
Communications Toolbox.

Dialog Box

Codeword length N
The codeword length, which is also the output vector length.

4-236
 Hamming Encoder

Message length K, or M-degree primitive polynomial

Either the message length, which is also the input vector length; or a
binary vector that represents a primitive polynomial for GF(2M).

Pair Block Hamming Decoder

See Also hammgen (Communications Toolbox)

4-237
Helical Deinterleaver

Purpose 4Helical Deinterleaver

Restore ordering of symbols permuted by a helical interleaver

Library Convolutional sublibrary of Interleaving

Description The Helical Deinterleaver block permutes the symbols in the input signal by
placing them in an array row by row and then selecting groups in a helical
fashion to send to the output port.
The block uses the array internally for its computations. If C is the Number of
columns in helical array parameter, then the array has C columns and
unlimited rows. If N is the Group size parameter, then the block accepts an
input of length C*N at each time step and inserts them into the next N rows of
the array. The block also places the Initial condition parameter into certain
positions in the top few rows of the array (not only to accommodate the helical
pattern but also to preserve the vector indices of symbols that pass through the
Helical Interleaver and Helical Deinterleaver blocks in turn).
The output consists of consecutive groups of N symbols. Counting from the
beginning of the simulation, the block selects the kth output group in the array
from column k mod C. The selection is helical because of the reduction modulo
C and because the first symbol in the kth group is in row 1+(k-1)*s, where s is
the Helical array step size parameter.
The number of elements of the input vector must be C times N. If the input is
frame-based, then it must be a column vector.

Delay of Interleaver-Deinterleaver Pair

After processing a message with the Helical Interleaver block and the Helical
Deinterleaver block, the deinterleaved data lags the original message by

s(C – 1)
CN --------------------
-
N
samples. Before this delay elapses, the deinterleaver output is either the
Initial condition parameter in the Helical Deinterleaver block or the Initial
condition parameter in the Helical Interleaver block.

If your model incurs an additional delay between the interleaver output and
the deinterleaver input, then the restored sequence lags the original sequence
by the sum of the additional delay and the amount in the formula above. For
proper synchronization, the delay between the interleaver and deinterleaver

4-238
 Helical Deinterleaver

must be m*C*N for some nonnegative integer m. You can use the Integer Delay
block in the DSP Blockset to adjust delays manually, if necessary.

Dialog Box

Number of columns in helical array

The number of columns, C, in the helical array.
Group size
The size, N, of each group of symbols. The input width is C times N.
Helical array step size
The number of rows of separation between consecutive output groups as
the block selects them from their respective columns of the helical array.
Initial condition
A scalar that fills the array before the first input is placed.

Pair Block Helical Interleaver

See Also General Multiplexed Deinterleaver

4-239
Helical Deinterleaver

References [1] Berlekamp, E. R. and P. Tong. “Improved Interleavers for Algebraic Block
Codes.” U. S. Patent 4559625, Dec. 17, 1985.

4-240
 Helical Interleaver

Purpose 4Helical Interleaver

Permute input symbols using a helical array

Library Convolutional sublibrary of Interleaving

Description The Helical Interleaver block permutes the symbols in the input signal by
placing them in an array in a helical fashion and then sending rows of the array
to the output port.
The block uses the array internally for its computations. If C is the Number of
columns in helical array parameter, then the array has C columns and
unlimited rows. If N is the Group size parameter, then the block accepts an
input of length C*N at each time step and partitions the input into consecutive
groups of N symbols. Counting from the beginning of the simulation, the block
places the kth group in the array along column k mod C. The placement is
helical because of the reduction modulo C and because the first symbol in the
kth group is in row 1+(k-1)*s, where s is the Helical array step size parameter.
Positions in the array that do not contain input symbols have default contents
specified by the Initial condition parameter.
The block sends C*N symbols from the array to the output port by reading the
next N rows sequentially. At a given time step, the output symbols might be
the Initial condition parameter value, symbols from that time step’s input
vector, or symbols left in the array from a previous time step.
The number of elements of the input vector must be C times N. If the input is
frame-based, then it must be a column vector.

4-241
Helical Interleaver

Dialog Box

Number of columns in helical array

The number of columns, C, in the helical array.
Group size
The size, N, of each group of input symbols. The input width is C times N.
Helical array step size
The number of rows of separation between consecutive input groups in
their respective columns of the helical array.
Initial condition
A scalar that fills the array before the first input is placed.

Examples Suppose that C = 3, N = 2, the Helical array step size parameter is 1, and the
Initial condition parameter is -1. After receiving inputs of [1:6]', [7:12]',
and [13:19]', the block’s internal array looks like the schematic below. The
coloring of the inputs and the array indicate how the input symbols are placed
within the array. The outputs at the first three time steps are
[1; -1; -1; 2; 3; -1], [7; 4; 5; 8; 9; 6], and
[13; 10; 11; 14; 15; 12]. (The outputs are not color-coded in the
schematic.)

4-242
 Helical Interleaver

Block’s Internal Array

1 -1 -1
Inputs Outputs from successive
rows of array
2 3 -1

7 4 5
13 7 1 13 7 1
14 8 2 10 4 -1
8 9 6
15 9 3 11 5 -1
16 10 4 14 8 2
13 10 11
17 11 5 15 9 3
18 12 6 12 6 -1
14 15 12

16 17

... 18

Pair Block Helical Deinterleaver

See Also General Multiplexed Interleaver

References [1] Berlekamp, E. R. and P. Tong. “Improved Interleavers for Algebraic Block
Codes.” U. S. Patent 4559625, Dec. 17, 1985.

4-243
Insert Zero

Purpose 4Insert Zero

Distribute input elements in output vector

Library Sequence Operations, in Basic Comm Functions

Description The Insert Zero block constructs an output vector by inserting zeros among the
elements of the input vector. The input can be real or complex. The block
determines where to place the zeros by using the Insert zero vector
parameter. The Insert zero vector parameter is a binary vector whose
elements are arranged so that:

• Each 1 indicates that the block should place the next element of the input in
the output vector
• Each 0 indicates that the block should place a 0 in the output vector

If the input signal is sample-based, then the input vector length must equal the
number of 1s in the Insert zero vector parameter.
To implement punctured coding using the Puncture and Insert Zero blocks, you
should use the same vector for the Insert zero vector parameter in this block
and for the Puncture vector parameter in the Puncture block.

Frame-Based Processing
If the input signal is frame-based, then both it and the Insert zero vector
parameter must be column vectors. The number of 1s in the Insert zero vector
parameter must divide the input vector length. If the input vector length is
greater than the number of 1s in the Insert zero vector parameter, then the
block repeats the insertion pattern until it has placed all input elements in the
output vector.

4-244
 Insert Zero

Dialog Box

Insert zero vector

A binary vector whose pattern of 0s and 1s indicates where the block should
place either 0s or input vector elements, respectively, in the output vector.

Examples If the Insert zero vector parameter is the six-element vector [1,0,1,1,1,0],
then the block inserts zeros after the first and last elements of each consecutive
grouping of four input elements. It considers groups of four elements because
the Insert zero vector parameter has four 1s.
The diagram below depicts the block’s operation using this Insert zero vector
parameter. Notice that the insertion pattern applies twice.

Group of 4 Group of 4
[1 3 4 5 7 9 10 11]

Shading Key for Output Vector

= Inserted zero
[1 0 3 4 5 0 7 0 9 10 11 0]
= Entry from input vector

Compare this example with that on the reference page for the Puncture block.
See Also Puncture

4-245
Integer-Input RS Encoder

Purpose 4Integer-Input RS Encoder

Create a Reed-Solomon code from integer vector data

Library Block sublibrary of Channel Coding

Description The Integer-Input RS Encoder block creates a Reed-Solomon code with

message length K and codeword length N. You specify both N and K directly in
the block mask. N must have the form 2M-1, where M is an integer greater than
or equal to 3. The code is more efficient if N-K is an even integer.
The input and output are integer-valued signals that represent messages and
codewords, respectively. The integers that form the messages and codewords
represent elements of the finite field GF(2M) and hence must be between 0 and
2M-1.
The input must contain exactly K elements. If it is frame-based, then it must
be a column vector. The output is a vector of length N.
An (N,K) Reed-Solomon code can correct up to floor((N-K)/2) symbol errors
(not bit errors) in each codeword.

Examples Suppose M = 3, N = 23-1 = 7, and K = 5. Then a message is a vector of length 5

whose entries are integers between 0 and 7. A corresponding codeword is a
vector of length 7 whose entries are integers between 0 and 7. The figure below
illustrates possible input and output signals to this block, when the block
parameters are set to their defaults of 7 and 5, respectively.

6 3
2 2
2 6 2 6
3 7 3 7
5 4 5 4
2 0 message 2 0 code
0 4 0 4
t=1 t=0 t=1 t=0

4-246
 Integer-Input RS Encoder

Dialog Box

Codeword length N
The codeword length, which is also the output vector length.
Message length K
The message length, which is also the input vector length.

Pair Block Integer-Output RS Decoder

See Also Binary-Input RS Encoder

4-247
Integer-Output RS Decoder

Purpose 4Integer-Output RS Decoder

Decode a Reed-Solomon code to recover integer vector data

Library Block sublibrary of Channel Coding

Description The Integer-Output RS Decoder block recovers a message vector from a

Reed-Solomon codeword vector. For proper decoding, the parameter values in
this block should match those in the corresponding Integer-Input RS Encoder
block.
If the Reed-Solomon code has message length K and codeword length N, then
N must have the form 2M-1 for some integer M greater than or equal to 3. The
code is more efficient if N-K is an even integer.
The input and first output are integer-valued signals that represent codewords
and messages, respectively. The integers in these signals represent elements
of the finite field GF(2M) and hence must be between 0 and 2M-1.
The input must contain exactly N elements. If it is frame-based, then it must
be a column vector. The first output is a vector of length K.
The second output is the number of errors detected during decoding of the
codeword. A negative integer indicates that the block detected more errors
than it could correct using the coding scheme. An (N,K) Reed-Solomon code can
correct up to floor((N-K)/2) symbol errors (not bit errors) in each codeword.
The sample times of the input and output signals are equal.

Dialog Box

4-248
 Integer-Output RS Decoder

Codeword length N
The codeword length, which is also the input vector length.
Message length K
The message length, which is also the output vector length.

Pair Block Integer-Input RS Encoder

See Also Binary-Output RS Decoder

4-249
Integer to Bit Converter

Purpose 4Integer to Bit Converter

Map a vector of integers to a vector of bits

Library Utility Functions

Description The Integer to Bit Converter block maps each integer in the input vector to a
group of bits in the output vector. If M is the Number of bits per integer
parameter, then the input integers must be between 0 and 2M-1. The block
maps each integer to a group of M bits, using the first bit as the most significant
bit. As a result, the output vector length is M times the input vector length.
The input can be either a scalar or a frame-based column vector.

Dialog Box

Number of bits per integer

The number of bits the block uses to represent each integer of the input.
This parameter must be an integer between 1 and 31.

Examples If the input is [7; 13] and the Number of bits per integer parameter is 4, then
the output is [0; 1; 1; 1; 1; 1; 0; 1]. The first group of four bits (0, 1, 1, 1)
represents 7 and the second group of four bits (1, 1, 0, 1) represents 13. Notice
that the output length is four times the input length.

Pair Block Bit to Integer Converter

4-250
 Integrate and Dump

Purpose 4Integrate and Dump

Integrate, resetting to zero periodically and reducing by a modulus

Library Integrators, in Basic Comm Functions

Description The Integrate and Dump block integrates the input signal in discrete time,
resets to zero according to a fixed schedule, and reduces modulo the Absolute
value bound parameter. If the Absolute value bound parameter is K, then
the block output is strictly between -K and K.
The reset times are the positive integral multiples of the Integration period
parameter. At each reset time, the block performs its final integration step,
sends the result to the output port, and then clears its internal state for the
next time step.
The input can be either a scalar, a sample-based vector, or a frame-based row
vector. The block processes each vector element independently.
This block uses the Forward Euler integration method.

Dialog Box

Absolute value bound

The modulus by which the integration result is reduced. This parameter
must be positive.

4-251
Integrate and Dump

Integration period (s)

The first reset time. This is also the time interval between resets.
Sample time
The integration sample time. This must not exceed the Integration
period.

Examples Integrate a constant signal whose value is 1 using these parameters:

• Absolute value bound = 5

• Integration period = 7
• Sample time = .5

You can use a Simulink Constant block for the input signal. The Simulink
Scope block shows the output below.

Notice that the output is 0 at time 0 and that the output never exceeds 5. Also
notice that the output at time 7.5 seconds (Integration period plus Sample
time) is the result of resetting the integrator after the previous time step and
then considering the input signal between times 7 and 7.5.

See Also Discrete Modulo Integrator, Windowed Integrator, Discrete-Time Integrator

(Simulink)

4-252
 Interlacer

Purpose 4Interlacer
Alternately select elements from two input vectors to generate output vector

Library Sequence Operations, in Basic Comm Functions

Description The Interlacer block accepts two inputs that have the same vector size,
complexity, and sample time. It produces one output vector by alternating
elements from the first input and from the second input. As a result, the output
vector size is twice that of either input. The output vector has the same
complexity and sample time of the inputs.
The inputs can be either scalars or frame-based column vectors.
This block can be useful for combining in-phase and quadrature information
from separate vectors into a single vector.

Dialog Box

Examples If the two input vectors are frame-based with values [1; 2; 3; 4] and
[5; 6; 7; 8], then the output vector is [1; 5; 2; 6; 3; 7; 4; 8].

Pair Block Deinterlacer

See Also General Block Interleaver; Mux (Simulink)

4-253
Linearized Baseband PLL

Purpose 4Linearized Baseband PLL

Implement a linearized version of a baseband phase-locked loop

Library Synchronization

Description The Linearized Baseband PLL block is a feedback control system that
automatically adjusts the phase of a locally generated signal to match the
phase of an input signal. Unlike the Phase-Locked Loop block, this block uses
a baseband model method. Unlike the Baseband PLL block, which uses a
nonlinear model, this block simplifies the computations by using x to
approximate sin(x). The baseband PLL model depends on the amplitude of the
incoming signal but does not depend on a carrier frequency.
This PLL has these three components:

• An integrator used as a phase detector.

• A filter. You specify the filter’s transfer function using the Lowpass filter
numerator and Lowpass filter denominator mask parameters. Each is a
vector that gives the respective polynomial’s coefficients in order of
descending powers of s.
To design a filter, you can use functions such as butter, cheby1, and cheby2
in the Signal Processing Toolbox. The default filter is a Chebyshev type II
filter whose transfer function arises from the command below.
[num, den] = cheby2(3,40,100,'s')

• A voltage-controlled oscillator (VCO). You specify the sensitivity of the VCO

signal to its input using the VCO input sensitivity parameter. This
parameter, measured in Hertz per volt, is a scale factor that determines how
much the VCO shifts from its quiescent frequency.

The input signal represents the received signal. The input must be a
sample-based scalar signal. The three output ports produce:

• The output of the filter

• The output of the phase detector
• The output of the VCO

4-254
 Linearized Baseband PLL

Dialog Box

Lowpass filter numerator

The numerator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
VCO input sensitivity (Hz/V)
This value scales the input to the VCO and, consequently, the shift from
the VCO’s quiescent frequency.

See Also Baseband PLL, Phase-Locked Loop

References For more information about phase-locked loops, see the works listed in
“Selected Bibliography for Synchronization” on page 2-92.

4-255
Matrix Deinterleaver

Purpose 4Matrix Deinterleaver

Permute input symbols by filling a matrix by columns and emptying it by rows

Library Block sublibrary of Interleaving

Description The Matrix Deinterleaver block performs block deinterleaving by filling a

matrix with the input symbols column by column and then sending the matrix
contents to the output port row by row. The Number of rows and Number of
columns parameters are the dimensions of the matrix that the block uses
internally for its computations.
The length of the input vector must be Number of rows times Number of
columns. If the input is frame-based, then it must be a column vector.

Dialog Box

Number of rows
The number of rows in the matrix that the block uses for its computations.
Number of columns
The number of columns in the matrix that the block uses for its
computations.

Examples If the Number of rows and Number of columns parameters are 2 and 3,
respectively, then the deinterleaver uses a 2-by-3 matrix for its internal
computations. Given an input signal of [1; 2; 3; 4; 5; 6], the block
produces an output of [1; 3; 5; 2; 4; 6].

Pair Block Matrix Interleaver

See Also General Block Deinterleaver

4-256
 Matrix Helical Scan Deinterleaver

Purpose 4Matrix Helical Scan Deinterleaver

Restore ordering of input symbols by filling a matrix along diagonals

Library Block sublibrary of Interleaving

Description The Matrix Helical Scan Deinterleaver block performs block deinterleaving by
filling a matrix with the input symbols in a helical fashion and then sending
the matrix contents to the output port row by row. The Number of rows and
Number of columns parameters are the dimensions of the matrix that the
block uses internally for its computations.
Helical fashion means that the block places input symbols along diagonals of
the matrix. The number of elements in each diagonal matches the Number of
columns parameter, after the block wraps past the edges of the matrix when
necessary. The block traverses diagonals so that the row index and column
index both increase. Each diagonal after the first one begins one row below the
first element of the previous diagonal.
The Array step size parameter is the slope of each diagonal, that is, the
amount by which the row index increases as the column index increases by one.
This parameter must be an integer between zero and the Number of rows
parameter. If the Array step size parameter is zero, then the block does not
deinterleave and the output is the same as the input.
The number of elements of the input vector must be the product of Number of
rows and Number of columns. If the input is frame-based, then it must be a
column vector.

