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 Edited by: Louise Crockett David Northcote Robert W. Stewart

Software Defined Radio with

Zynq UltraScale+ RFSoC
Software Defined Radio
This book introduces Zynq UltraScale+ RFSoC, a technology that brings real, single-chip, software
defined radio (SDR) to the marketplace. RFSoC devices are the first adaptive SoCs (Systems-on-Chip) to
monolithically integrate multiple RF signal chains along with Arm application and real-time, multi-core

®
with
processors and programmable logic. By eliminating the need for dozens of discrete devices, RFSoC chips
offer unprecedented flexibility and reduced power consumption when compared to alternative, multi-

Zynq UltraScale + RFSoC

component solutions. RFSoC is not so much a radio on a chip, but almost an entire base station on a chip!
Moreover, besides widespread application in current 5G mobile communication networks, RFSoC devices ®
also enable the design and development of emerging 6G systems and are now being used in many other
domains including high-speed radar, advanced instrumentation, radio astronomy and quantum computing.

We anticipate that the book will be of interest and use across a number of technical areas. It serves as an
introduction to the family of RFSoC devices and its key features and programmability. Special attention is
paid to the RF signal chains including the high-resolution, direct RF data converters, the digital up-converters
and digital down-converters, and the quadrature mixers. Further sections explore the forward error
correction (FEC) units and the interfaces between the RF, programmable and the processor subsystems.
The book explores software defined radio concepts and architecture and key DSP algorithms such as multi-
Nyquist zone operation, frequency planning, multi-rate FIR filters and FFTs. By integrating high-bandwidth,
high-resolution, direct-RF, analogue-to-digital and digital-to-analogue converters, RFSoC devices can
access more of the electromagnetic spectrum than any previous SoC. Whatever signal bands are of interest
to you, RFSoC technology provides a programmable platform for innovative research and design!

A selection of hands-on exercises via Jupyter Lab notebooks accompany the book and are available from
the book’s companion GitHub repository. There are also design examples (including SDR designs) to build
and implement real systems based on PYNQ (Python open-source, design framework) and supported
boards, such as the RFSoC4x2. Wherever you are in your career, whether you are a student, a researcher,
an educator, a professional engineer or manager, we hope that you find this book a useful and pragmatic
reference on the incredible RFSoC technology.

www.RFSoCbook.com

Robert W. Stewart
David Northcote
Louise Crockett
Edited by:
Printed Book Front Cover Downloaded from www.RFSoCbook.com
 Edited by: Louise Crockett David Northcote Robert W. Stewart

Software Defined Radio with

Zynq UltraScale+ RFSoC
Software Defined Radio
This book introduces Zynq UltraScale+ RFSoC, a technology that brings real, single-chip, software
defined radio (SDR) to the marketplace. RFSoC devices are the first adaptive SoCs (Systems-on-Chip) to
monolithically integrate multiple RF signal chains along with Arm application and real-time, multi-core

®
with
processors and programmable logic. By eliminating the need for dozens of discrete devices, RFSoC chips
offer unprecedented flexibility and reduced power consumption when compared to alternative, multi-

Zynq UltraScale + RFSoC

component solutions. RFSoC is not so much a radio on a chip, but almost an entire base station on a chip!
Moreover, besides widespread application in current 5G mobile communication networks, RFSoC devices ®
also enable the design and development of emerging 6G systems and are now being used in many other
domains including high-speed radar, advanced instrumentation, radio astronomy and quantum computing.

We anticipate that the book will be of interest and use across a number of technical areas. It serves as an
introduction to the family of RFSoC devices and its key features and programmability. Special attention is
paid to the RF signal chains including the high-resolution, direct RF data converters, the digital up-converters
and digital down-converters, and the quadrature mixers. Further sections explore the forward error
correction (FEC) units and the interfaces between the RF, programmable and the processor subsystems.
The book explores software defined radio concepts and architecture and key DSP algorithms such as multi-
Nyquist zone operation, frequency planning, multi-rate FIR filters and FFTs. By integrating high-bandwidth,
high-resolution, direct-RF, analogue-to-digital and digital-to-analogue converters, RFSoC devices can
access more of the electromagnetic spectrum than any previous SoC. Whatever signal bands are of interest
to you, RFSoC technology provides a programmable platform for innovative research and design!