4-257
Matrix Helical Scan Deinterleaver

Dialog Box

Number of rows
The number of rows in the matrix that the block uses for its computations.
Number of columns
The number of columns in the matrix that the block uses for its
computations.
Array step size
The slope of the diagonals that the block writes.

Pair Block Matrix Helical Scan Interleaver

See Also General Block Deinterleaver

4-258
 Matrix Helical Scan Interleaver

Purpose 4Matrix Helical Scan Interleaver

Permute input symbols by selecting matrix elements along diagonals

Library Block sublibrary of Interleaving

Description The Matrix Helical Scan Interleaver block performs block interleaving by
filling a matrix with the input symbols row by row and then sending the matrix
contents to the output port in a helical fashion. The Number of rows and
Number of columns parameters are the dimensions of the matrix that the
block uses internally for its computations.
Helical fashion means that the block selects output symbols by selecting
elements along diagonals of the matrix. The number of elements in each
diagonal matches the Number of columns parameter, after the block wraps
past the edges of the matrix when necessary. The block traverses diagonals so
that the row index and column index both increase. Each diagonal after the
first one begins one row below the first element of the previous diagonal.
The Array step size parameter is the slope of each diagonal, that is, the
amount by which the row index increases as the column index increases by one.
This parameter must be an integer between zero and the Number of rows
parameter. If the Array step size parameter is zero, then the block does not
interleave and the output is the same as the input.
The number of elements of the input vector must be the product of Number of
rows and Number of columns. If the input is frame-based, then it must be a
column vector.

4-259
Matrix Helical Scan Interleaver

Dialog Box

Number of rows
The number of rows in the matrix that the block uses for its computations.
Number of columns
The number of columns in the matrix that the block uses for its
computations.
Array step size
The slope of the diagonals that the block reads.

Examples If the Number of rows and Number of columns parameters are 6 and 4,
respectively, then the interleaver uses a 6-by-4 matrix for its internal
computations. If the Array step size parameter is 1, then the diagonals are as
shown in the figure below. Positions with the same color form part of the same
diagonal, and diagonals with darker colors precede those with lighter colors in
the output signal.
Given an input signal of [1:24]', the block produces an output of
[1; 6; 11; 16; 5; 10; 15; 20; 9; 14; 19; 24; 13; 18; 23;...
4; 17; 22; 3; 8; 21; 2; 7; 12]

4-260
 Matrix Helical Scan Interleaver

Block’s Internal Array

1 2 3 4

5 6 7 8
[1, 6, 11, 16,...
9 10 11 12
5, 10, 15, 20,...
[1:24]' 9, 14, 19, 24,...
13 14 15 16
13, 18, 23, 4,...
17, 22, 3, 8,...
17 18 19 20
21, 2, 7, 12]'

21 22 23 24

Pair Block Matrix Helical Scan Deinterleaver

See Also General Block Interleaver

4-261
Matrix Interleaver

Purpose 4Matrix Interleaver

Permute input symbols by filling a matrix by rows and emptying it by columns

Library Block sublibrary of Interleaving

Description The Matrix Interleaver block performs block interleaving by filling a matrix
with the input symbols row by row and then sending the matrix contents to the
output port column by column.
The Number of rows and Number of columns parameters are the dimensions
of the matrix that the block uses internally for its computations.
The number of elements of the input vector must be the product of Number of
rows and Number of columns. If the input is frame-based, then it must be a
column vector.

Dialog Box

Number of rows
The number of rows in the matrix that the block uses for its computations.
Number of columns
The number of columns in the matrix that the block uses for its
computations.

Examples If the Number of rows and Number of columns parameters are 2 and 3,
respectively, then the interleaver uses a 2-by-3 matrix for its internal
computations. Given an input signal of [1; 2; 3; 4; 5; 6], the block
produces an output of [1; 4; 2; 5; 3; 6].

4-262
 Matrix Interleaver

Pair Block Matrix Deinterleaver

See Also General Block Interleaver

4-263
M-DPSK Demodulator Baseband

Purpose 4M-DPSK Demodulator Baseband

Demodulate DPSK-modulated data

Library PM, in Digital Baseband sublibrary of Modulation

Description The M-DPSK Demodulator Baseband block demodulates a signal that was
modulated using the M-ary differential phase shift keying method. The input
is a baseband representation of the modulated signal. The input and output for
this block are discrete-time signals. The input can be either a scalar or a
frame-based column vector.
The M-ary number parameter, M, is the number of possible output symbols
that can immediately follow a given output symbol. The block compares the
current symbol to the previous symbol. The block’s first output is the initial
condition of zero (or a group of zeros, if the Output type parameter is set to Bit)
because there is no previous symbol.

Binary or Integer Outputs

If the Output type parameter is set to Integer, then the block maps a phase
difference of
θ + 2πm/M
to m, where θ is the Phase offset parameter and m is an integer between 0 and
M-1.
If the Output type parameter is set to Bit and the M-ary number parameter
has the form 2K for some positive integer K, then the block outputs binary
representations of integers between 0 and M-1. It outputs a group of K bits,
called a binary word, for each symbol.
In binary output mode, the Constellation ordering parameter indicates how
the block maps an integer to a corresponding group of K output bits. See the
reference pages for the M-DPSK Modulator Baseband and M-PSK Modulator
Baseband blocks for details.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. If it is greater than
1, then the demodulated signal is delayed by one output sample. For more
information, see “Upsampled Signals and Rate Changes” on page 2-72.

4-264
 M-DPSK Demodulator Baseband

Dialog Box

M-ary number
The number of possible modulated symbols that can immediately follow a
given symbol.
Output type
Determines whether the output consists of integers or groups of bits.
Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Phase offset (rad)
The phase difference between the previous and current modulated symbols
when the input is zero.
Samples per symbol
The number of input samples that represent each modulated symbol.

4-265
M-DPSK Demodulator Baseband

Pair Block M-DPSK Modulator Passband

See Also DBPSK Demodulator Baseband, DQPSK Demodulator Baseband, M-PSK

Demodulator Baseband

References [1] Pawula, R. F. “On M-ary DPSK Transmission Over Terrestrial and Satellite
Channels.” IEEE Transactions on Communications, vol. COM-32, July 1984.
752-761.

4-266
 M-DPSK Demodulator Passband

Purpose 4M-DPSK Demodulator Passband

Demodulate DPSK-modulated data

Library PM, in Digital Passband sublibrary of Modulation

Description The M-DPSK Demodulator Passband block demodulates a signal that was
modulated using the M-ary differential phase shift keying method. The input
is a passband representation of the modulated signal. The input and output for
this block are discrete-time signals. The input must be a sample-based scalar
signal.
The M-ary number parameter, M, is the number of possible output symbols
that can immediately follow a given output symbol. The block compares the
current symbol to the previous symbol. The block’s first output is the initial
condition of zero because there is no previous symbol.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, M-DPSK Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• M-ary number
• Output type
• Constellation ordering

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1

4-267
M-DPSK Demodulator Passband

• Input sample time = K*Symbol period*Baseband samples per symbol for

some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

Dialog Box

M-ary number
The number of possible modulated symbols that can immediately follow a
given symbol.
Output type
Determines whether the output consists of integers or groups of bits.

4-268
 M-DPSK Demodulator Passband

Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.

Pair Block M-DPSK Modulator Passband

See Also M-DPSK Demodulator Baseband

References [1] Pawula, R. F. “On M-ary DPSK Transmission Over Terrestrial and Satellite
Channels.” IEEE Transactions on Communications, vol. COM-32, July 1984.
752-761.

4-269
M-DPSK Modulator Baseband

Purpose 4M-DPSK Modulator Baseband

Modulate using the M-ary differential phase shift keying method

Library PM, in Digital Baseband sublibrary of Modulation

Description The M-DPSK Modulator Baseband block modulates using the M-ary
differential phase shift keying method. The output is a baseband
representation of the modulated signal. The M-ary number parameter, M, is
the number of possible output symbols that can immediately follow a given
output symbol.
The input must be a discrete-time signal.

Inputs and Constellation Types

If the Input type parameter is set to Integer, then valid input values are
integers between 0 and M-1. In this case, the input can be either a scalar or a
frame-based column vector. If the first input is m, then the modulated symbol
is
exp(jθ + jπm/2)
where θ is the Phase offset parameter. If a successive input is m, then the
modulated symbol is the previous modulated symbol multiplied by
exp(jθ + jπm/2).
If the Input type parameter is set to Bit and the M-ary number parameter has
the form 2K for some positive integer K, then the block accepts binary
representations of integers between 0 and M-1. It modulates each group of K
bits, called a binary word. The input can be either a vector of length K or a
frame-based column vector whose length is an integer multiple of K.
In binary input mode, the Constellation ordering parameter indicates how
the block maps a group of K input bits to a corresponding phase difference. The
Binary option uses a natural binary-to-integer mapping, while the Gray option
uses a Gray-coded assignment of phase differences. For example, the table

4-270
 M-DPSK Modulator Baseband

below indicates the assignment of phase difference to three-bit inputs, for both
the Binary and Gray options. θ is the Phase offset parameter.

Input Binary-Coded Phase Gray-Coded Phase

Differences Differences

[0 0 0] jθ jθ

[0 0 1] jθ + jπ/2 jθ + jπ/2
[0 1 0] jθ + jπ2/2 jθ + jπ3/2

[0 1 1] jθ + jπ3/2 jθ + jπ2/2

[1 0 0] jθ + jπ4/2 jθ + jπ6/2

[1 0 1] jθ + jπ5/2 jθ + jπ7/2

[1 1 0] jθ + jπ6/2 jθ + jπ5/2

[1 1 1] jθ + jπ7/2 jθ + jπ4/2

For more details about the Binary and Gray options, see the reference page for
the M-PSK Modulator Baseband block. The signal constellation for that block
corresponds to the arrangement of phase differences for this block.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-271
M-DPSK Modulator Baseband

Dialog Box

M-ary number
The number of possible output symbols that can immediately follow a given
output symbol.
Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Phase offset (rad)
The phase difference between the previous and current modulated symbols
when the input is zero.

4-272
 M-DPSK Modulator Baseband

Samples per symbol

The number of output samples that the block produces for each integer or
binary word in the input.

Pair Block M-DPSK Demodulator Baseband

See Also DBPSK Modulator Baseband, DQPSK Modulator Baseband, M-PSK

Modulator Baseband

References [1] Pawula, R. F. “On M-ary DPSK Transmission Over Terrestrial and Satellite
Channels.” IEEE Transactions on Communications, vol. COM-32, July 1984.
752-761.

4-273
M-DPSK Modulator Passband

Purpose 4M-DPSK Modulator Passband

Modulate using the M-ary differential phase shift keying method

Library PM, in Digital Passband sublibrary of Modulation

Description The M-DPSK Modulator Passband block modulates using the M-ary
differential phase shift keying method. The output is a passband
representation of the modulated signal. The M-ary number parameter, M, is
the number of possible output symbols that can immediately follow a given
output symbol.
This block uses the baseband equivalent block, M-DPSK Modulator Baseband,
for internal computations and converts the resulting baseband signal to a
passband representation. The following parameters in this block are the same
as those of the baseband equivalent block:
• M-ary number
• Input type
• Constellation ordering
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.
The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1

4-274
 M-DPSK Modulator Passband

• Symbol period = K*Output sample time*Baseband samples per symbol

for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

M-ary number
The number of possible output symbols that can immediately follow a given
output symbol.
Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.

4-275
M-DPSK Modulator Passband

Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block M-DPSK Demodulator Passband

See Also M-DPSK Modulator Baseband

References [1] Pawula, R. F. “On M-ary DPSK Transmission Over Terrestrial and Satellite
Channels.” IEEE Transactions on Communications, vol. COM-32, July 1984.
752-761.

4-276
 M-FSK Demodulator Baseband

Purpose 4M-FSK Demodulator Baseband

Demodulate FSK-modulated data

Library FM, in Digital Baseband sublibrary of Modulation

Description The M-FSK Demodulator Baseband block demodulates a signal that was
modulated using the M-ary frequency shift keying method. The input is a
baseband representation of the modulated signal. The input and output for this
block are discrete-time signals. The input can be either a scalar or a
frame-based column vector.
The M-ary number parameter, M, is the number of frequencies in the
modulated signal. The Frequency separation parameter is the distance, in
Hz, between successive frequencies of the modulated signal.

Binary or Integer Outputs

If the Output type parameter is set to Integer, then the block outputs integers
between 0 and M-1.
If the Output type parameter is set to Bit and the M-ary number parameter
has the form 2K for some positive integer K, then the block outputs binary
representations of integers between 0 and M-1. It outputs a group of K bits,
called a binary word, for each symbol.
In binary output mode, the Symbol set ordering parameter indicates how the
block maps an integer to a corresponding group of K output bits. See the
reference pages for the M-FSK Modulator Baseband and M-PSK Modulator
Baseband blocks for details.
Whether the output is an integer or a binary representation of an integer, the
block maps the highest frequency to the integer 0 and maps the lowest
frequency to the integer M-1. In baseband simulation, the lowest frequency is
the negative frequency with the largest absolute value.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-277
M-FSK Demodulator Baseband

Dialog Box

M-ary number
The number of frequencies in the modulated signal.
Output type
Determines whether the output consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Symbol set ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Frequency separation (Hz)
The distance between successive frequencies in the modulated signal.
Samples per symbol
The number of input samples that represent each modulated symbol.

4-278
 M-FSK Demodulator Baseband

Pair Block M-FSK Modulator Baseband

See Also CPFSK Demodulator Baseband

4-279
M-FSK Demodulator Passband

Purpose 4M-FSK Demodulator Passband

Modulate using the M-ary frequency shift keying method

Library FM, in Digital Passband sublibrary of Modulation

Description The M-FSK Demodulator Passband block demodulates a signal that was
modulated using the M-ary frequency shift keying method. The input is a
passband representation of the modulated signal. The M-ary number
parameter, M, is the number of frequencies in the modulated signal.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, M-FSK Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• M-ary number
• Output type
• Signal set ordering
• Frequency separation
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1
• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

4-280
 M-FSK Demodulator Passband

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

Dialog Box

M-ary number
The number of frequencies in the modulated signal.
Output type
Determines whether the output consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Symbol set ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.

4-281
M-FSK Demodulator Passband

Frequency separation (Hz)

The distance between successive frequencies in the modulated signal.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.

Pair Block M-FSK Modulator Passband

See Also M-FSK Demodulator Baseband, CPFSK Demodulator Passband

4-282
 M-FSK Modulator Baseband

Purpose 4M-FSK Modulator Baseband

Modulate using the M-ary frequency shift keying method

Library FM, in Digital Baseband sublibrary of Modulation

Description The M-FSK Modulator Baseband block modulates using the M-ary frequency
shift keying method. The output is a baseband representation of the modulated
signal.
The M-ary number parameter, M, is the number of frequencies in the
modulated signal. The Frequency separation parameter is the distance, in
Hz, between successive frequencies of the modulated signal. If the Phase
continuity parameter is set to Continuous, then the modulated signal
maintains its phase even when it changes its frequency. If the Phase
continuity parameter is set to Discontinuous, then the modulated signal
comprises portions of M sinusoids of different frequencies; thus, a change in the
input value might cause a change in the phase of the modulated signal.

Input Signal Values

The input and output for this block are discrete-time signals. The Input type
parameter determines whether the block accepts integers between 0 and M-1,
or binary representations of integers:

• If Input type is set to Integer, then the block accepts integers. The input can
be either a scalar or a frame-based column vector.
• If Input type is set to Bit, then the block accepts groups of K bits, called
binary words. The input can be either a vector of length K or a frame-based
column vector whose length is an integer multiple of K. The Symbol set
ordering parameter indicates how the block assigns binary words to
corresponding integers.
- If Symbol set ordering is set to Binary, then the block uses a natural
binary-coded ordering.
- If Symbol set ordering is set to Gray, then the block uses a Gray-coded
ordering. For details about the Gray coding, see the reference page for the
M-PSK Modulator Baseband block.
Whether the input is an integer or a binary representation of an integer, the
block maps the integer 0 to the highest frequency and maps the integer M-1 to
the lowest frequency. In baseband simulation, the lowest frequency is the
negative frequency with the largest absolute value.

4-283
M-FSK Modulator Baseband

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

M-ary number
The number of frequencies in the modulated signal.
Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.

4-284
 M-FSK Modulator Baseband

Symbol set ordering

Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Frequency separation (Hz)
The distance between successive frequencies in the modulated signal.
Phase continuity
Determines whether the modulated signal changes phases in a continuous
or discontinuous way.
Samples per symbol
The number of output samples that the block produces for each integer or
binary word in the input.