A selection of hands-on exercises via Jupyter Lab notebooks accompany the book and are available from
the book’s companion GitHub repository. There are also design examples (including SDR designs) to build
and implement real systems based on PYNQ (Python open-source, design framework) and supported
boards, such as the RFSoC4x2. Wherever you are in your career, whether you are a student, a researcher,
an educator, a professional engineer or manager, we hope that you find this book a useful and pragmatic
reference on the incredible RFSoC technology.

www.RFSoCbook.com

Robert W. Stewart
David Northcote
Louise Crockett
Edited by:
Printed Book Back Cover Downloaded from www.RFSoCbook.com
 Software Defined Radio
with
Zynq® UltraScale+™ RFSoC

With 19 Chapters, 9 Jupyter Notebooks, and 717 pages

the printed version of this pdf book is available from
Amazon and other on-line book-sellers.

More information on printed books at:

https://www/RFSoCbook.com

Web Version v.20230123 Downloaded from www.RFSoCbook.com

 Open Source Licence to Use and Reproduce
Text and diagrams from this PDF book can be reproduced in their entirety and used
for non-profit academic teaching and research purposes, provided that a clear
reference to the original source is made in all derivative documents and/or
publications. This reference should be of the following form:
L.H. Crockett, D. Northcote, R. W. Stewart (Editors), Software Defined
Radio with Zynq UltraScale+ RFSoC, First Edition, Strathclyde Academic
Media, 2023. https;//www.RFSoCbook.com.
Requests to use content from this book for other than non-profit academic purposes
should be directed to the publisher at info@RFSoCbook.com.

Available PDF Book Downloads

This PDF book is available for free download only from the book website at:
https://www.RFSoCbook.com
It is also available in published and printed book form from on-line booksellers.
This book must not be reproduced by any third parties in its original form for the
purposes of selling in printed or electronic form. It must also not be electronically
distributed by any unauthorised third party, and it cannot be hosted on any third
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Anyone requiring a PDF copy can get one freely from the book website. Or to point
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Software Defined Radio
with
Zynq UltraScale+ RFSoC

Louise H. Crockett

David Northcote

Robert W. Stewart

(editors)

Department of Electronic & Electrical Engineering

University of Strathclyde
Glasgow, Scotland, UK.

January 2023

www.RFSoCbook.com

Downloaded from www.RFSoCbook.com

First published January 2023 by Strathclyde Academic Media.
© Strathclyde Academic Media.
Cover design by Mario Stomboli, Scribble Design. Photography by Kenneth Barlee.

Open Source Licence to Use and Reproduce

This book is available in print and as an electronic book (in PDF format) from https://www.RFSoCbook.com.
Text and diagrams from this book may be reproduced in their entirety and used for non-profit academic purposes, provided that a clear
reference to the original source is made in all derivative documents. This reference should be of the following form:
L.H. Crockett, D. Northcote, R. W. Stewart (Editors), Software Defined Radio with Zynq UltraScale+ RFSoC, First Edition,
Strathclyde Academic Media, 2023. https;//www.RFSoCbook.com.
Requests to use content from this book for other than non-profit academic purposes should be directed to the publisher, contactable via
the book webpages at https://www.RFSoCbook.com.
This book may not be reproduced in its original form and may not be sold or electronically distributed by any unauthorised third party.

Warning and Disclaimer

The best efforts of the authors and publisher have been used to ensure that accurate and current information is presented in this book.
This includes researching the topics covered, and developing examples. The material included is provided on an “as-is” basis in the best
of faith, and neither the authors nor publishers make any warranty of any kind, expressed or implied, with regard to the documentation
contained in this book. The authors and publisher shall not be held liable for any loss or damage resulting directly or indirectly from
any information contained herein.