Pair Block M-FSK Demodulator Baseband

See Also CPFSK Modulator Baseband

4-285
M-FSK Modulator Passband

Purpose 4M-FSK Modulator Passband

Modulate using the M-ary frequency shift keying method

Library FM, in Digital Passband sublibrary of Modulation

Description The M-FSK Modulator Passband block modulates using the M-ary frequency
shift keying method. The output is a passband representation of the modulated
signal. The M-ary number parameter, M, is the number of frequencies in the
modulated signal.
This block uses the baseband equivalent block, M-FSK Modulator Baseband,
for internal computations and converts the resulting baseband signal to a
passband representation. The following parameters in this block are the same
as those of the baseband equivalent block:
• M-ary number
• Input type
• Symbol set ordering
• Frequency separation
• Phase continuity
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Whether the input is an integer or a binary representation of an integer, the

block maps the integer 0 to the highest frequency and maps the integer M-1 to
the lowest frequency.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.

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 M-FSK Modulator Passband

The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1
• Symbol period = K*Output sample time*Baseband samples per symbol
for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

M-ary number
The number of frequencies in the modulated signal.

4-287
M-FSK Modulator Passband

Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Symbol set ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Frequency separation (Hz)
The distance between successive frequencies in the modulated signal.
Phase continuity
Determines whether the modulated signal changes phases in a continuous
or discontinuous way.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block M-FSK Demodulator Passband

See Also M-FSK Modulator Baseband, CPFSK Modulator Passband

4-288
 Modulo Integrator

Purpose 4Modulo Integrator

Integrate in continuous time and reduce by a modulus

Library Integrators, in Basic Comm Functions

Description The Modulo Integrator block integrates its input signal in continuous time and
then reduces modulo the Absolute value bound parameter. If the Absolute
value bound parameter is K, then the block output is strictly between -K and
K.
The input must be sample-based. The block processes each vector element
independently.
This block’s functionality is useful for monotonically increasing or decreasing
functions, but works with any integrable function. This block uses the Forward
Euler integration method.

Dialog Box

Absolute value bound

The modulus by which the integration result is reduced. This parameter
must be nonzero.
Initial condition
The initial condition for integration.

See Also Discrete Modulo Integrator, Integrator (Simulink)

4-289
M-PAM Demodulator Baseband

Purpose 4M-PAM Demodulator Baseband

Demodulate PAM-modulated data

Library AM, in Digital Baseband sublibrary of Modulation

Description The M-PAM Demodulator Baseband block demodulates a signal that was
modulated using the M-ary pulse amplitude modulation. The input is a
baseband representation of the modulated signal.
The signal constellation has M points, where M is the M-ary number
parameter. M must be an even integer. The block scales the signal constellation
based on how you set the Normalization method parameter. For details on the
constellation and its scaling, see the reference page for the M-PAM Modulator
Baseband block.
The input can be either a scalar or a frame-based column vector.

Output Signal Values

The Output type parameter determines whether the block produces integers
or binary representations of integers. If Output type is set to Integer, then the
block produces integers. If Output type is set to Bit, then the block produces a
group of K bits, called a binary word, for each symbol. The Constellation
ordering parameter indicates how the block assigns binary words to points of
the signal constellation. More details are on the reference page for the M-PAM
Modulator Baseband block.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer.
For more information, see “Upsampled Signals and Rate Changes” on page
2-72.

4-290
 M-PAM Demodulator Baseband

Dialog Box

M-ary number
The number of points in the signal constellation. It must be an even
integer.
Output type
Determines whether the output consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

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M-PAM Demodulator Baseband

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power of the symbols in the constellation. This field appears
only when Normalization method is set to Peak Power.
Samples per symbol
The number of input samples that represent each modulated symbol.

Pair Block M-PAM Modulator Baseband

See Also General QAM Demodulator Baseband

4-292
 M-PAM Demodulator Passband

Purpose 4M-PAM Demodulator Passband

Demodulate PAM-modulated data

Library AM, in Digital Passband sublibrary of Modulation

Description The M-PAM Demodulator Passband block demodulates a signal that was
modulated using M-ary pulse amplitude modulation. The input is a passband
representation of the modulated signal. The input must be a sample-based
scalar signal.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, M-PAM Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• M-ary number
• Output type
• Constellation ordering
• Normalization method
• Minimum distance
• Average power
• Peak power

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1

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M-PAM Demodulator Passband

• Input sample time = K*Symbol period*Baseband samples per symbol for

some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

Dialog Box

M-ary number
The number of points in the signal constellation. It must be an even
integer.

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 M-PAM Demodulator Passband

Output type
Determines whether the output consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power of the symbols in the constellation. This field appears
only when Normalization method is set to Peak Power.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.

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M-PAM Demodulator Passband

Input sample time

The sample time of the input signal.

Pair Block M-PAM Modulator Passband

See Also M-PAM Demodulator Baseband

4-296
 M-PAM Modulator Baseband

Purpose 4M-PAM Modulator Baseband

Modulate using M-ary pulse amplitude modulation

Library AM, in Digital Baseband sublibrary of Modulation

Description The M-PAM Modulator Baseband block modulates using M-ary pulse
amplitude modulation. The output is a baseband representation of the
modulated signal. The M-ary number parameter, M, is the number of points
in the signal constellation. It must be an even integer.

Constellation Size and Scaling

Baseband M-ary pulse amplitude modulation using the block’s default signal
constellation maps an integer m between 0 and M-1 to the complex value
2m - M + 1

Note This is actually a real number. The block’s output signal is a complex
data-type signal whose imaginary part is zero.

The block scales the default signal constellation based on how you set the
Normalization method parameter. The table below lists the possible scaling
conditions.

Value of Normalization method Scaling Condition

Parameter

Min. distance between symbols The nearest pair of points in the

constellation is separated by the value
of the Minimum distance parameter
Average Power The average power of the symbols in
the constellation is the Average
power parameter

Peak Power The maximum power of the symbols in

the constellation is the Peak power
parameter

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M-PAM Modulator Baseband

Input Signal Values

The input and output for this block are discrete-time signals. The Input type
parameter determines whether the block accepts integers between 0 and M-1,
or binary representations of integers.

• If Input type is set to Integer, then the block accepts integers. The input can
be either a scalar or a frame-based column vector.
• If Input type is set to Bit, then the block accepts groups of K bits, called
binary words. The input can be either a vector of length K or a frame-based
column vector whose length is an integer multiple of K. The Constellation
ordering parameter indicates how the block assigns binary words to points
of the signal constellation.
- If Constellation ordering is set to Binary, then the block uses a natural
binary-coded constellation.
- If Constellation ordering is set to Gray, then the block uses a Gray-coded
constellation.
For details about the Gray coding, see the reference page for the M-PSK
Modulator Baseband block.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

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 M-PAM Modulator Baseband

Dialog Box

M-ary number
The number of points in the signal constellation. It must be an even
integer.
Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.

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M-PAM Modulator Baseband

Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power of the symbols in the constellation. This field appears
only when Normalization method is set to Peak Power.
Samples per symbol
The number of output samples that the block produces for each integer or
binary word in the input.

Pair Block M-PAM Demodulator Baseband

See Also General QAM Modulator Baseband

4-300
 M-PAM Modulator Passband

Purpose 4M-PAM Modulator Passband

Modulate using M-ary pulse amplitude modulation

Library AM, in Digital Passband sublibrary of Modulation

Description The M-PAM Modulator Passband block modulates using M-ary pulse
amplitude modulation. The output is a passband representation of the
modulated signal. The M-ary number parameter, M, is the number of points
in the signal constellation. It must be an even integer.
This block uses the baseband equivalent block, M-PAM Modulator Baseband,
for internal computations and converts the resulting baseband signal to a
passband representation. The following parameters in this block are the same
as those of the baseband equivalent block:
• M-ary number
• Input type
• Constellation ordering
• Normalization method
• Minimum distance
• Average power
• Peak power
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.

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M-PAM Modulator Passband

The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1
• Symbol period = K*Output sample time*Baseband samples per symbol
for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

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 M-PAM Modulator Passband

M-ary number
The number of points in the signal constellation. It must be an even
integer.
Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power of the symbols in the constellation. This field appears
only when Normalization method is set to Peak Power.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.

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M-PAM Modulator Passband

Carrier initial phase (rad)

The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block M-PAM Demodulator Passband

See Also M-PAM Modulator Baseband

4-304
 M-PSK Demodulator Baseband

Purpose 4M-PSK Demodulator Baseband

Demodulate PSK-modulated data

Library PM, in Digital Baseband sublibrary of Modulation

Description The M-PSK Demodulator Baseband block demodulates a signal that was
modulated using the M-ary phase shift keying method. The input is a baseband
representation of the modulated signal. The input and output for this block are
discrete-time signals. The input can be either a scalar or a frame-based column
vector. The M-ary number parameter, M, is the number of points in the signal
constellation.

Binary or Integer Outputs

If the Output type parameter is set to Integer, then the block maps the point
exp(jθ + j2πm/M)
to m, where θ is the Phase offset parameter and m is an integer between 0 and
M-1.
If the Output type parameter is set to Bit and the M-ary number parameter
has the form 2K for some positive integer K, then the block outputs binary
representations of integers between 0 and M-1. It outputs a group of K bits,
called a binary word, for each symbol.
In binary output mode, the Constellation ordering parameter indicates how
the block maps an integer to a corresponding group of K output bits. See the
reference page for the M-PSK Modulator Baseband block for details.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-305
M-PSK Demodulator Baseband

Dialog Box

M-ary number
The number of points in the signal constellation.
Output type
Determines whether the output consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Phase offset (rad)
The phase of the zeroth point of the signal constellation.
Samples per symbol
The number of input samples that represent each modulated symbol.

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 M-PSK Demodulator Baseband

Pair Block M-PSK Modulator Baseband

See Also BPSK Demodulator Baseband, QPSK Demodulator Baseband, M-DPSK

Demodulator Baseband

4-307
M-PSK Demodulator Passband

Purpose 4M-PSK Demodulator Passband

Demodulate PSK-modulated data

Library PM, in Digital Passband sublibrary of Modulation

Description The M-PSK Demodulator Passband block demodulates a signal that was
modulated using the M-ary phase shift keying method. The input is a passband
representation of the modulated signal. The M-ary number parameter, M, is
the number of points in the signal constellation.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, M-PSK Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• M-ary number
• Output type
• Constellation ordering
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1
• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

4-308
 M-PSK Demodulator Passband

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

Dialog Box

M-ary number
The number of points in the signal constellation.
Output type
Determines whether the output consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.

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M-PSK Demodulator Passband

Symbol period (s)

The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.

Pair Block M-PSK Modulator Passband

See Also M-PSK Demodulator Baseband

4-310
 M-PSK Modulator Baseband

Purpose 4M-PSK Modulator Baseband

Modulate using the M-ary phase shift keying method

Library PM, in Digital Baseband sublibrary of Modulation

Description The M-PSK Modulator Baseband block modulates using the M-ary phase shift
keying method. The output is a baseband representation of the modulated
signal. The M-ary number parameter, M, is the number of points in the signal
constellation.
Baseband M-ary phase shift keying modulation with a phase offset of θ maps
an integer m between 0 and M-1 to the complex value
exp(jθ + j2πm/M)
The input and output for this block are discrete-time signals. To use integers
between 0 and M-1 as input values, set the Input type parameter to Integer.
In this case, the input can be either a scalar or a frame-based column vector.
Alternative configurations of the block determine how the block interprets its
input and arranges its output, as explained in the sections below.

Binary Inputs
If the Input type parameter is set to Bit and the M-ary number parameter has
the form 2K for some positive integer K, then the block accepts binary
representations of integers between 0 and M-1. It modulates each group of K
bits, called a binary word. The input can be either a vector of length K or a
frame-based column vector whose length is an integer multiple of K.
In binary input mode, the Constellation ordering parameter indicates how
the block maps a group of K input bits to a corresponding integer. Choices are
Binary and Gray. For more information, see “Binary-Valued and
Integer-Valued Signals” on page 2-68.
If Constellation ordering is set to Gray, then the block uses a Gray-coded
signal constellation; as a result, binary representations that differ in more than
one bit cannot map to consecutive integers modulo M. The explicit mapping is
described in “Algorithm” below.

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M-PSK Modulator Baseband

Frame-Based Inputs
If the input is a frame-based column vector, then the block processes several
integers or several binary words, in each time step. (If the Input type
parameter is set to Bit, then a binary word consists of log2(M) bits.)
For example, the schematics below illustrate how the block processes two 8-ary
integers or binary words in one time step. The signals involved are all
frame-based column vectors. In both cases, the Phase offset parameter is 0.

6 -j Input type parameter is Integer.

2 j

1
1
Input type parameter is Bit and
0 -j
Constellation ordering
0 j parameter is Binary.
1
0

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-312
 M-PSK Modulator Baseband

Dialog Box

M-ary number
The number of points in the signal constellation.
Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Phase offset (rad)
The phase of the zeroth point of the signal constellation.

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M-PSK Modulator Baseband

Samples per symbol

The number of output samples that the block produces for each integer or
binary word in the input.

Algorithm If the Constellation ordering parameter is set to Gray, then the block
internally assigns the binary inputs to points of a predefined Gray-coded signal
constellation. The block’s predefined M-ary Gray-coded signal constellation
assigns the binary representation
de2bi(bitxor(m,floor(m/2)), log2(M),'left-msb')

to the mth phase. The zeroth phase in the constellation is the Phase offset
parameter, and successive phases are counted in a counterclockwise direction.

Note This transformation might seem counterintuitive because it constitutes

a Gray-to-binary mapping. However, the block must use it to impose a Gray
ordering on the signal constellation, which has a natural binary ordering.

In other words, if the block input is the natural binary representation, u, of the
integer U, then the block output has phase
jθ + j2πm/M
where θ is the Phase offset parameter and m is an integer between 0 and M-1
that satisfies

m XOR m ⁄ 2 = U
For example, if M = 8, then the binary representations that correspond to the
zeroth through seventh phases are below.
M = 8; m = [0:M-1]';
de2bi(bitxor(m,floor(m/2)), log2(M),'left-msb')

ans =

0 0 0
0 0 1
0 1 1
0 1 0

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 M-PSK Modulator Baseband

1 1 0
1 1 1
1 0 1
1 0 0

Below is the 8-ary Gray-coded constellation that the block uses if the Phase
offset parameter is π/8.

011 001

010 000

110 100

111 101

Pair Block M-PSK Demodulator Baseband

See Also BPSK Modulator Baseband, QPSK Modulator Baseband, M-DPSK Modulator
Baseband

4-315
M-PSK Modulator Passband

Purpose 4M-PSK Modulator Passband

Modulate using the M-ary phase shift keying method

Library PM, in Digital Passband sublibrary of Modulation

Description The M-PSK Modulator Passband block modulates using the M-ary phase shift
keying method. The output is a passband representation of the modulated
signal. The M-ary number parameter, M, is the number of points in the signal
constellation.
This block uses the baseband equivalent block, M-PSK Modulator Baseband,
for internal computations and converts the resulting baseband signal to a
passband representation. The following parameters in this block are the same
as those of the baseband equivalent block:
• M-ary number
• Input type
• Constellation ordering
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.
The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1

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 M-PSK Modulator Passband

• Symbol period = K*Output sample time*Baseband samples per symbol

for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

M-ary number
The number of points in the signal constellation.
Input type
Indicates whether the input consists of integers or groups of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.

4-317
M-PSK Modulator Passband

Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block M-PSK Demodulator Passband

See Also M-PSK Modulator Baseband

4-318
 MSK Demodulator Baseband

Purpose 4MSK Demodulator Baseband

Demodulate MSK-modulated data

Library CPM, in Digital Baseband sublibrary of Modulation

Description The MSK Demodulator Baseband block demodulates a signal that was
modulated using the minimum shift keying method. The input is a baseband
representation of the modulated signal. The Phase offset parameter is the
initial phase of the modulated waveform.

Traceback Length and Output Delays

Internally, this block creates a trellis description of the modulation scheme and
uses the Viterbi algorithm. The Traceback length parameter, D, in this block
is the number of trellis branches used to construct each traceback path. D
influences the output delay, which is the number of zero symbols that precede
the first meaningful demodulated value in the output.

• If the input signal is sample-based, then the delay consists of D+1 zero
symbols.
• If the input signal is frame-based, then the delay consists of D zero symbols.

Inputs and Outputs

The input can be either a scalar or a frame-based column vector. If the Output
type parameter is set to Integer, then the block produces values of 1 and -1. If
the Output type parameter is set to Bit, then the block produces values of 0
and 1.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-319
MSK Demodulator Baseband

Dialog Box

Output type
Determines whether the output consists of bipolar or binary values.
Phase offset (rad)
The initial phase of the modulated waveform.
Samples per symbol
The number of input samples that represent each modulated symbol.
Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.

Pair Block MSK Modulator Baseband

See Also CPM Demodulator Baseband, Viterbi Decoder

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-320
 MSK Demodulator Passband

Purpose 4MSK Demodulator Passband

Demodulate MSK-modulated data

Library CPM, in Digital Passband sublibrary of Modulation

Description The MSK Demodulator Passband block demodulates a signal that was
modulated using the minimum shift keying method. The input is a passband
representation of the modulated signal.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, MSK Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• Output type
• Traceback length
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1
• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

4-321
MSK Demodulator Passband

Dialog Box

Output type
Determines whether the output consists of bipolar or binary values.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.