Trademarks
AMD, the AMD logo, LogiCORE, MicroBlaze, Spartan, UltraScale, UltraScale+, Versal, Vitis, Vivado, Xilinx, the Xilinx logo and Zynq,
are all trademarks or registered trademarks of Advanced Micro Devices, Inc.
MATLAB and Simulink are registered trademarks of MathWorks, Inc.
Linux® is the registered trademark of Linus Torvalds in the U.S. and other countries.
Arm, Cortex, AMBA, Mali, Neon, and TrustZone are registered trademarks of Arm Limited (or its subsidiaries) in the EU and/or
elsewhere. All rights reserved. This publication is independent and it is not affiliated with, or endorsed, sponsored or authorised by
Arm Limited.
Dell is a trademark of Dell Inc. or its subsidiaries.
Intel and Xeon are trademarks of Intel Corporation or its subsidiaries.
Wi-Fi® is a registered trademark of the Wi-Fi Alliance®.
Android is a trademark of Google LLC.
Ettus Research and USRP are trademarks of National Instruments. Neither Strathclyde Academic Media, nor any software programs or
other goods or services offered by Strathclyde Academic Media, are affiliated with, endorsed by, or sponsored by National Instruments.
All other trademarks used in this book are acknowledged as belonging to their respective companies. The use of trademarks in this
book does not imply any affiliation with, or endorsement of, this book by trademark owners.

Downloaded from www.RFSoCbook.com

Table of Contents

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Introducing the Team . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1) Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1) The Coming of SDR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2) SDR with Zynq UltraScale+ RFSoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3) Design Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4) How to Use this Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5) Related Work and Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6) Chapter Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Notebook Set A) Introduction to Jupyter Notebooks and PYNQ . . . . . . . . . . . . . . . . . . . . .7

A.1) Getting Started with Jupyter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
A.2) Visualisation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
A.3) The PYNQ Framework and RFSoC-PYNQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
A.4) Overlays and Hardware Interfacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2) Software Defined Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

2.1) Radio Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2) What is Software Defined Radio (SDR)? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3) Motivations for SDR: Then and Now . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4) The Radio Frequency Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5) Spectrum Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6) Wireless Communications Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7) SDR Radio Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.8) Key Radio Terminology and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.9) SDR Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.10) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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Table of Contents

3) Introduction to Zynq UltraScale+ RFSoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1) RFSoC as an SDR Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2) A System on Chip for RF Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3) Zynq UltraScale+ RFSoC Architecture Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4) RFSoC Development Boards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5) Key Features and Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4) DSP Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1) Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2) Quantisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3) Time and Frequency Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4) Fixed Point Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5) Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.6) The Analogue-Digital Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.7) Multirate Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.8) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Notebook Set B) DSP Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

B.1) Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
B.2) Quantisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
B.3) ADCs and DACs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
B.4) Filtering and Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5) Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.1) Fourier Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2) Understanding The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3) The Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.4) The Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.5) Short-Time Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.6) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Notebook Set C) Exploring the Spectrum with the RFSoC . . . . . . . . . . . . . . . . . . . . . . . 183

C.1) Exploring the Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
C.2) The RFSoC Spectrum Analyser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
C.3) Additional Spectral Analysis Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

6) Wireless Communications Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

6.1) Layered Models for Communications Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

ii

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 Table of Contents

6.2) The Wireless Physical Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

6.3) Baseband Modulation (Bits to Symbols) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.4) Baseband Demodulation (Symbols to Bits) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
6.5) The Radio Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.6) Pulse Shaping and Matched Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
6.7) Bit Error Rate (BER) Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
6.8) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

Notebook Set D) Wireless Communications Fundamentals . . . . . . . . . . . . . . . . . . . . . . .229

D.1) Baseband Modulation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
D.2) Noise and Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
D.3) Pulse Shaping and Matched Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

7) Quadrature Modulation & Complex Exponentials . . . . . . . . . . . . . . . . . . . . . . . . . . .233

7.1) Signal Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
7.2) Amplitude Modulation and Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
7.3) Quadrature Amplitude Modulation and Demodulation . . . . . . . . . . . . . . . . . . . . . . . . 251
7.4) Quadrature Modulation and Demodulation with Complex Notation . . . . . . . . . . . . . 256
7.5) Spectral Representation of Complex Exponential Demodulation . . . . . . . . . . . . . . . . 260
7.6) Receiver Frequency Offset Error and Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
7.7) Equivalence of Quadrature and Complex Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . 267
7.8) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

Notebook Set E) Complex Frequency Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .271

E.1) Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
E.2) Quadrature Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
E.3) Complex Quadrature Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

8) SDR Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275

8.1) SDR Architectures Through the Ages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
8.2) Multiple Input, Multiple Output (MIMO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
8.3) The Digital Baseband Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
8.4) Digital Up- and Downconversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
8.5) Front End Analogue Signal Conditioning, and Antennae . . . . . . . . . . . . . . . . . . . . . . . 297
8.6) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