4-322
 MSK Demodulator Passband

Input sample time

The sample time of the input signal.
Traceback length
The number of trellis branches that the Viterbi Decoder block uses to
construct each traceback path.

Pair Block MSK Modulator Passband

See Also MSK Demodulator Baseband, Viterbi Decoder

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-323
MSK Modulator Baseband

Purpose 4MSK Modulator Baseband

Modulate using the minimum shift keying method

Library CPM, in Digital Baseband sublibrary of Modulation

Description The MSK Modulator Baseband block modulates using the minimum shift
keying method. The output is a baseband representation of the modulated
signal.
The Modulation index parameter times π radians is the phase shift due to the
latest symbol when that symbol is the integer 1. The Phase offset parameter
is the initial phase of the output waveform, measured in radians.

Input Attributes
The input can be either a scalar or a frame-based column vector. If the Input
type parameter is set to Integer, then the block accepts values of 1 and -1. If
the Input type parameter is set to Bit, then the block accepts values of 0 and 1.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

4-324
 MSK Modulator Baseband

Input type
Indicates whether the input consists of bipolar or binary values.
Phase offset (rad)
The initial phase of the output waveform.
Samples per symbol
The number of output samples that the block produces for each integer or
bit in the input.

Pair Block MSK Demodulator Baseband

See Also CPM Modulator Baseband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-325
MSK Modulator Passband

Purpose 4MSK Modulator Passband

Modulate using the minimum shift keying method

Library CPM, in Digital Passband sublibrary of Modulation

Description The MSK Modulator Passband block modulates using the minimum shift
keying method. The output is a passband representation of the modulated
signal.
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M), containing values of 0 and 1. If the
Input type parameter is Integer, then the input must be a scalar containing
values of 1 and -1.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.
The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1
• Symbol period = K*Output sample time*Baseband samples per symbol
for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

4-326
 MSK Modulator Passband

Dialog Box

Input type
Indicates whether the input consists of bipolar or binary values.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block MSK Demodulator Passband

4-327
MSK Modulator Passband

See Also MSK Modulator Baseband

References [1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase
Modulation. New York: Plenum Press, 1986.

4-328
 Mu-Law Compressor

Purpose Implement µ-law compressor for source coding

4Mu-Law Compressor

Library Source Coding

Description The Mu-Law Compressor block implements a µ-law compressor for the input
signal. The formula for the µ-law compressor is

V log ( 1 + µ x ⁄ V )
y = --------------------------------------------- sgn ( x )
log ( 1 + µ )
where µ is the µ-law parameter of the compressor, V is the peak magnitude of
x, log is the natural logarithm, and sgn is the signum function (sign in
MATLAB).
The input can have any shape or frame status. This block processes each vector
element independently.

Dialog Box

mu value
The µ-law parameter of the compressor.
Peak signal magnitude
The peak value of the input signal. This is also the peak value of the output.
Pair Block Mu-Law Expander

See Also A-Law Compressor

References [1] Sklar, Bernard. Digital Communications: Fundamentals and Applications.

Englewood Cliffs, N.J.: Prentice-Hall, 1988.

4-329
Mu-Law Expander

Purpose Implement µ-law expander for source coding

4Mu-Law Expander

Library Source Coding

Description The Mu-Law Expander block recovers data that the Mu-Law Compressor block
compressed. The formula for the µ-law expander, shown below, is the inverse
of the compressor function.

V y log ( 1 + µ ) ⁄ V
x = ---- ( e – 1 ) sgn ( y )
µ
The input can have any shape or frame status. This block processes each vector
element independently.

Dialog Box

mu value
The µ-law parameter of the compressor.
Peak signal magnitude
The peak value of the input signal. This is also the peak value of the output.

Pair Block Mu-Law Compressor

See Also A-Law Expander

References [1] Sklar, Bernard. Digital Communications: Fundamentals and Applications.

Englewood Cliffs, N.J.: Prentice-Hall, 1988.

4-330
 Multipath Rayleigh Fading Channel

Purpose 4Multipath Rayleigh Fading Channel

Simulate a multipath Rayleigh fading propagation channel

Library Channels

Description The Multipath Rayleigh Fading Channel block implements a baseband

simulation of a multipath Rayleigh fading propagation channel. This block is
useful for modeling mobile wireless communication systems. For details about
fading channels, see the works listed in “References” on page 4-333.
The input can be either a scalar or a frame-based column vector. The input is
a complex signal.
Relative motion between the transmitter and receiver causes Doppler shifts in
the signal frequency. The Doppler frequency parameter is the maximum
Doppler shift that the signal undergoes. The Jakes PSD (power spectral
density) determines the spectrum of the Rayleigh process.
Since a multipath channel reflects signals at multiple places, a transmitted
signal travels to the receiver along several paths that may have different
lengths and hence different associated time delays. Fading occurs when signals
traveling along different paths interfere with each other. In the block’s
parameter mask, the Delay vector specifies the time delay for each path. If the
Normalize gain vector to 0 dB overall gain box is unchecked, then the Gain
vector specifies the gain for each path. If the box is checked, then the block
uses a multiple of Gain vector instead of the Gain vector itself, choosing the
scaling factor so that the channel’s effective gain considering all paths is 0 dB.
The number of paths is the length of Delay vector or Gain vector, whichever
is larger. If both of these parameters are vectors, then they must have the same
length; if exactly one of these parameters is a scalar, then the block expands it
into a vector whose size matches that of the other vector parameter.
The Sample time parameter is the time between successive elements of the
input signal. Note that if the input is a frame-based column vector of length n,
then the frame period (as Simulink’s Probe block reports, for example) is
n*Sample time.
The block multiplies the input signal by samples of a Rayleigh-distributed
complex random process. The scalar Initial seed parameter seeds the random
number generator.

4-331
Multipath Rayleigh Fading Channel

Dialog Box

Doppler frequency (Hz)

A positive scalar that indicates the maximum Doppler shift.
Sample time
The period of each element of the input signal.
Delay vector (s)
A vector that specifies the propagation delay for each path.
Gain vector (dB)
A vector that specifies the gain for each path.
Normalize gain vector to 0 dB overall gain
Checking this box causes the block to scale the Gain vector parameter so
that the channel’s effective gain (considering all paths) is 0 decibels.
Initial seed
The scalar seed for the Gaussian noise generator.

4-332
 Multipath Rayleigh Fading Channel

Algorithm This implementation is based on the direct form simulator described in [1].
Some wireless applications, such as standard GSM (Global System for Mobile
Communication) systems, prefer to specify Doppler shifts in terms of the speed
of the mobile. If the mobile moves at speed v making an angle of θ with the
direction of wave motion, then the Doppler shift is
fd = (vf/c)cos θ

where f is the transmission carrier frequency and c is the speed of light. The
Doppler frequency is the maximum Doppler shift arising from motion of the
mobile.

See Also Rayleigh Noise Generator, Rician Fading Channel

References [1] Fechtel, Stefan A. “A Novel Approach to Modeling and Efficient Simulation
of Frequency-Selective Fading Radio Channels.” IEEE Journal on Selected
Areas in Communications, vol. 11, April 1993. 422-431.
[2] Jakes, William C., ed. Microwave Mobile Communications. New York: IEEE
Press, 1974.
[3] Lee, William C. Y. Mobile Communications Design Fundamentals, 2nd ed.
New York: Wiley, 1993.

4-333
OQPSK Demodulator Baseband

Purpose 4OQPSK Demodulator Baseband

Demodulate OQPSK-modulated data

Library PM, in Digital Baseband sublibrary of Modulation

Description The OQPSK Demodulator Baseband block demodulates a signal that was
modulated using the offset quadrature phase shift keying method. The input is
a baseband representation of the modulated signal.
The input must be a discrete-time complex signal. The input can be either a
scalar or a frame-based column vector.
If the Output type parameter is set to Integer, then the block outputs integers
between 0 and 3. If the Output type parameter is set to Bit, then the block
outputs binary representations of such integers, in a binary-valued vector
whose length is an even number.
The input symbol period is half the period of each output integer or bit pair.
The constellation used to map bit pairs to symbols is on the reference page for
the OQPSK Modulator Baseband block.

Frame-Based Inputs
If the input is a frame-based column vector, then the block processes several
integers or several pairs of bits, in each time step. In this case, the output
sample time equals the input sample time, even though the symbol period is
half the output period.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer.

• If the input is a frame-based column vector, then the output vector contains
1/2S integers or pairs of bits for each sample in the input vector, while the
output sample time equals the input sample time.
• If the input is a sample-based scalar, then the output vector contains a single
integer or pair of bits, while the output sample time is 2S times the input
sample time.

4-334
 OQPSK Demodulator Baseband

Dialog Box

Output type
Determines whether the output consists of integers or pairs of bits.
Phase offset (rad)
The amount by which the phase of the zeroth point of the signal
constellation is shifted from π/4.
Samples per symbol
The number of input samples that represent each modulated symbol.

Pair Block OQPSK Modulator Baseband

See Also QPSK Demodulator Baseband

4-335
OQPSK Demodulator Passband

Purpose 4OQPSK Demodulator Passband

Demodulate OQPSK-modulated data

Library PM, in Digital Passband sublibrary of Modulation

Description The OQPSK Demodulator Passband block demodulates a signal that was
modulated using the offset quadrature phase shift keying method. The input is
a passband representation of the modulated signal.
If the Output type parameter is set to Integer, then the block outputs integers
between 0 and 3. If the Output type parameter is set to Bit, then the block
outputs binary representations of such integers, in binary-valued vectors of
length two. The constellation used to map bit pairs to symbols is on the
reference page for the OQPSK Modulator Passband block.
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1
• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

4-336
 OQPSK Demodulator Passband

Dialog Box

Output type
Indicates whether the output consists of integers or groups of bits.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.

4-337
OQPSK Demodulator Passband

Pair Block OQPSK Modulator Passband

See Also OQPSK Demodulator Baseband

4-338
 OQPSK Modulator Baseband

Purpose 4OQPSK Modulator Baseband

Modulate using the offset quadrature phase shift keying method

Library PM, in Digital Baseband sublibrary of Modulation

Description The OQPSK Modulator Baseband block modulates using the offset quadrature
phase shift keying method. The output is a baseband representation of the
modulated signal.
If the Input type parameter is set to Integer, then valid input values are 0, 1,
2, and 3. In this case, the input can be either a scalar or a frame-based column
vector.
If the Input type parameter is set to Bit, then the input must be a
binary-valued vector. In this case, the input can be either a vector of length two
or a frame-based column vector whose length is an even integer.
The symbol period is half the input period. The first output symbol is an initial
condition of zero that is unrelated to the input values.
The constellation used to map bit pairs to symbols is in the figure below. If the
block’s Phase offset parameter is nonzero, then this constellation is rotated by
that parameter value.

10 00

11 01

Frame-Based Inputs
If the input is a frame-based column vector, then the block processes several
integers or several pairs of bits in each time step. In this case, the output

4-339
OQPSK Modulator Baseband

sample time equals the input sample time, even though the period of each
output symbol is half the period of each integer or bit pair in the input.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter, S, is the upsampling factor. It must be a
positive integer.

• If the input is a frame-based column vector, then the output vector length is
2S times the number of integers or pairs of bits in the input vector, while the
output sample time equals the input sample time. The one-symbol initial
condition inherent in this block corresponds to the first S elements of the first
output vector.
• If the input is a sample-based scalar, then the output vector is a scalar, while
the output sample time is 1/2S times the input sample time. The one-symbol
initial condition inherent in this block corresponds to the first S samples.

Dialog Box

Input type
Indicates whether the input consists of integers or pairs of bits.

4-340
 OQPSK Modulator Baseband

Phase offset (rad)

The amount by which the phase of the zeroth point of the signal
constellation is shifted from π/4.
Samples per symbol
The number of output samples that the block produces for each integer or
pair of bits in the input.

Pair Block OQPSK Demodulator Baseband

See Also QPSK Modulator Baseband

4-341
OQPSK Modulator Passband

Purpose 4OQPSK Modulator Passband

Modulate using the offset quadrature phase shift keying method

Library PM, in Digital Passband sublibrary of Modulation

Description The OQPSK Modulator Passband block modulates using the offset quadrature
phase shift keying method. The output is a passband representation of the
modulated signal.
If the Input type parameter is set to Integer, then valid input values are 0, 1,
2, and 3. In this case, the input must be a sample-based scalar. If the Input
type parameter is set to Bit, then the input must be a binary-valued
sample-based vector of length two.
The constellation used to map bit pairs to symbols is in the figure below.

10 00

11 01

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.

4-342
 OQPSK Modulator Passband

The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1
• Symbol period = K*Output sample time*Baseband samples per symbol
for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

Input type
Indicates whether the input consists of integers or pairs of bits. If this
parameter is set to Bit, then the M-ary number parameter must be 2K for
some positive integer K.
Symbol period (s)
The symbol period, which must equal the sample time of the input.

4-343
OQPSK Modulator Passband

Baseband samples per symbol

The number of baseband samples that correspond to each integer or pair of
bits in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Output sample time
The sample time of the output signal.

Pair Block OQPSK Demodulator Passband

See Also OQPSK Modulator Baseband

4-344
 Phase-Locked Loop

Purpose 4Phase-Locked Loop

Implement a phase-locked loop to recover the phase of the input signal

Library Synchronization

Description The Phase-Locked Loop (PLL) block is a feedback control system that
automatically adjusts the phase of a locally generated signal to match the
phase of an input signal. This block is most appropriate when the input is a
narrowband signal.
This PLL has these three components:

• A multiplier used as a phase detector.

• A filter. You specify the filter’s transfer function using the Lowpass filter
numerator and Lowpass filter denominator mask parameters. Each is a
vector that gives the respective polynomial’s coefficients in order of
descending powers of s.
To design a filter, you can use functions such as butter, cheby1, and cheby2
in the Signal Processing Toolbox. The default filter is a Chebyshev type II
filter whose transfer function arises from the command below.
[num, den] = cheby2(3,40,100,'s')

• A voltage-controlled oscillator (VCO). You specify characteristics of the VCO

using the VCO quiescent frequency, VCO initial phase, and VCO output
amplitude parameters.

The input signal represents the received signal. The input must be a
sample-based scalar signal. The three output ports produce:

• The output of the filter

• The output of the phase detector
• The output of the VCO

4-345
Phase-Locked Loop

Dialog Box

Lowpass filter numerator

The numerator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter’s transfer function, represented as a
vector that lists the coefficients in order of descending powers of s.
VCO input sensitivity (Hz/V)
This value scales the input to the VCO and, consequently, the shift from
the VCO quiescent frequency value. The units of VCO input sensitivity
are Hertz per volt.
VCO quiescent frequency (Hz)
The frequency of the VCO signal when the voltage applied to it is zero. This
should match the carrier frequency of the input signal.
VCO initial phase (rad)
The initial phase of the VCO signal.

4-346
 Phase-Locked Loop

VCO output amplitude

The amplitude of the VCO signal.

See Also Baseband PLL, Linearized Baseband PLL, Charge Pump PLL

References For more information about phase-locked loops, see the works listed in
“Selected Bibliography for Synchronization” on page 2-92.

4-347
PM Demodulator Baseband

Purpose 4PM Demodulator Baseband

Demodulate PM-modulated data

Library Analog Baseband Modulation, in Modulation

Description The PM Demodulator Baseband block demodulates a signal that was

modulated using phase modulation. The input is a baseband representation of
the modulated signal. The input is complex, while the output is real. The input
must be a sample-based scalar signal.
This block uses a phase-locked loop containing a voltage-controlled oscillator
(VCO). The VCO Gain parameter specifies the input sensitivity of the VCO.
In the course of demodulating, the block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Box

Initial phase (rad)

The initial phase in the corresponding PM Modulator Baseband block.

4-348
 PM Demodulator Baseband

Modulation constant (Radians per volt)

The modulation constant in the corresponding PM Modulator Baseband
block.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
VCO gain (Hertz per volt)
The input sensitivity of the voltage-controlled oscillator.
Sample time
The sample time of the output signal.

Pair Block PM Modulator Baseband

4-349
PM Demodulator Passband

Purpose 4PM Demodulator Passband

Demodulate PM-modulated data

Library Analog Passband Modulation, in Modulation

Description The PM Demodulator Passband block demodulates a signal that was

modulated using phase modulation. The input is a passband representation of
the modulated signal. Both the input and output signals are real sample-based
scalar signals.
This block uses a phase-locked loop containing a voltage-controlled oscillator
(VCO). The VCO Gain parameter specifies the input sensitivity of the VCO.
In the course of demodulating, the block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

By the Nyquist sampling theorem, the reciprocal of the Sample time

parameter must exceed twice the Carrier frequency parameter.

Dialog Box

4-350
 PM Demodulator Passband

Carrier frequency (Hz)

The carrier frequency in the corresponding PM Modulator Passband block.
Initial phase (rad)
The carrier signal’s initial phase in the corresponding PM Modulator
Passband block.
Modulation constant (Radians per volt)
The modulation constant in the corresponding PM Modulator Passband
block.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
VCO Gain (Hertz per volt)
The input sensitivity of the voltage-controlled oscillator.
Sample time
The sample time of the output signal.

Pair Block PM Modulator Passband

4-351
PM Modulator Baseband

Purpose 4PM Modulator Baseband

Modulate using phase modulation

Library Analog Baseband Modulation, in Modulation

Description The PM Modulator Baseband block modulates using phase modulation. The
output is a baseband representation of the modulated signal. The input signal
is real, while the output signal is complex. The input must be a sample-based
scalar signal.
If the input is u(t) as a function of time t, then the output is

exp ( jθ + jKc u ( t ) )

where θ is the Initial phase parameter and Kc is the Modulation constant

parameter.

Dialog Box

Initial phase (rad)

The phase of the modulated signal when the input is zero.
Modulation constant (Radians per volt)
Modulation constant Kc.

Pair Block PM Demodulator Baseband

4-352
 PM Modulator Passband

Purpose 4PM Modulator Passband

Modulate using phase modulation

Library Analog Passband Modulation, in Modulation

Description The PM Modulator Passband block modulates using phase modulation. The
output is a passband representation of the modulated signal. The output
signal’s frequency varies with the input signal’s amplitude. Both the input and
output signals are real sample-based scalar signals.
If the input is u(t) as a function of time t, then the output is

cos ( 2πf c t + K c u ( t ) + θ )

where fc is the Carrier frequency parameter, θ is the Initial phase parameter,

and Kc is the Modulation constant parameter.
An appropriate Carrier frequency value is generally much higher than the
highest frequency of the input signal. To avoid having to use a high carrier
frequency and consequently a high sampling rate, you can use baseband
simulation (PM Modulator Baseband block) instead of passband simulation.

Dialog Box

Carrier frequency (Hz)

The frequency of the carrier.

4-353
PM Modulator Passband

Initial phase (rad)

The initial phase of the carrier in radians.
Modulation constant (Radians per volt)
The modulation constant Kc.
Symbol interval
Inf by default. To use this block to model PSK, set this parameter to the
length of time required to transmit a single information bit.

Pair Block PM Demodulator Passband

See Also PM Modulator Baseband

4-354
 PN Sequence Generator

Purpose 4PN Sequence Generator

Generate pseudonoise sequence

Library Comm Sources

Description The PN Sequence Generator block generates a sequence of pseudorandom

binary numbers. A pseudonoise sequence can be used in a pseudorandom
scrambler and descrambler. It can also be used in a direct-sequence
spread-spectrum system.
Below is a schematic of the pseudorandom sequence generator. All adders
perform addition modulo 2.

PN sequence
1 2 M-1 M

+ + +

All M registers in the generator update their values at each time step. The
state of each switch is defined by the generator polynomial, which is a
polynomial in z-1 having binary coefficients. The constant term of the generator
polynomial must be 1. You can specify the Generator polynomial parameter
using either of these formats:

• A vector of coefficients of the polynomial, starting with the constant term and
proceeding in order of increasing powers of z-1. The first and last elements
must be 1.
• A vector containing the exponents of z (not z-1) for the nonzero terms of the
polynomial. The first element must be zero.

For example, p = [1 0 0 0 0 0 1 0 1] and p = [0 -6 -8] represent the same

polynomial p(z) = 1 + z-6 + z-8.
It is very important that the Initial states parameter have a suitable value.
The initial state of at least one of the registers must be nonzero in order to
generate a nonzero sequence. The length of the Initial states vector must equal
the order of the generator polynomial, and its elements must be binary
numbers. If the Generator polynomial parameter is a vector that lists the

4-355
PN Sequence Generator

coefficients in order, then the order of the generator polynomial is one less than
the vector length.

Attributes of Output Signal

If the Frame-based outputs box is checked, then the output signal is a
frame-based column vector whose length is the Samples per frame parameter.
Otherwise, the output signal is a one-dimensional scalar.

Dialog Box

Generator polynomial
A polynomial that determines the shift register’s feedback connections.
Initial states
A vector of initial states of the shift registers.
Sample time
The period of each element of the output signal.
Frame-based outputs
Determines whether the output is frame-based or sample-based.

4-356
 PN Sequence Generator

Samples per frame

The number of samples in a frame-based output signal. This field is active
only if Frame-based outputs is checked.

See Also Scrambler

4-357
Poisson Int Generator

Purpose 4Poisson Int Generator

Generate Poisson-distributed random integers

Library Comm Sources

Description The Poisson Int Generator block generates random integers using a Poisson
distribution. The probability of generating a nonnegative integer k is
λkexp(-λ) / (k!), where λ is a positive number known as the Poisson parameter.
You can use the Poisson Int Generator to generate noise in a binary
transmission channel. In this case, the Poisson parameter Lambda should be
less than 1, usually much less.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret
vector parameters as 1-D parameters. See “Signal Attribute Parameters for
Random Sources” on page 2-7 for more details.
The number of elements in the Initial seed parameter becomes the number of
columns in a frame-based output or the number of elements in a sample-based
vector output. Also, the shape (row or column) of the Initial seed parameter
becomes the shape of a sample-based two-dimensional output signal.

Dialog Box

4-358
 Poisson Int Generator

Lambda
The Poisson parameter λ. If it is a scalar, then every element in the output
vector shares the same Poisson parameter.
Initial seed
The initial seed value for the random number generator.
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.
Samples per frame
The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.
Interpret vector parameters as 1-D
If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

See Also Random-Integer Generator; poissrnd (Statistics Toolbox)

4-359
Puncture

Purpose 4Puncture
Output the elements which correspond to 1s in the binary Puncture vector

Library Sequence Operations, in Basic Comm Functions

Description The Puncture block creates an output vector by removing selected elements of
the input vector and preserving others. The input can be a real or complex
vector of length K. The block determines which elements to remove or preserve
by using the binary Puncture vector parameter:

• If Puncture vector(k) = 0, then the kth element of the input vector does not
become part of the output vector.
• If Puncture vector(k) = 1, then the kth element of the input vector is
preserved in the output vector.

Here, k is between 1 and K. The preserved elements appear in the output

vector in the same order in which they appear in the input vector.

Frame-Based Processing
If the input is frame-based, then both it and the Puncture vector parameter
must be column vectors. The length of the Puncture vector parameter must
divide K. The block repeats the puncturing pattern, if necessary, to cover all
input elements. That is, in the bulleted items above you can replace
Puncture vector(k) by Puncture vector(n), where

n = mod(k,length(Puncture vector))
and mod is the modulus function (mod in MATLAB).

Dialog Box

4-360
 Puncture

Puncture vector
A binary vector whose pattern of 0s (1s) indicates which elements of the
input the block should remove (preserve).

Examples If the Puncture vector parameter is the six-element vector [1;0;1;1;1;0],

then the block:

• Removes the second and sixth elements from the group of six input elements.
• Sends the first, third, fourth, and fifth elements to the output vector.

The diagram below depicts the block’s operation on an input vector of [1:6],
using this Puncture vector parameter.

[1 2 3 4 5 6] Shading Key for Input Vector

= Remove entry when creating output
= Preserve entry in output

[1 3 4 5]

See Also Insert Zero

4-361
QPSK Demodulator Baseband

Purpose 4QPSK Demodulator Baseband

Demodulate QPSK-modulated data

Library PM, in Digital Baseband sublibrary of Modulation

Description The QPSK Demodulator Baseband block demodulates a signal that was
modulated using the quaternary phase shift keying method. The input is a
baseband representation of the modulated signal.
The input must be a discrete-time complex signal. The input can be either a
scalar or a frame-based column vector.
If the Output type parameter is set to Integer, then the block maps the point
exp(jθ + jπm/2)
to m, where θ is the Phase offset parameter and m is 0, 1, 2, or 3.
If the Output type parameter is set to Bit, then the output contains pairs of
binary values. The reference page for the QPSK Modulator Baseband block
shows the signal constellations for the cases when the Constellation ordering
parameter is either Binary or Gray.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer.
For more information, see “Upsampled Signals and Rate Changes” on page
2-72.

4-362
 QPSK Demodulator Baseband

Dialog Box

Output type
Determines whether the output consists of integers or pairs of bits.
Constellation ordering
Determines how the block maps each integer to a pair of output bits. This
field is active only when Output type is set to Bit.
Phase offset (rad)
The phase of the zeroth point of the signal constellation.
Samples per symbol
The number of input samples that represent each modulated symbol.

Pair Block QPSK Demodulator Baseband

See Also M-PSK Demodulator Baseband, BPSK Modulator Baseband, DQPSK

Demodulator Baseband

4-363
QPSK Modulator Baseband

Purpose 4QPSK Modulator Baseband

Modulate using the quaternary phase shift keying method

Library PM, in Digital Baseband sublibrary of Modulation

Description The QPSK Modulator Baseband block modulates using the quaternary phase
shift keying method. The output is a baseband representation of the modulated
signal.

Inputs and Constellation Types

If the Input type parameter is set to Integer, then valid input values are 0, 1,
2, and 3. If the input is m, then the output symbol is
exp(jθ + jπm/2)
where θ is the Phase offset parameter. In this case, the input can be either a
scalar or a frame-based column vector.
If the Input type parameter is set to Bit, then the input contains pairs of
binary values. The input can be either a vector of length two or a frame-based
column vector whose length is an even integer. If the Phase offset parameter
is set to pi/4, then the block uses one of the signal constellations in the figure
below, depending on whether the Constellation ordering parameter is set to
Binary or Gray.

Binary Gray

01 00 01 00

10 11 11 10

4-364
 QPSK Modulator Baseband

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

Dialog Box

Input type
Indicates whether the input consists of integers or pairs of bits.
Constellation ordering
Determines how the block maps each pair of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Phase offset (rad)
The phase of the zeroth point of the signal constellation.
Samples per symbol
The number of output samples that the block produces for each integer or
pair of bits in the input.

4-365
QPSK Modulator Baseband

Pair Block QPSK Demodulator Baseband

See Also M-PSK Modulator Baseband, BPSK Modulator Baseband, DQPSK Modulator
Baseband

4-366
 Quantizer Decode

Purpose 4Quantizer Decode

Decode quantization index according to codebook

Library Source Coding

Description The Quantizer Decode block recovers a message from a quantized signal,
converting the quantization index into the corresponding codebook value. The
Quantization codebook parameter, a vector of length N, prescribes the
possible output values. If the input is an integer k between 0 and N-1, then the
output is the (k+1)st element of Quantization codebook.
The input can be either a scalar, a sample-based vector, or a frame-based row
vector. This block processes each vector element independently. Each output
signal is a vector of the same length as the input signal.

Note The Sampled Quantizer Encode and Enabled Quantizer Encode blocks
also use a Quantization codebook parameter. The first output of those blocks
corresponds to the input of Quantizer Decode; the second output of those
blocks corresponds to the output of Quantizer Decode.

Dialog Box

Quantization codebook
A real vector that prescribes the output value corresponding to each input
integer.

Pair Block Sampled Quantizer Encode or Enabled Quantizer Encode

4-367
Random Deinterleaver

Purpose 4Random Deinterleaver

Restore ordering of the input symbols using a random permutation

Library Block sublibrary of Interleaving

Description The Random Deinterleaver block rearranges the elements of its input vector
using a random permutation. The Initial seed parameter initializes the
random number generator that the block uses to determine the permutation. If
this block and the Random Interleaver block have the same value for Initial
seed, then the two blocks are inverses of each other.

The Number of elements parameter indicates how many numbers are in the
input vector.If the input is frame-based, then it must be a column vector.

Dialog Box

Number of elements
The number of elements in the input vector.
Initial seed
The initial seed value for the random number generator.

Pair Block Random Interleaver

See Also General Block Deinterleaver

4-368
 Random-Integer Generator

Purpose 4Random-Integer Generator

Generate integers randomly distributed in the range [0, M-1]

Library Comm Sources

Description The Random-Integer Generator block generates uniformly distributed random

integers in the range [0, M-1], where M is the M-ary number defined in the
dialog box.
The M-ary number can be either a scalar or a vector. If it is a scalar, then all
output random variables are independent and identically distributed (i.i.d.). If
the M-ary number is a vector, then its length must equal the length of the
Initial seed; in this case each output has its own output range.

If the Initial seed parameter is a constant, then the resulting noise is

repeatable.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret
vector parameters as 1-D parameters. See “Signal Attribute Parameters for
Random Sources” on page 2-7 for more details.
The number of elements in the Initial seed parameter becomes the number of
columns in a frame-based output or the number of elements in a sample-based
vector output. Also, the shape (row or column) of the Initial seed parameter
becomes the shape of a sample-based two-dimensional output signal.

4-369
Random-Integer Generator

Dialog Box

M-ary number
The positive integer, or vector of positive integers, that indicates the range
of output values.
Initial seed
The initial seed value for the random number generator. The vector length
of the seed determines the length of the output vector.
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.
Samples per frame
The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.

4-370
 Random-Integer Generator

Interpret vector parameters as 1-D

If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

See Also randint (Communications Toolbox)

4-371
Random Interleaver

Purpose 4Random Interleaver

Reorder the input symbols using a random permutation

Library Block sublibrary of Interleaving

Description The Random Interleaver block rearranges the elements of its input vector
using a random permutation. The Number of elements parameter indicates
how many numbers are in the input vector.If the input is frame-based, then it
must be a column vector.
The Initial seed parameter initializes the random number generator that the
block uses to determine the permutation. The block is predictable for a given
seed, but different seeds produce different permutations.

Dialog Box

Number of elements
The number of elements in the input vector.
Initial seed
The initial seed value for the random number generator.

Pair Block Random Deinterleaver

See Also General Block Interleaver

4-372
 Rayleigh Noise Generator

Purpose 4Rayleigh Noise Generator

Generate Rayleigh distributed noise

Library Comm Sources

Description The Rayleigh Noise Generator block generates Rayleigh distributed noise. The
Rayleigh probability density function is given by

 x
2

 – --------2-
 x 2σ
x≥0
f ( x ) =  -----2- e
 σ
 0 x<0
î
2
where σ is known as the fading envelope of the Rayleigh distribution.
The block requires you to specify the Initial seed for the random number
generator. If it is a constant, then the resulting noise is repeatable. The sigma
parameter can be either a vector of the same length as the Initial seed, or a
scalar. When sigma is a scalar, every element of the output signal shares that
same value.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret
vector parameters as 1-D parameters. See “Signal Attribute Parameters for
Random Sources” on page 2-7 for more details.
The number of elements in the Initial seed parameter becomes the number of
columns in a frame-based output or the number of elements in a sample-based
vector output. Also, the shape (row or column) of the Initial seed parameter
becomes the shape of a sample-based two-dimensional output signal.

4-373
Rayleigh Noise Generator

Dialog Box

Sigma
Specify σ as defined in the Rayleigh probability density function.
Initial seed
The initial seed value for the random number generator.
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.
Samples per frame
The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.
Interpret vector parameters as 1-D
If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

4-374
 Rayleigh Noise Generator

See Also Multipath Rayleigh Fading Channel; raylrnd (Statistics Toolbox)

References [1] Proakis, John G. Digital Communications, Third edition. New York:
McGraw Hill, 1995.

4-375
Rectangular QAM Demodulator Baseband

Purpose 4Rectangular QAM Demodulator Baseband

Demodulate QAM-modulated data

Library AM, in Digital Baseband sublibrary of Modulation

Description The Rectangular QAM Demodulator Baseband block demodulates a signal that
was modulated using quadrature amplitude modulation with a constellation on
a rectangular lattice.
The signal constellation has M points, where M is the M-ary number
parameter. M must have the form 2K for some positive integer K. The block
scales the signal constellation based on how you set the Normalization
method parameter. For details, see the reference page for the Rectangular
QAM Modulator Baseband block.
The input can be either a scalar or a frame-based column vector.

Output Signal Values

The Output type parameter determines whether the block produces integers
or binary representations of integers. If Output type is set to Integer, then the
block produces integers. If Output type is set to Bit, then the block produces a
group of K bits, called a binary word, for each symbol. The Constellation
ordering parameter indicates how the block assigns binary words to points of
the signal constellation. More details are on the reference page for the
Rectangular QAM Modulator Baseband block.

Processing an Upsampled Modulated Signal

The input signal can be an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-376
 Rectangular QAM Demodulator Baseband

Dialog Box

M-ary number
The number of points in the signal constellation. It must have the form 2K
for some positive integer K.
Output type
Indicates whether the output consists of integers or groups of bits.
Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

4-377
Rectangular QAM Demodulator Baseband

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power among the symbols in the constellation. This field
appears only when Normalization method is set to Peak Power.
Phase offset (rad)
The rotation of the signal constellation, in radians.
Samples per symbol
The number of input samples that represent each modulated symbol.

Pair Block Rectangular QAM Modulator Baseband

See Also General QAM Demodulator Baseband

References [1] Smith, Joel G. “Odd-Bit Quadrature Amplitude-Shift Keying.” IEEE

Transactions on Communications, vol. COM-23, March 1975. 385-389.