9) RF Data Converters: Analogue to Digital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .301

9.1) Analogue to Digital Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
9.2) ADCs for RF Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
9.3) RF-ADCs on RFSoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

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9.4) RF-ADC Processing Stages: The Digital Complex Mixer . . . . . . . . . . . . . . . . . . . . . . . 313

9.5) RF-ADC Processing Stages: the Programmable Decimator . . . . . . . . . . . . . . . . . . . . . 316
9.6) Principles of RF-ADC Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
9.7) Design Tool Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
9.8) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

10) RF Data Converters: Example Receiver Architectures . . . . . . . . . . . . . . . . . . . . . . . 337

10.1) Example 1: Nyquist Zone 1, Direct-RF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
10.2) Example 2: Nyquist Zone 2, Direct-RF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
10.3) Example 3: Nyquist Zone 1, Analogue IF Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
10.4) Example 4: I/Q Mixer to Analogue Baseband and Sampling . . . . . . . . . . . . . . . . . . . . 348
10.5) Example 5: Custom Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
10.6) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

11) RF Data Converters: Digital to Analogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

11.1) Digital to Analogue Conversion Recap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
11.2) DACs for RF Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
11.3) RF-DACs on RFSoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
11.4) RF-DAC Processing Stages: The Programmable Interpolator . . . . . . . . . . . . . . . . . . . 367
11.5) RF-DAC Processing Stages: The Digital Complex Mixer . . . . . . . . . . . . . . . . . . . . . . . 370
11.6) RF-DAC Processing Stages: The Image Rejection (IMR) Filter . . . . . . . . . . . . . . . . . . 372
11.7) Principles of RF-DAC Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
11.8) Design Tool Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
11.9) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

12) RF Data Converters: Figures of Merit and Frequency Planning . . . . . . . . . . . . . . . 383

12.1) Noise and Spurious Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
12.2) Traditional Data Converter Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
12.3) Frequency Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
12.4) RF-Sampling Data Converter Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
12.5) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

Notebook Set F) Frequency Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

F.1) Introduction to Frequency Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
F.2) RFSoC Frequency Planner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

13) Design Tools and Workflows for RFSoC SDR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

13.1) High Level Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
13.2) Programmable Logic (PL) Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
13.3) Processing System (PS) Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

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13.4) Hardware-Software Co-Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

13.5) Dynamic Function eXchange (DFX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
13.6) Clocks, Timing, and Sample Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
13.7) Antennas, Filters, and Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
13.8) SDR Design Flow for PYNQ on RFSoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
13.9) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

Notebook Set G) RFSoC Radio Demonstrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .457

G.1) The Radio System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
G.2) Observing the Radio Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
G.3) Transmit and Receive: “Hello World!” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

14) Forward Error Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .461

14.1) Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
14.2) Principles of Forward Error Correction (FEC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
14.3) Hamming Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
14.4) Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
14.5) Viterbi Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
14.6) The BCJR, Log MAP and Max Log MAP Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 478
14.7) Performance of Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
14.8) FEC for Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
14.9) Turbo Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
14.10) LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
14.11) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

15) Practical SD-FEC Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .505

15.1) SD-FEC Blocks and IP Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
15.2) Hardware Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
15.3) Run-Time PYNQ Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
15.4) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

Notebook Set H) Forward Error Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .533

H.1) First Principles FEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
H.2) Using the Hardened SD-FEC Block for Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
H.3) Communications Channel Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
H.4) Using the Hardened FEC Block for Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
H.5) Bit Error Rate and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

16) OFDM: Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . . . . . . . . . . . .537

16.1) Motivation for OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

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16.2) Multi-Carrier Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

16.3) OFDM Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
16.4) OFDM Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
16.5) Impairments in OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
16.6) OFDM Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
16.7) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

Notebook Set I) Practical OFDM Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

I.1) OFDM Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
I.2) Channel Estimation and Equalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
I.3) RFSoC OFDM Transceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

17) RFSoC Applications in Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

17.1) Introduction to 4G/5G Radio Access Networks (RANs) . . . . . . . . . . . . . . . . . . . . . . . . 573
17.2) Evolution to 4G/5G OpenRAN Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
17.3) RFSoC Products for Applications in Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . 582
17.4) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