4-378
 Rectangular QAM Demodulator Passband

Purpose 4Rectangular QAM Demodulator Passband

Demodulate QAM-modulated data

Library AM, in Digital Passband sublibrary of Modulation

Description The Rectangular QAM Demodulator Passband block demodulates a signal that
was modulated using quadrature amplitude modulation with a constellation on
a rectangular lattice. The signal constellation has M points, where M is the
M-ary number parameter. M must have the form 2K for some positive integer
K.
This block converts the input to an equivalent baseband representation and
then uses the baseband equivalent block, M-PAM Demodulator Baseband, for
internal computations. The following parameters in this block are the same as
those of the baseband equivalent block:
• M-ary number
• Output type
• Constellation ordering
• Normalization method
• Minimum distance
• Average power
• Peak power
The input must be a sample-based scalar signal.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Input sample time parameter specifies
the sample time of the input signal, while the Symbol period parameter
equals the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate signal during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the output.
The timing-related parameters must satisfy these relationships:

• Input sample time > (Carrier frequency)-1

4-379
Rectangular QAM Demodulator Passband

• Symbol period < [2*Carrier frequency + 2/(Input sample time)]-1

• Input sample time = K*Symbol period*Baseband samples per symbol for
some integer K

Also, this block incurs an extra output period of delay compared to its baseband
equivalent block.

Dialog Box

M-ary number
The number of points in the signal constellation. It must have the form 2K
for some positive integer K.

4-380
 Rectangular QAM Demodulator Passband

Output type
Indicates whether the output consists of integers or groups of bits.
Constellation ordering
Determines how the block maps each integer to a group of output bits. This
field is active only when Output type is set to Bit.
Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power among the symbols in the constellation. This field
appears only when Normalization method is set to Peak Power.
Symbol period (s)
The symbol period, which equals the sample time of the output.
Baseband samples per symbol
The number of baseband samples that represent each modulated symbol,
after the block converts the passband input to a baseband intermediary
signal.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.
Input sample time
The sample time of the input signal.

4-381
Rectangular QAM Demodulator Passband

Pair Block Rectangular QAM Modulator Passband

See Also General QAM Demodulator Passband, Rectangular QAM Demodulator

Baseband

References [1] Smith, Joel G. “Odd-Bit Quadrature Amplitude-Shift Keying.” IEEE

Transactions on Communications, vol. COM-23, March 1975. 385-389.

4-382
 Rectangular QAM Modulator Baseband

Purpose 4Rectangular QAM Modulator Baseband

Modulate using M-ary quadrature amplitude modulation

Library AM, in Digital Baseband sublibrary of Modulation

Description The Rectangular QAM Modulator Baseband block modulates using M-ary
quadrature amplitude modulation with a constellation on a rectangular lattice.
The output is a baseband representation of the modulated signal.

Constellation Size and Scaling

The signal constellation has M points, where M is the M-ary number
parameter. M must have the form 2K for some positive integer K. The block
scales the signal constellation based on how you set the Normalization
method parameter. The table below lists the possible scaling conditions.

Value of Normalization method Scaling Condition

parameter

Min. distance between symbols The nearest pair of points in the

constellation is separated by the value
of the Minimum distance parameter.
Average Power The average power of the symbols in
the constellation is the Average
power parameter.

Peak Power The maximum power of the symbols in

the constellation is the Peak power
parameter.

Input Signal Values

The input and output for this block are discrete-time signals. The Input type
parameter determines whether the block accepts integers between 0 and M-1,
or binary representations of integers:

• If Input type is set to Integer, then the block accepts integers. The input can
be either a scalar or a frame-based column vector.
• If Input type is set to Bit, then the block accepts groups of K bits, called
binary words. The input can be either a vector of length K or a frame-based

4-383
Rectangular QAM Modulator Baseband

column vector whose length is an integer multiple of K. The Constellation

ordering parameter indicates how the block assigns binary words to points
of the signal constellation. Such assignments apply independently to the
in-phase and quadrature components of the input:
- If Constellation ordering is set to Binary, then the block uses a natural
binary-coded constellation.
- If Constellation ordering is set to Gray and K is even, then the block uses
a Gray-coded constellation.
- If Constellation ordering is set to Gray and K is odd, then the block codes
the constellation so that pairs of nearest points differ in one or two bits.
The constellation is cross-shaped, and the schematic below indicates
which pairs of points differ in two bits. The schematic uses M = 128, but
suggests the general case.

Hollow vertical pairs of

adjacent points differ by two

Other pairs of adjacent

points differ by one bit

For details about the Gray coding, see the reference page for the M-PSK
Modulator Baseband block and the paper listed in “References” below. Note
that since the in-phase and quadrature components are assigned
independently, the Gray and binary orderings coincide when M = 4.

Upsampling the Modulated Signal

This block can output an upsampled version of the modulated signal. The
Samples per symbol parameter is the upsampling factor. It must be a positive
integer. For more information, see “Upsampled Signals and Rate Changes” on
page 2-72.

4-384
 Rectangular QAM Modulator Baseband

Dialog Box

M-ary number
The number of points in the signal constellation. It must have the form 2K
for some positive integer K.
Input type
Indicates whether the input consists of integers or groups of bits.
Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.

4-385
Rectangular QAM Modulator Baseband

Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power of the symbols in the constellation. This field appears
only when Normalization method is set to Peak Power.
Phase offset (rad)
The rotation of the signal constellation, in radians.
Samples per symbol
The number of output samples that the block produces for each integer or
binary word in the input.

Pair Block Rectangular QAM Demodulator Baseband

See Also General QAM Modulator Baseband

References [1] Smith, Joel G. “Odd-Bit Quadrature Amplitude-Shift Keying.” IEEE

Transactions on Communications, vol. COM-23, March 1975. 385-389.

4-386
 Rectangular QAM Modulator Passband

Purpose 4Rectangular QAM Modulator Passband

Modulate using M-ary quadrature amplitude modulation

Library AM, in Digital Passband sublibrary of Modulation

Description The Rectangular QAM Modulator Passband block modulates using M-ary
quadrature amplitude modulation with a constellation on a rectangular lattice.
The output is a passband representation of the modulated signal. The signal
constellation has M points, where M is the M-ary number parameter. M must
have the form 2K for some positive integer K.
This block uses the baseband equivalent block, Rectangular QAM Modulator
Baseband, for internal computations and converts the resulting baseband
signal to a passband representation. The following parameters in this block are
the same as those of the baseband equivalent block:
• M-ary number
• Input type
• Constellation ordering
• Normalization method
• Minimum distance
• Average power
• Peak power
The input must be sample-based. If the Input type parameter is Bit, then the
input must be a vector of length log2(M). If the Input type parameter is
Integer, then the input must be a scalar.

Parameters Specific to Passband Simulation

Passband simulation uses a carrier signal. The Carrier frequency and
Carrier initial phase parameters specify the frequency and initial phase,
respectively, of the carrier signal. The Symbol period parameter must equal
the sample time of the input signal, while the Output sample time parameter
determines the sample time of the output signal.
This block uses a baseband representation of the modulated signal as an
intermediate result during internal computations. The Baseband samples per
symbol parameter indicates how many baseband samples correspond to each
integer or binary word in the input, before the block converts them to a
passband output.

4-387
Rectangular QAM Modulator Passband

The timing-related parameters must satisfy these relationships:

• Symbol period > (Carrier frequency)-1

• Output sample time < [2*Carrier frequency + 2/(Symbol period)]-1
• Symbol period = K*Output sample time*Baseband samples per symbol
for some integer K

Furthermore, Carrier frequency is typically much larger than the highest

frequency of the unmodulated signal.

Dialog Box

4-388
 Rectangular QAM Modulator Passband

M-ary number
The number of points in the signal constellation. It must have the form 2K
for some positive integer K.
Input type
Indicates whether the input consists of integers or groups of bits.
Constellation ordering
Determines how the block maps each group of input bits to a corresponding
integer. This field is active only when Input type is set to Bit.
Normalization method
Determines how the block scales the signal constellation. Choices are Min.
distance between symbols, Average Power, and Peak Power.

Minimum distance
The distance between two nearest constellation points. This field appears
only when Normalization method is set to Min. distance between
symbols.

Average power (watts)

The average power of the symbols in the constellation. This field appears
only when Normalization method is set to Average Power.
Peak power (watts)
The maximum power of the symbols in the constellation. This field appears
only when Normalization method is set to Peak Power.
Symbol period (s)
The symbol period, which must equal the sample time of the input.
Baseband samples per symbol
The number of baseband samples that correspond to each integer or binary
word in the input, before the block converts them to a passband output.
Carrier frequency (Hz)
The frequency of the carrier.
Carrier initial phase (rad)
The initial phase of the carrier in radians.

4-389
Rectangular QAM Modulator Passband

Output sample time

The sample time of the output signal.

Pair Block Rectangular QAM Demodulator Passband

See Also General QAM Modulator Passband, Rectangular QAM Modulator Baseband

References [1] Smith, Joel G. “Odd-Bit Quadrature Amplitude-Shift Keying.” IEEE

Transactions on Communications, vol. COM-23, March 1975. 385-389.

4-390
 Rician Fading Channel

Purpose 4Rician Fading Channel

Simulate a Rician fading propagation channel

Library Channels

Description The Rician Fading Channel block implements a baseband simulation of a

Rician fading propagation channel. This block is useful for modeling mobile
wireless communication systems when the transmitted signal can travel to the
receiver along a dominant line-of-sight or direct path. If the signal can travel
along a line-of-sight path and also along other fading paths, then you can use
this block in parallel with the Multipath Rayleigh Fading Channel block. For
details about fading channels, see the works listed in “References” on page
4-393.
The input can be either a scalar or a frame-based column vector. The input is
a complex signal.
Fading causes the signal to spread and become diffuse. The K-factor
parameter, which is part of the statistical description of the Rician
distribution, represents the ratio between direct-path (unspread) power and
diffuse power. The ratio is expressed linearly, not in decibels. While the Gain
parameter controls the overall gain through the channel, the K-factor
parameter controls the gain’s partition into direct and diffuse components.
Relative motion between the transmitter and receiver causes Doppler shifts in
the signal frequency. The Doppler frequency parameter is the maximum
Doppler shift that the signal undergoes. The Jakes PSD (power spectral
density) determines the spectrum of the Rician process.
The Sample time parameter is the time between successive elements of the
input signal. Note that if the input is a frame-based column vector of length n,
then the frame period (as Simulink’s Probe block reports, for example) is
n*Sample time.
The Delay parameter specifies a time delay in seconds and the Gain parameter
specifies a gain that applies to the input signal. Both parameters are scalars.
The scalar Initial seed parameter seeds the random number generator that
the block uses to generate its Rician-distributed complex random process.

4-391
Rician Fading Channel

Dialog Box

K-factor
The ratio of power in the direct path to diffuse power. The ratio is expressed
linearly, not in decibels.
Doppler frequency (Hz)
A positive scalar that indicates the maximum Doppler shift.
Sample time
The period of each element of the input signal.
Delay (s)
A scalar that specifies the propagation delay.
Gain (dB)
A scalar that specifies the gain.
Initial seed
The scalar seed for the Gaussian noise generator.

4-392
 Rician Fading Channel

See Also Rician Noise Generator, Multipath Rayleigh Fading Channel

References [1] Fechtel, Stefan A. “A Novel Approach to Modeling and Efficient Simulation
of Frequency-Selective Fading Radio Channels.” IEEE Journal on Selected
Areas in Communications, vol. 11, April 1993. 422-431.
[2] Jakes, William C., ed. Microwave Mobile Communications. New York: IEEE
Press, 1974.
[3] Lee, William C. Y. Mobile Communications Design Fundamentals, 2nd ed.
New York: Wiley, 1993.

4-393
Rician Noise Generator

Purpose 4Rician Noise Generator

Generate Rician distributed noise

Library Comm Sources

Description The Rician Noise Generator block generates Rician distributed noise. The
Rician probability density function is given by

 2
x +m
2

 – ------------------
2
-
 x mx 2σ
x≥0
f ( x ) =  -----2- I 0  -------
2
- e
 σ σ
 0 x<0
î

where:

• σ is the standard deviation of the Gaussian distribution that underlies the

Rician distribution noise
2 2
• m 2 = m I + m Q , where mI and mQ are the mean values of two independent
Gaussian components
• I0 is the modified 0th-order Bessel function of the first kind given by
π
1 y cos t
I 0 ( y ) = ------
2π ò– π e dt

Note that m and σ are not the mean value and standard deviation for the
Rician noise.
You must specify the Initial seed for the random number generator. When it
is a constant, the resulting noise is repeatable. The vector length of the Initial
seed parameter should equal the number of columns in a frame-based output
or the number of elements in a sample-based output. The set of numerical
parameters above the Initial seed parameter in the dialog box can consist of
vectors having the same length as the Initial seed, or scalars.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret

4-394
 Rician Noise Generator

vector parameters as 1-D parameters. See “Signal Attribute Parameters for

Random Sources” on page 2-7 for more details.
The number of elements in the Initial seed and Sigma parameters becomes
the number of columns in a frame-based output or the number of elements in
a sample-based vector output. Also, the shape (row or column) of the Initial
seed and Sigma parameters becomes the shape of a sample-based
two-dimensional output signal.

Dialog Box

Specification method
Either K-factor or Quadrature components.
Rician K-factor
K = m2/(2σ2), where m is as in the Rician probability density function. This
field appears only if Specification method is K-factor.
In-phase component (mean), Quadrature component (mean)
The mean values mI and mQ, respectively, of the Gaussian components.
These fields appear only if Specification method is Quadrature
components.

4-395
Rician Noise Generator

Sigma
The variable σ in the Rician probability density function.
Initial seed
The initial seed value for the random number generator.
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.
Samples per frame
The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.
Interpret vector parameters as 1-D
If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

See Also Rician Fading Channel

References [1] Proakis, John G. Digital Communications, Third edition. New York:
McGraw Hill, 1995.

4-396
 Sampled Quantizer Encode

Purpose 4Sampled Quantizer Encode

Quantize a signal, indicating quantization index, coded signal, and distortion

Library Source Coding

Description The Sampled Quantizer Encode block encodes an input signal using scalar
quantization. The block outputs the quantization levels (or quantization index)
of the input signal, the encoded signal, and the mean square distortion.
The input can be either a scalar, a sample-based vector, or a frame-based row
vector. This block processes each vector element independently. Each output
signal is a vector of the same length as the input signal.
The Quantization partition parameter is a length-n real vector whose entries
are in strictly ascending order. The first output signal corresponding to an
input signal of x is:

• 0 if x ≤ Quantization partition(1)
• m if Quantization partition(m) < x ≤ Quantization partition(m+1)
• n if Quantization partition(n) < x

The Quantization codebook parameter, whose length exceeds the length of

Quantization partition by one, prescribes a value for each partition in the
quantization. The first element of Quantization codebook is the value for the
interval between negative infinity and the first element of Quantization
partition. The second output signal from this block contains the quantization
of the input based on the quantization levels and prescribed values.
At a given time, the third output signal measures the mean square distortion
between the input and the second output, considering the stream of data up
through that time.
You can use the function lloyds in the Communications Toolbox with a
representative sample of your data as training data, to obtain appropriate
partition and codebook parameters.

4-397
Sampled Quantizer Encode

Dialog Box

Quantization partition
The vector of endpoints of the partition intervals. The elements must be in
strictly ascending order.
Quantization codebook
The vector of output values assigned to each partition.
Input signal vector length
The length of the input signal.
Sample time
The output sample time.

Pair Block Quantizer Decode

See Also Enabled Quantizer Encode; lloyds (Communications Toolbox)

4-398
 Scrambler

Purpose 4Scrambler
Scramble the input signal

Library Sequence Operations, in Basic Comm Functions

Description The Scrambler block scrambles the scalar input signal. If the Calculation base
parameter is N, then the input values must be integers between 0 and N-1.
One purpose of scrambling is to reduce the length of strings of 0s or 1s in a
transmitted signal, since a long string of 0s or 1s may cause transmission
synchronization problems. Below is a schematic of the scrambler. All adders
perform addition modulo N.

Scrambled data

Input data + 1 2 M-1 M

+ + +

At each time step, the input causes the contents of the registers to shift
sequentially. Each switch in the scrambler is on or off as defined by the
Scramble polynomial parameter. You can specify the polynomial by listing its
coefficients in order of ascending powers of z-1, or by listing the powers of z that
appear in the polynomial with a coefficient of 1. For example p = [1 0 0 0 0 0 1
0 1] and p = [0 -6 -8] both represent the polynomial p(z-1) = 1 + z-6 + z-8.
The Initial states parameter lists the states of the scrambler’s registers when
the simulation starts. The elements of this vector must be integers between 0
and N-1. The vector length of this parameter must equal the order of the
scramble polynomial. (If the Scramble polynomial parameter is a vector that
lists the coefficients in order, then the order of the scramble polynomial is one
less than the vector length.)

4-399
Scrambler

Dialog Box

Calculation base
The calculation base N. The input and output of this block are integers in
the range [0, N-1].
Scramble polynomial
A polynomial that defines the connections in the scrambler.
Initial states
The states of the scrambler’s registers when the simulation starts.