18) MIMO and Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

18.1) Introduction to MIMO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594
18.2) Spatial Multiplexing and Spatial Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595
18.3) MIMO Channel Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
18.4) Receiver Processing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597
18.5) Transmitter Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
18.6) MIMO Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601
18.7) MIMO Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
18.8) Phased Array Beamformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
18.9) Beamforming Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
18.10) Beamforming Implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615
18.11) RFSoC Support for MIMO and Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
18.12) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627

19) Dynamic Spectrum Access and Cognitive Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

19.1) Spectrum Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
19.2) Dynamic Spectrum Access (DSA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
19.3) DSA Frameworks in Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638
19.4) Deployment of Fully Dynamic Spectrum Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642
19.5) Advancing DSA Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
19.6) Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664

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List of References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .669

List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .689

List of Equations and Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .703

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .705

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 Foreword
In 2019, Xilinx announced its Zynq UltraScale+ RF System on Chip (RFSoC) product portfolio, manufactured
using advanced FinFET transistor technology. A confluence of compelling factors motivated the development
of the RFSoC: the emergence of wideband, digitally assisted, RF data converters; the superior analog perfor-
mance of FinFET transistors; the demand for large arrays of digitized RF channels in emerging 5G Massive-
MIMO radios; the imperative to maximise bandwidth at low power though monolithic integration of RF and
digital signal processing functions; and the success and widespread adoption of the Zynq SoC and MPSoC
product families. The software adaptability, small form factor and low power operation of the RFSoC has
resulted in its widespread deployment not only in 5G networks and proprietary software defined radio (SDR)
implementations but also in radar systems, test and measurement equipment, and cabled networks. For some
of the world’s evolving RF sampling rate enabled research, design and development programmes, the RFSoC
will also provide a platform for the rapidly advancing 6G communications domain, and provide capability for
the high speed control and implementation requirements of quantum computing.

Building on the success of The Zynq Book and Exploring Zynq MPSoC, we were delighted to collaborate with
the University of Strathclyde in this latest book 'Software Defined Radio with Zynq UltraScale+ RFSoC'. The
book introduces the reader to important fundamental theory and architectures in advanced digital communi-
cations system, which can then be explored for implementation on the RFSoC platform. While the RFSoC
incorporates all the features of the Zynq MPSoC including the multi-core ARM processor, complex and
software programmable hardware fabric, it additionally supplies up to 16 high performance transmit and
receive RF-subsystems which can synthesize and digitise wideband, RF signals all the way to-6 GHz. Tradi-
tional RF functions such as oscillators, mixers and filters are now integrated digitally as part of each RF-
subsystem. Throughout the book, practical examples are provided in the form of Jupyter Notebooks on the
PYNQ development platform.

Given that the RFSoC enables developers to architect a software-programmable RF radio in a single device, it
is entirely appropriate that the Software Defined Radio (SDR) concept is introduced at the outset. This is
followed by an overview of the RFSoC architecture, features, and available hardware development platforms.
DSP and Wireless Communications fundamentals are then covered followed by an examination of SDR archi-

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this number, it is impossible. Enough has been indicated above, to
show her strong sympathy with her daughter’s tastes, and how
much she aided in forming them.

The January Number.—We confess to a great degree of pride, from

the reception of our January number, by the newspaper press all
over the country, and from the regular subscribers to the work. It
has been pronounced, indeed, in several influential quarters, “The
best number of a monthly magazine ever issued in the language,”
and this not alone from the number and beauty of the
embellishments—every one of which imparted a value as a work of
art to the number—but from the worth, variety and amount of
literary matter. In issuing a double number to our readers, we were
fully aware that we were repaying but a part of what we owe them,
for the liberal encouragement extended to us for a period of ten
years, without deviation or diminution; but we were scarcely
prepared for the large increase to our list of new friends which, in
two cities alone, extended to over three thousand new names.
From every part of the country each mail comes freighted with
clubs from persons with whose subscriptions we have not heretofore
been honored, and our old friends, with astonishing unanimity,
continue to cling to “Graham as the best and only good Magazine”
amidst the mass of periodicals which now make up in noise and
promises, what they lack in merit and ability to perform. To say that
we are not flattered by this mark of favor extended to us by the
readers of this country would be useless, but so far from this fact
lessening our exertions, it only spurs us on to new endeavors to
maintain that ascendancy over all others which we have always held,
by issuing a Magazine incomparably better than any that attempts to
rival it.
Our February number, we think, will show no falling off in our
exertions, and the two numbers of the volume are an earnest of
what our readers may expect during the whole year of 1849. May it
prove a prosperous and happy one to our subscribers, as it has
opened auspiciously for ourselves.

A New Sea Story.—We are gratified to be able to announce a new

Sea Story for the pages of Graham’s Magazine, by W. F. Lynch, of the
navy, whose recent explorations of the Dead Sea and vicinity, have
so much occupied the attention of the newspapers and scientific
bodies generally. The story is written with marked ability, and will be
quite an attraction in the coming numbers of Graham.

Our Premium Plate.—We shall forward promptly to clubs and

subscribers entitled to our large premium plate, copies, carefully
done up for preservation, as soon as the artist completes it. It will be
a very beautiful parlor ornament when properly framed.

Our Fashion Plate for this month has been delayed by the ocean
steamer, and as we issue this number early, we postpone it till next
month.
Painted by Cook Engd by Rawdon, Wright & Hatch

(OUR CONTRIBUTORS)

Mrs. M. M. Davidson
Engraved Expressly for Graham’s Magazine
 THE BELLS OF OSTEND.
WRITTEN ON A BEAUTIFUL MORNING AFTER A STORM,
BY W. L. BOWLES,

THE MUSIC COMPOSED AND RESPECTFULLY DEDICATED TO

SAMUEL MOFFAT JR. ESQ. OF ALBANY,
BY J. HILTON JONES.
No, I never, till life and its shadows shall end,
Can forget the sweet sound of the bells of Ostend!
The day set in darkness, the wind it blew loud,
And rung as it pass’d thro’ each
 murmuring shroud.

My forehead was wet with the foam of the spray,

My heart sighed in secret for those far away;
When slowly the morning advanc’d from the east,
The toils and the noise of the tempest had ceased:
The peal from a land I ne’er saw seemed to say,
Let the stranger forget all his sorrow to-day.

SECOND VERSE.

Yet the short-lived emotion was mingled with pain—

I thought of those eyes I should ne’er see again;
I thought of the kiss, the last kiss which I gave,
And a tear of regret fell unseen on the wave;
I thought of the schemes fond affection had planned,
Of the trees, of the towers of my own native land;
But still the sweet sounds, as they swelled on the air
Seemed tidings of pleasure, though mournful to bear;
And I never, till life and its shadows shall end,
Can forget the sweet sound of the bells of Ostend.

Transcriber’s Notes:
For illustrations, some caption text may be missing or incomplete
due to condition of the originals available for preparation of the
ebook. In the story The Wager of Battle, the Chapter VI heading is
missing due to being absent from the original publication.
Hyphenation and archaic spellings have been retained. Punctuation
has been corrected without note. Obvious typographical errors have
been corrected as noted below.

page 90, leaves are sear, ==> leaves are sere,

page 93, to make their ==> to make to their
page 104, whispered a page ==> whispered to a page
page 106, cylinders and guaging ==> cylinders and gauging
page 107, for the denouément ==> for the dénouement
page 107, I glad ==> I am glad
page 110, from all wordly ==> from all worldly
page 111, none was politec ==> none was politic
page 111, of their Lupercalla ==> of their Lupercalia
page 113, the wordly advantages ==> the worldly advantages
page 113, Mendelsshon’s music ==> Mendelssohn’s music
page 114, Druid chorusses ==> Druid choruses
page 119, Greydon, then she ==> Greydon, than she
page 121, tonge of flame ==> tongue of flame
page 125, from a regime forcé ==> from a régime forcé
page 127, merchans of celebrity ==> merchants of celebrity
page 128, ask him them ==> ask him then
page 132, sod have been ==> sod had been
page 132, sear turf of ==> sere turf of
page 145, havn’t told us ==> haven’t told us
page 146, physican arrived ==> physician arrived
page 150, maiden-thought be- becomes ==> maiden-thought
becomes
page 151, style and rythm ==> style and rhythm
page 152, invaluabte companion ==> invaluable companion
page 153, with the orginal ==> with the original
page 154, down and mak ==> down and make
page 155, was her’s ==> was hers
page 155, an open sessame ==> an open sesame
*** END OF THE PROJECT GUTENBERG EBOOK GRAHAM'S
MAGAZINE, VOL. XXXIV, NO. 2, FEBRUARY 1849 ***

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