Pair Block Descrambler

See Also PN Sequence Generator

4-400
 SSB AM Demodulator Baseband

Purpose 4SSB AM Demodulator Baseband

Demodulate SSB-AM-modulated data

Library Analog Baseband Modulation, in Modulation

Description The SSB AM Demodulator Baseband block demodulates a signal that was
modulated using single-sideband amplitude modulation. The input is a
baseband representation of the modulated signal. The input is complex, while
the output is real. The input must be a sample-based scalar signal.
In the course of demodulating, the block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Box

Lowpass filter numerator

The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.
Lowpass filter denominator
The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
Initial phase (rad)
The initial phase in the corresponding SSB AM Modulator Baseband block.

4-401
SSB AM Demodulator Baseband

Sample time
The sample time of the output signal.

Pair Block SSB AM Modulator Baseband

See Also DSB AM Demodulator Baseband, DSBSC AM Demodulator Baseband

4-402
 SSB AM Demodulator Passband

Purpose 4SSB AM Demodulator Passband

Demodulate SSB-AM-modulated data

Library Analog Passband Modulation, in Modulation

Description The SSB AM Demodulator Passband block demodulates a signal that was
modulated using single-sideband amplitude modulation. The input is a
passband representation of the modulated signal. Both the input and output
signals are real sample-based scalar signals.
In the course of demodulating, this block uses a filter whose transfer function
is described by the Lowpass filter numerator and Lowpass filter
denominator parameters.

Dialog Box

Carrier frequency (Hz)

The carrier frequency in the corresponding SSB AM Modulator Passband
block.
Lowpass filter numerator
The numerator of the lowpass filter transfer function. It is represented as
a vector that lists the coefficients in order of descending powers of s.

4-403
SSB AM Demodulator Passband

Lowpass filter denominator

The denominator of the lowpass filter transfer function. It is represented
as a vector that lists the coefficients in order of descending powers of s. For
an FIR filter, set this parameter to 1.
Initial phase (rad)
The initial phase of the carrier in radians.
Sample time
The sample time of the output signal.

Pair Block SSB AM Modulator Passband

See Also SSB AM Demodulator Baseband, DSB AM Demodulator Passband, DSBSC

AM Demodulator Passband

4-404
 SSB AM Modulator Baseband

Purpose 4SSB AM Modulator Baseband

Modulate using single-sideband amplitude modulation

Library Analog Baseband Modulation, in Modulation

Description The SSB AM Modulator Baseband block modulates using single-sideband

amplitude modulation with a Hilbert transform filter. The output is a
baseband representation of the modulated signal. The input signal is real,
while the output signal is complex. The input must be a sample-based scalar
signal.
SSB AM Modulator Baseband transmits either the lower or upper sideband
signal, but not both. To control which sideband it transmits, use the “upper”
sideband or “lower” sideband parameter.

If the input is u(t) as a function of time t, then the output is

− jû ( t ) )e
(u(t) +
jθ

where θ is the Initial phase parameter and û(t) is the Hilbert transform of the
input u(t). The minus sign indicates the upper sideband and the plus sign
indicates the lower sideband.

Hilbert Tranform Filter Parameters

This block uses a Hilbert transform filter, possibly with a compensator. The
filter produces a Hilbert transform of its input signal. These mask parameters
relate to the Hilbert transform filter:

• The Time delay for Hilbert transform filter parameter specifies the delay
in the filter design. You should choose a value of the form
(N+1/2)*(Sample time parameter)
where N is a positive integer.
• The Bandwidth of the input signal parameter is the estimated highest
frequency component in the input message signal. This parameter is used to
design a compensator for the Hilbert transform filter, which would force the
message signal amplitude to remain within the assigned range.
If this parameter is either 0 or larger than 1/(2*Sample time), then the block
does not generate a compensator.

4-405
SSB AM Modulator Baseband

This block uses the hilbiir function in the Communications Toolbox to design
the Hilbert transform filter.

Dialog Box

Initial phase (rad)

The phase offset, θ, of the modulated signal.
Bandwidth of the input signal (Hz)
The highest frequency component of the message signal. To avoid using a
compensator in the Hilbert transform filter design, set this to 0.
Time delay for Hilbert transform filter (s)
The time delay in the design of the Hilbert transform filter.
Sample time
The sample time of the Hilbert transform filtering.
“upper” sideband or “lower” sideband
A string that specifies whether to transmit the upper or lower sideband.
Choices are 'upper' and 'lower'.

Pair Block SSB AM Demodulator Baseband

See Also DSB AM Modulator Baseband, DSBSC AM Modulator Baseband

4-406
 SSB AM Modulator Baseband

References [1] Peebles, Peyton Z, Jr. Communication System Principles. Reading, Mass.:
Addison-Wesley, 1976.

4-407
SSB AM Modulator Passband

Purpose 4SSB AM Modulator Passband

Modulate using single-sideband amplitude modulation

Library Analog Passband Modulation, in Modulation

Description The SSB AM Modulator Passband block modulates using single-sideband

amplitude modulation with a Hilbert transform filter. The output is a passband
representation of the modulated signal. Both the input and output signals are
real sample-based scalar signals.
SSB AM Modulator Passband transmits either the lower or upper sideband
signal, but not both. To control which sideband it transmits, use the “upper”
sideband or “lower” sideband parameter.

If the input is u(t) as a function of time t, then the output is

u ( t ) cos ( f c t + θ ) ± û ( t ) sin ( f c t + θ )

where:

• fc is the Carrier frequency parameter.

• θ is the Initial phase parameter.
• û(t) is the Hilbert transform of the input u(t).
• The plus sign indicates the upper sideband and the minus sign indicates the
lower sideband.

Hilbert Tranform Filter Parameters

This block uses a Hilbert transform filter, possibly with a compensator. These
mask parameters relate to the Hilbert transform filter:

• The Time delay for Hilbert transform filter parameter specifies the delay
in the filter design. You should choose a value of the form
(N+1/2)*(Sample time parameter)
where N is a positive integer.
• The Bandwidth of the input signal parameter is the estimated highest
frequency component in the input message signal.
This parameter is used to design a compensator for the Hilbert transform
filter, which would force the message signal amplitude to remain within the

4-408
 SSB AM Modulator Passband

assigned range. If this parameter is either 0 or larger than 1/(2*Sample

time), then the block does not generate a compensator.
This block uses the hilbiir function in the Communications Toolbox to design
the Hilbert transform filter.
Typically, an appropriate Carrier frequency value is much higher than the
highest frequency of the input signal. To avoid having to use a high carrier
frequency and consequently a high sampling rate, you can use baseband
simulation (SSB AM Modulator Baseband block) instead of passband
simulation.

Dialog Box

Carrier frequency (Hz)

The frequency of the carrier.
Initial phase (rad)
The phase offset, θ, of the modulated signal.
Bandwidth of the input signal (Hz)
The highest frequency component of the message signal. To avoid using a
compensator in the Hilbert transform filter design, set this to 0.

4-409
SSB AM Modulator Passband

Time delay for Hilbert transform filter (s)

The time delay in the design of the Hilbert transform filter.
Sample time
The sample time of the Hilbert transform filtering.
“upper” sideband or “lower sideband”
A string that specifies whether to transmit the upper or lower sideband.
Choices are 'upper' and 'lower'.

Pair Block SSB AM Demodulator Passband

See Also SSB AM Modulator Baseband, DSB AM Modulator Passband, DSBSC AM

Modulator Passband; hilbiir (Communications Toolbox)

References [1] Peebles, Peyton Z, Jr. Communication System Principles. Reading, Mass.:
Addison-Wesley, 1976.

4-410
 Triggered Read From File

Purpose 4Triggered Read From File

Read from a file, refreshing the output at rising edges of an input signal

Library Comm Sources

Description The Triggered Read From File block reads a new record from a file only at the
rising edge of the input trigger signal. The output is a sample-based signal.

Note The triggered behavior of this block is one difference between this block
and Simulink’s From File block. However, the From File block is useful for
reading platform-independent MAT-files.

The file can be an ASCII text file, a file containing integer or floating point
numbers, or a binary file (in the format of the C fwrite function). The file must
be either in the current working directory on the MATLAB path.
When a rising edge of the input trigger signal is detected, this block reads from
the file a record whose length is specified in the parameter Output vector
length. The first reading always occurs at the first rising edge. After that, if
the Decimation parameter is a positive integer k, then the block reads at
every kth rising edge. If Decimation is 1, then the block reads at every rising
edge.
When the block reaches the end-of-file marker, it either:

• Rereads from the beginning of the file, if the Cyclic repeat box is checked, or
• Outputs zeros, if the Cyclic repeat box is not checked

If the Data type parameter is ASCII, then the output is an integer. The
mapping between decimal integers and ASCII characters is shown below.

Integer ASCII Integer ASCII Integer ASCII Integer ASCII

0 NUL 32 SP 64 @ 96 \
1 SOH 33 ! 65 A 97 a
2 STX 34 “ 66 B 98 b
3 ETX 35 # 67 C 99 c
4 EOT 36 $ 68 D 100 d

4-411
Triggered Read From File

Integer ASCII Integer ASCII Integer ASCII Integer ASCII

5 ENQ 37 % 69 E 101 e
6 ACK 38 & 70 F 102 f
7 BEL 39 ‘ 71 G 103 g
8 BS 40 ( 72 H 104 h
9 HT 41 ) 73 I 105 i
10 LF 42 * 74 J 106 j
11 VT 43 + 75 K 107 k
12 FF 44 , 76 L 108 l
13 CR 45 - 77 M 109 m
14 SO 46 . 78 N 110 n
15 SI 47 / 79 O 111 o
16 DLE 48 0 80 P 112 p
17 DC1 49 1 81 Q 113 q
18 DC2 50 2 82 R 114 r
19 DC3 51 3 83 S 115 s
20 DC4 52 4 84 T 116 t
21 NAK 53 5 85 U 117 u
22 SYN 54 6 86 V 118 v
23 ETB 55 7 87 W 119 w
24 CAN 56 8 88 X 120 x
25 EM 57 9 89 Y 121 y
26 SUB 58 : 90 Z 122 z
27 ESC 59 ; 91 [ 123 {
28 FS 60 < 92 \ 124 |
29 GS 61 = 93 ] 125 }
30 RS 62 > 94 ^ 126 ~
31 US 63 ? 95 _ 127 DEL

4-412
 Triggered Read From File

Dialog Box

File name
The filename, including its extension, as a string.
Data type
The data type. Choices are ASCII, binary, float, and integer.
Decimation
A decimation factor. If it is 1, then the block reads at every rising edge.
Output vector length
The vector length of the block’s output.
Cyclic repeat
Specifies whether to cycle continuously through the contents of File name
or to output only zeros after reaching the end-of-file marker.
Threshold in detecting trigger signal
The threshold for the rising edge of the trigger signal.

Pair Block Triggered Write to File

See Also To File (Simulink)

4-413
Triggered Write to File

Purpose 4Triggered Write to File

Write to a file at each rising edge of an input signal

Library Comm Sinks

Description The Triggered Write to File block creates a file containing selected data from
the input signal. Unlike Simulink’s To File block, the Triggered Write to File
block writes new data to the file only at the rising edge of the input trigger
signal. However, the To File block is useful for creating platform-independent
MAT-files.
The file can be an ASCII text file, a file containing integer or floating-point
numbers, or a binary file (in the format of the C fwrite function). You specify
the file type using the Data type parameter. If Data type is ASCII then this
block converts the data into ASCII characters before writing, using the
mapping shown on the reference page for the Triggered Read From File block.
For example, an input of 65 would cause the the block to write the character
“A” to the file. Other file types receive the data directly.

Caution If the destination file already exists, then this block overwrites it.

The first input signal contains the data to write. This input must be
sample-based. The second input signal is a sample-based scalar trigger signal
that controls the timing of writing. When a rising edge of the input trigger
signal is detected, this block writes the elements of the data signal to the file.
The file does not contain information about the dimension or orientation of the
data input, however.
The first write always occurs at the first rising edge. After that, the
Decimation parameter determines how many triggers the block receives
between successive file writes. Setting this parameter to 1 causes the block to
write at every rising edge.

4-414
 Triggered Write to File

Dialog Box

File name
The filename, including its extension, as a string.
Data type
The data type. Choices are ASCII, binary, float, and integer.
Decimation
A decimation factor. If it is 1, then the block writes at every rising edge.
Threshold in detecting trigger signal
The threshold for the rising edge of the trigger signal.

Pair Block Triggered Read From File

See Also To File (Simulink)

4-415
Uniform Noise Generator

Purpose 4Uniform Noise Generator

Generate uniformly distributed noise between the upper and lower bounds

Library Comm Sources

Description The Uniform Noise Generator block generates uniformly distributed noise. The
output data of this block is uniformly distributed between the specified lower
and upper bounds. The upper bound must be greater than or equal to the lower
bound.
You must specify the Initial seed in the simulation. When it is a constant, the
resulting noise is repeatable.
If all the elements of the output vector are to be independent and identically
distributed (i.i.d.), then you can use a scalar for the Noise lower bound and
Noise upper bound parameters. Alternatively, you can specify the range for
each element of the output vector individually, by using vectors for the Noise
lower bound and Noise upper bound parameters. If the bounds are vectors,
then their length must equal the length of the Initial seed parameter.

Attributes of Output Signal

The output signal can be a frame-based matrix, a sample-based row or column
vector, or a sample-based one-dimensional array. These attributes are
controlled by the Frame-based outputs, Samples per frame, and Interpret
vector parameters as 1-D parameters. See “Signal Attribute Parameters for
Random Sources” on page 2-7 for more details.
The number of elements in the Initial seed parameter becomes the number of
columns in a frame-based output or the number of elements in a sample-based
vector output. Also, the shape (row or column) of the Initial seed parameter
becomes the shape of a sample-based two-dimensional output signal.

4-416
 Uniform Noise Generator

Dialog Box

Noise lower bound, Noise upper bound

The lower and upper bounds of the interval over which noise is uniformly
distributed.
Initial seed
The initial seed value for the random number generator.
Sample time
The period of each sample-based vector or each row of a frame-based
matrix.
Frame-based outputs
Determines whether the output is frame-based or sample-based. This box
is active only if Interpret vector parameters as 1-D is unchecked.
Samples per frame
The number of samples in each column of a frame-based output signal. This
field is active only if Frame-based outputs is checked.

4-417
Uniform Noise Generator

Interpret vector parameters as 1-D

If this box is checked, then the output is a one-dimensional signal.
Otherwise, the output is a two-dimensional signal. This box is active only
if Frame-based outputs is unchecked.

See Also Random Source (DSP Blockset); rand (built-in MATLAB function)

4-418
 Viterbi Decoder

Purpose 4Viterbi Decoder

Decode convolutionally encoded data using the Viterbi algorithm

Library Convolutional sublibrary of Channel Coding

Description The Viterbi Decoder block decodes input symbols to produce binary output
symbols. This block can process several symbols at a time for faster
performance.

Input and Output Sizes

If the convolutional code uses an alphabet of 2n possible symbols, then this
block’s input vector length is L*n for some positive integer L. Similarly, if the
decoded data uses an alphabet of 2k possible output symbols, then this block’s
output vector length is L*k. The integer L is the number of frames that the
block processes in each step.
The input can be either a sample-based vector with L = 1, or a frame-based
column vector with any positive integer for L.

Input Values and Decision Types

The entries of the input vector are either bipolar, binary, or integer data,
depending on the Decision type parameter.

Decision type Possible Entries in Interpretation of Values

Parameter Decoder Input

Unquantized Real numbers +1: logical zero

-1: logical one

4-419
Viterbi Decoder

Decision type Possible Entries in Interpretation of Values

Parameter Decoder Input

Hard Decision 0, 1 0: logical zero

1: logical one
Soft Decision Integers between 0 0: most confident decision for
and 2b-1, where b is logical zero
the Number of soft
decision bits 2b-1: most confident decision
parameter for logical one

Other values represent less

confident decisions

To illustrate the soft decision situation more explicitly, the table below lists
interpretations of values for 3-bit soft decisions.

Input Value Interpretation

0 Most confident zero

1 Second most confident zero

2 Third most confident zero

3 Least confident zero

4 Least confident one

5 Third most confident one

6 Second most confident one

7 Most confident one

Operation Modes for Frame-Based Inputs

If the input signal is frame-based, then the block has three possible methods
for transitioning between successive frames. The Operation mode parameter
controls which method the block uses:

4-420
 Viterbi Decoder

• In Continuous mode, the block saves its internal state metric at the end of
each frame, for use with the next frame. Each traceback path is treated
independently.
• In Truncated mode, the block treats each frame independently. The
traceback path starts at the state with the best metric and always ends in
the all-zeros state. This mode is appropriate when the corresponding
Convolutional Encoder block has its Reset parameter set to On each frame.
• In Terminated mode, the block treats each frame independently, and the
traceback path always starts and ends in the all-zeros state. This mode is
appropriate when the uncoded message signal (that is, the input to the
corresponding Convolutional Encoder block) has enough zeros at the end of
each frame to fill all memory registers of the encoder. If the encoder has k
input streams and constraint length vector constr (using the polynomial
description), then “enough” means k*max(constr-1).

In the special case when the frame-based input signal contains only one
symbol, the Continuous mode is most appropriate.

Traceback Depth and Decoding Delay

The Traceback depth parameter, D, influences the decoding delay. The
decoding delay is the number of zero symbols that precede the first decoded
symbol in the output.

• If the input signal is sample-based, then the decoding delay consists of D zero
symbols
• If the input signal is frame-based and the Operation mode parameter is set
to Continuous, then the decoding delay consists of D zero symbols
• If the Operation mode parameter is set to Truncated or Terminated, then
there is no output delay and the Traceback depth parameter must be less
than or equal to the number of symbols in each frame.

If the code rate is 1/2, then a typical Traceback depth value is about five times
the constraint length of the code.

Reset Port
The reset port is usable only when the Operation mode parameter is set to
Continuous. Checking the Reset input check box causes the block to have an

4-421
Viterbi Decoder

additional input port, labeled Rst. When the Rst input is nonzero, the decoder
returns to its initial state by configuring its internal memory as follows:

• Sets the all-zeros state metric to zero

• Sets all other state metrics to the maximum value
• Sets the traceback memory to zero

Using a reset port on this block is analogous to setting the Reset parameter in
the Convolutional Encoder block to On nonzero Rst input.

Dialog Box

Trellis structure
MATLAB structure that contains the trellis description of the
convolutional encoder. Use the same value here and in the corresponding
Convolutional Encoder block.
Decision type
Unquantized, Hard Decision, or Soft Decision.

Number of soft decision bits

The number of soft decision bits used to represent each input. This field is
active only when Decision type is set to Soft Decision.
Traceback depth
The number of trellis branches used to construct each traceback path.

4-422
 Viterbi Decoder

Operation mode
Method for transitioning between successive input frames. For
frame-based input, the choices are Continuous, Terminated, and
Truncated. Sample-based input must use the Continuous mode.

Reset input
When you check this box, the decoder has a second input port labeled Rst.
Providing a nonzero input value to this port causes the internal memory to
be set to its initial state prior to processing the input data.

See Also Convolutional Encoder, APP Decoder

References [1] Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital
Communications. New York: Plenum Press, 1981.
[2] Gitlin, Richard D., Jeremiah F. Hayes, and Stephen B. Weinstein. Data
Communications Principles. New York: Plenum, 1992.
[3] Heller, Jerrold A. and Irwin Mark Jacobs. “Viterbi Decoding for Satellite
and Space Communication.” IEEE Transactions on Communication
Technology, vol. COM-19, October 1971. 835-848.

4-423
Voltage-Controlled Oscillator

Purpose 4Voltage-Controlled Oscillator

Implement a voltage-controlled oscillator

Library Comm Sources

Description The Voltage-Controlled Oscillator (VCO) block generates a signal whose

frequency shift from the Oscillation frequency parameter is proportional to
the input signal. The input signal is interpreted as a voltage. If the input signal
is u(t), then the output signal is
t
y ( t ) = A c cos ( 2πf c t + 2πk c ò0 u ( τ )dτ + ϕ )
where Ac is the Output amplitude parameter, fc is the Oscillation frequency
parameter, kc is the Input sensitivity parameter, and ϕ is the Initial phase
parameter.
This block uses a continuous-time integrator to interpret the equation above.
The input and output signals are both sample-based scalars.

Dialog Box

Output amplitude
The amplitude of the output.
Oscillation frequency (Hz)
The frequency of the oscillator output when the input signal is zero.

4-424
 Voltage-Controlled Oscillator

Input sensitivity
This value scales the input voltage and, consequently, the shift from the
Oscillation frequency value. The units of Input sensitivity are Hertz per
volt.
Initial phase (rad)
The initial phase of the oscillator in radians.

See Also Discrete-Time VCO

4-425
Windowed Integrator

Purpose 4Windowed Integrator

Integrate over a time window of fixed length

Library Integrators, in Basic Comm Functions

Description The Windowed Integrator block integrates the input signal in discrete time,
over a sliding time window of fixed length. If the Integration window length
parameter is T, then the output at time t is the result of integrating the input
signal from t-T to t. The block assumes that the input signal is zero for all
negative t.
You can choose one of three integration methods: Forward Euler, Backward
Euler, and Trapezoidal.

The input can be either a scalar, a sample-based vector, or a frame-based row

vector. The block processes each vector element independently. If the input
signal is a vector, then the output is a vector of the same length. This length
appears as the Input vector size parameter.

Dialog Box

Input vector size

The length of the input vector.
Integration window length (s)
The length of the interval of integration, in seconds.

4-426
 Windowed Integrator

Method
The integration method. Choices are Forward Euler, Backward Euler,
and Trapezoidal.
Sample time
The integration sample time. This must not exceed the Integration
window length parameter.

Examples Integrate a scalar constant signal whose value is 1 using these parameters:

• Input vector size = 5

• Integration window length = 4
• Method = Forward Euler
• Sample time = .5

You can use a Simulink Constant block for the input signal. The Simulink
Scope block shows the output below.

Notice that the output from time 0 to time 4 is a discrete approximation of a

ramp. During this period, the interval of integration increases with time. Also
notice that the output after time 4 is a constant value of 4. This is the result of
integrating the value 1 over the full integration window length of 4 seconds.
See Also Discrete Modulo Integrator, Integrate and Dump, Discrete-Time Integrator
(Simulink)

4-427
Windowed Integrator

4-428
 Index

A
A-law companders 2-24 Bit to Integer Converter block 4-89
A-Law Compressor block 4-47 block coding
A-Law Expander block 4-49 features of blockset 2-28
Algebraic Deinterleaver block 4-51 methods supported in blockset 2-28
Algebraic Interleaver block 4-53 techniques for 2-28
amplitude modulation (AM) terminology and notation 2-29
example model 2-59 block coding library 2-27
analog modulation libraries 2-53 reference for 4-9
reference for 4-24 block interleaving library 2-46
analog-to-digital conversion 2-16 reference for 4-13
APP Decoder block 4-56 BPSK Demodulator Baseband block 4-90
AWGN Channel block 4-60 BPSK Modulator Baseband block 4-92

B C
baseband Channel Coding library 2-27
simulation 2-54 reference for 4-9
Baseband PLL block 4-64 Channels library 2-84
Basic Comm Functions library 4-37 reference for 4-34
BCH Decoder block 4-66 Charge Pump PLL block 4-94
BCH Encoder block 4-68 code generator matrices
Bernoulli Random Binary Generator block 4-70 representing 2-36
binary codebooks
codes 2-28 representing 2-17
numbers, order of digits and 2-31 codewords
vector format for messages and codewords definition 2-29
2-29 representing 2-29
in Reed-Solomon codes 2-30 coding, source
Binary Cyclic Decoder block 4-73 features of the blockset 2-16
Binary Cyclic Encoder block 4-75 column vector signals xviii
Binary Linear Decoder block 4-79 Comm Sinks library 2-12
Binary Linear Encoder block 4-81 reference for 4-5
Binary Symmetric Channel block 4-84 Comm Sources library 2-6
Binary Vector Noise Generator block 4-86 reference for 4-3
Binary-Input RS Encoder block 4-77 companders 2-24
Binary-Output RS Decoder block 4-82 example 2-24

I-1
 Index

Complex Phase Difference block 4-97 Deinterlacer block 4-146

Complex Phase Shift block 4-98 delays
compression from analog demodulator’s filter 2-62
of data 2-16 in convolutional coding 2-42
compressors 2-24 in digital modulation 2-69
example 2-24 in example model 1-25
Continuous-Time Eye and Scatter Diagrams in interleaving 2-49
block 4-99 in serial-signal channel coding 2-30
converting delta modulation 2-21
analog to digital 2-16 example 2-22
convolutional coding See also differential pulse code modulation
delays 2-42 demodulation
convolutional coding library 2-40 definition of 2-53
reference for 4-11 Derepeat block 4-147
Convolutional Deinterleaver block 4-103 Descrambler block 4-150
Convolutional Encoder block 4-105 diagrams
Convolutional Interleaver block 4-107 eye 2-13
convolutional interleaving library 2-47 example 2-14
reference for 4-15 scatter 2-13
CPFSK Demodulator Baseband block 4-109 Differential Decoder block 4-152
CPFSK Demodulator Passband block 4-112 Differential Encoder block 4-153
CPFSK Modulator Baseband block 4-115 differential pulse code modulation (DPCM) 2-21
CPFSK Modulator Passband block 4-118 example 2-22
CPM Demodulator Baseband block 4-121 parameters, representing 2-17
CPM Demodulator Passband block 4-125 digital modulation libraries 2-64
CPM Modulator Baseband block 4-130 reference for 4-18
CPM Modulator Passband block 4-134 Discrete Modulo Integrator block 4-154
Discrete-Time Eye and Scatter Diagrams block
4-156
D Discrete-Time VCO block 4-159
data compression 2-16 DPCM Decoder block 4-161
Data Mapper block 4-139 DPCM Encoder block 4-163
DBPSK Demodulator Baseband block 4-142 DQPSK Demodulator Baseband block 4-165
DBPSK Modulator Baseband block 4-144 DQPSK Modulator Baseband block 4-167
decision timing DSB AM Demodulator Baseband block 4-171
and eye diagrams 2-13 DSB AM Demodulator Passband block 4-173
and scatter diagrams 2-13 DSB AM Modulator Baseband block 4-175

I-2
 Index

DSB AM Modulator Passband block 4-176 expanders 2-24

DSBSC AM Demodulator Baseband block 4-178 example 2-24
DSBSC AM Demodulator Passband block 4-180 eye diagrams 2-13
DSBSC AM Modulator Baseband block 4-182 example 2-14
DSBSC AM Modulator Passband block 4-183

F
E features
Enabled Quantizer Encode block 4-185 analog modulation 2-53
error block coding 2-28
predictive 2-21 channel 2-84
Error Rate Calculation block 4-187 digital modulation 2-65
error-control coding interleaving 2-46
base 2 only 2-28 sink 2-12
error-correction capability source 2-6
of Hamming codes 2-36 source coding 2-16
of Reed-Solomon codes 2-38 synchronization 2-90
examples filters
analog modulation step sizes 2-57 use after demodulating
analog modulation timing 2-55 choosing cutoff frequency 2-59
companders 2-24 resulting time lag 2-62
continuous phase modulation 2-78 FM Demodulator Baseband block 4-194
convolutional coding 2-42 FM Demodulator Passband block 4-196
convolutional interleaving 2-50 FM Modulator Baseband block 4-198
delays from filtering 2-62 FM Modulator Passband block 4-200
delays in digital demodulation 2-71 frame attribute xviii
differential pulse code modulation 2-22 frame-based signals, definition of xviii
eye and scatter diagrams 2-14 full matrix signal, definition of xviii
fading channels 2-86
filter cutoffs 2-59
Hamming coding 2-32 G
passband digital modulation 2-81 Gaussian Noise Generator block 4-202
quantization 2-18 General Block Deinterleaver block 4-205
quantized sine wave 2-19 General Block Interleaver block 4-207
Reed-Solomon coding 2-33 General Multiplexed Deinterleaver block 4-208
scatter diagrams 2-76 General Multiplexed Interleaver block 4-210
signal constellations 2-75

I-3
 Index

General QAM Demodulator Baseband block L

4-212 linear predictors
General QAM Demodulator Passband block representing 2-22
4-214 Linearized Baseband PLL block 4-254
General QAM Modulator Baseband block 4-217
General QAM Modulator Passband block 4-219
generator matrices M
representing 2-36 Matrix Deinterleaver block 4-256
GMSK Demodulator Baseband block 4-222 Matrix Helical Scan Deinterleaver block 4-257
GMSK Demodulator Passband block 4-225 Matrix Helical Scan Interleaver block 4-259
GMSK Modulator Baseband block 4-228 Matrix Interleaver block 4-262
GMSK Modulator Passband block 4-231 M-DPSK Demodulator Baseband block 4-264
M-DPSK Demodulator Passband block 4-267
M-DPSK Modulator Baseband block 4-270
H M-DPSK Modulator Passband block 4-274
Hamming coding messages
for single-error-correction 2-36 definition 2-29
Hamming Decoder block 4-234 representing 2-29
Hamming Encoder block 4-236 M-FSK Demodulator Baseband block 4-277
Helical Deinterleaver block 4-238 M-FSK Demodulator Passband block 4-280
Helical Interleaver block 4-241 M-FSK Modulator Baseband block 4-283
M-FSK Modulator Passband block 4-286
µ-law companders 2-24
I example 2-24
Insert Zero block 4-244 modulation
integer format for messages and codewords 2-31 analog 2-53
Integer to Bit Converter block 4-250 methods supported in blockset 2-53
Integer-Input RS Encoder block 4-246 definition of 2-53
Integer-Output RS Decoder block 4-248 delta 2-21
Integrate and Dump block 4-251 example 2-22
Integrators library 4-37 See also differential pulse code modulation
Interlacer block 4-253 differential pulse code. See differential pulse
interleaving delays 2-49 code modulation
Interleaving library 2-46, 4-13 digital 2-64
methods supported in blockset 2-65
Modulation library 2-53
reference for 4-18

I-4
 Index

Modulo Integrator block 4-289 passband

M-PAM Demodulator Baseband block 4-290 simulation 2-54
M-PAM Demodulator Passband block 4-293 phase modulation (PM)
M-PAM Modulator Baseband block 4-297 example model 2-62
M-PAM Modulator Passband block 4-301 Phase-Locked Loop block 4-345
M-PSK Demodulator Baseband block 4-305 pi/4 DQPSK modulation 2-75
M-PSK Demodulator Passband block 4-308 PLLs
M-PSK Modulator Baseband block 4-311 features of the blockset 2-90
M-PSK Modulator Passband block 4-316 PM Demodulator Baseband block 4-348
MSK Demodulator Baseband block 4-319 PM Demodulator Passband block 4-350
MSK Demodulator Passband block 4-321 PM Modulator Baseband block 4-352
MSK Modulator Baseband block 4-324 PM Modulator Passband block 4-353
MSK Modulator Passband block 4-326 PN Sequence Generator block 4-355
Mu-Law Compressor block 4-329 Poisson Int Generator block 4-358
Mu-Law Expander block 4-330 predictive
Multipath Rayleigh Fading Channel block 4-331 error 2-21
predictive quantization 2-21
example 2-22
N features of the blockset 2-16
nonbinary codes 2-28 parameters, representing 2-17
Reed-Solomon 2-38 predictors 2-21
representing 2-22
Puncture block 4-360
O
one-dimensional arrays, definition of xviii
OQPSK Demodulator Baseband block 4-334 Q
OQPSK Demodulator passband block 4-336 QPSK Demodulator Baseband block 4-362
OQPSK Modulator Baseband block 4-339 QPSK Modulator Baseband block 4-364
OQPSK Modulator Passband block 4-342 quantization
order of digits in binary numbers 2-31 coding 2-20
orientations, of vector signals xviii example 2-18
features of the blockset 2-16
parameters, representing 2-17
P predictive 2-21
π/4 DQPSK modulation 2-75 example 2-22
partitions vector 2-16
representing 2-17 Quantizer Decode block 4-367

I-5
 Index

R example 2-18
random features of the blockset 2-16
signals 2-6 parameters, representing 2-17
Random Deinterleaver block 4-368 scalar signals
Random Interleaver block 4-372 definition of xviii
Random-Integer Generator block 4-369 scatter diagrams 2-13
Rayleigh Noise Generator block 4-373 Scrambler block 4-399
Rectangular QAM Demodulator Baseband block Sequence Operations library 4-38
4-376 signal formatting
Rectangular QAM Demodulator Passband block features of the blockset 2-16
4-379 Signal Processing Toolbox
Rectangular QAM Modulator Baseband block for filter design 2-59
4-383 sinks library 2-12
Rectangular QAM Modulator Passband block reference for 4-5
4-387 sizes, of matrix signals xviii
references source coding
error-correction coding 2-39 features of the blockset 2-16
representing Source Coding library 2-16
codebooks 2-17 reference for 4-7
codewords 2-29 sources library 2-6
generator matrices 2-36 reference for 4-3
messages 2-29 SSB AM Demodulator Baseband block 4-401
partitions 2-17 SSB AM Demodulator Passband block 4-403
predictors 2-22 SSB AM Modulator Baseband block 4-405
quantization parameters 2-17 SSB AM Modulator Passband block 4-408
truth tables 2-36 synchronization
Rician Fading Channel block 4-391 features of the blockset 2-90
Rician Noise Generator block 4-394 Synchronization library 2-90
row vector signals xviii reference for 4-36

S T
sample times, in sources 2-7 timing, decision
sample-based signals, definition of xviii and eye diagrams 2-13
Sampled Quantizer Encode block 4-397 and scatter diagrams 2-13
scalar quantization truth tables
coding 2-20 representing 2-36

I-6
 Index

U
Uniform Noise Generator block 4-416
Utility Functions library 4-41

V
vector quantization 2-16
vector signals, definition of xviii
Viterbi Decoder block 4-419
Voltage-Controlled Oscillator block 4-424

W
Windowed Integrator block 4-426

I-7