Link Budget Analysis: Digital Modulation, Part 1
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Presentation Content
Link Budget Analysis: Digital Modulation, Part 1
1. Sources of Communication Data.
2. Metrics for Choice of Modulation.
A. Power Efficiency.
B. Bandwidth Efficiency.
3.
4.
5.
6.
7.
8.
9.
Digital Modulation Trade-offs.
Modulation: Types & Techniques.
Power Transfer into Free Space.
Digital Bandpass Modulations.
Modulation in Wireless App.
Performance Advantages.
Digital Modulation Process.
10. Digital Communication System.
11. BER: An Introduction.
12. Bit Rates & Transmission Channels
13. ASK: Amplitude Shift Keying.
14. ASK: Basis of operation.
15. ASK: Implementation.
16. PSD of Bandpass Binary ASK.
17. Error Probability of M-ary ASK.
18. Executive Summary.
Refer to Atlanta RFs presentation titled: Link Budget Getting Started,
which can be downloaded from our website: www.AtlantaRF.com.
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Typical Sources of Communication Data
1. Analog Data Sources: Produces continuous-time output using a device
that converts the real analog signal to electrical voltage.
A.
B.
C.
D.
Speech/Voice/Telephone.
Music/Sound.
Moving and static images.
And also: temperature, speed, time...
2. Digital Data Sources: Produces discrete-time output using a device that
processes logical digital signals (binary, ASCII).
A.
B.
C.
D.
Computer files/Keyboards/Monitors/Printers.
E-mail sent over the internet.
Digital storage devices (Compact Discs, DVDs, etc)
JPEG/MPEG files.
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Metrics for Choice of Modulation Scheme
1. High spectral efficiency: b . . . . Signal uses a small bandwidth.
A. Transmitted signal occupies the minimum RF channel bandwidth.
2. High power efficiency: p . . . . . . Detect a small signal power.
A. Provides low bit-error rates (BER) at low Signal-to-Noise (S/N) ratios.
3. High data rates: Bits per second.
4. Robust to multipath effects & fading conditions.
5. Easy to implement and cost-effective to operate.
6. Low carrier-to-cochannel signal interference ratio.
7. Low out-of-band radiation.
8. Constant or near constant envelope:
A. Constant envelope: Only phase is modulated; can use power-efficient
non-linear amplifiers.
B. Non-constant envelope: Phase and amplitude modulated; may need
power-inefficient linear amplifiers.
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Power Efficiency of Digital Modulation
A performance metric for digital communication systems
1. Power efficiency is the ability of a modulation technique to preserve the
fidelity/quality of digital messages at low power levels, and is
expressed as the ratio of the signal energy per bit (Eb , watt-sec) to the
noise power spectral density per bit (N0 , watts/hertz) required to
achieve a given probability of bit error rate, say BER ~ 105 :
E
Power Efficiency : p b
N0
required at the receiver input for certain
BER
2. To obtain good fidelity/quality, the signal power usually needs to be
increased for better noise immunity.
A. Tradeoff between signal fidelity (BER) and signal power (Eb/No).
B. Power efficiency describes how efficient this tradeoff is made.
3. There are cases when bandwidth is available but transmit power is limited.
A. In these cases as M goes up, the bandwidth increases but the required
power levels to meet a specified BER remains stable.
4. Modulations that are power-limited achieve their goals with minimum
expenditure of power at the expense of bandwidth. Examples are MFSK
and other orthogonal signaling.
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Bandwidth Efficiency of Digital Modulation
A performance metric for digital communication systems
1. Bandwidth (Spectral) efficiency describes the ability of a modulation scheme to
accommodate data within a limited frequency bandwidth. In general, it is defined
as the ratio of the throughput data bit rate: Rb, in bits per second, to the required
frequency bandwidth occupied by the modulated RF signal: BT, in hertz:
Bandwidth Efficiency : B
Rb
, bits/second/Hz
BT
2. Bandwidth efficiency reflects how efficiently the allocated frequency bandwidth is
utilized. Tradeoff between data rate: Rb and pulse width: Ts (BT ~ 1/Ts).
3. Channel capacity gives an upper bound of achievable bandwidth efficiency.
4. There are situations where bandwidth is at a premium, so modulations with large
throughput data rate per hertz are needed (large B = Rb/BT).
5. Hence we need standards with large time-bandwidth product: BTTb.
6. The GSM standard uses Gaussian minimum shift keying (GMSK) with BTTb=0.3.
7. Modulations that achieve bit error rates at a minimum expenditure of bandwidth,
but possibly at the expense of too high a signal power, are bandwidth-limited.
A. Examples are variations of MPSK and many QAM.
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Tradeoff: BW Efficiency and Power Efficiency
1. Fundamental tradeoff between Bandwidth Efficiency: B and Power
Efficiency: p . . . . in general:
A. If B improves, then p deteriorates (or vice versa).
1) May need to waste more signal power: Eb/No to get a better data rate: Rb.
2) May need to use less signal power (to save on battery life) at the expense of
a lower data rate.
B. B versus p is not the only consideration.
1) Use other factors to evaluate system complexity, resistance to MRC
impairments, etc.
2. Adding error control coding improves the power efficiency (there
are fewer errors), but reduces the bandwidth efficiency (redundant
data bits are also transmitted, which requires more bandwidth).
3. M-ary modulation schemes increase the bandwidth efficiency but
requires higher transmission power to keep the same bit error rate:
BER.
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Digital Modulation Tradeoffs
1. Linear Modulation:
A. The amplitude of the modulated transmitted signal: s(t), varies linearly with
the modulating digital signal: m(t). Bandwidth efficient but power inefficient.
Examples: M-ASK, M-PAM, BPSK, DPSK, QPSK, /4 PSK, M-QAM.
B. Information encoded in carrier signals amplitude and/or in carriers phase.
C. Easier to adapt. More spectrally-efficient then nonlinear modulation.
D. Issues: differential encoding, pulse shaping, bit mapping.
A. Often requires linear power amplifiers to minimize signal distortions.
2. Nonlinear Modulation:
A. The amplitude of the modulated transmitted signal: s(t), does not vary
linearly with the modulating digital signal: m(t). Power efficient but bandwidth
inefficient. Examples: FSK, MSK, GMSK, constant envelope modulation.
B. Information encoded in carrier signals frequency.
C. Continuous phase (CPFSK) modulation is a special case of FM.
D. Bandwidth determined by Carsons rule(1) (pulse shaping).
E. More robust to channel and power amplifiers nonlinearities.
1: J.R. Carson, "Notes on the theory of modulation,
Proceedings of IRE, vol. 10, no. 1 (Feb. 1922), pp. 57-64.
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Modulation: Types and Techniques
1. Analog Modulation: When the information-bearing message signal is
continuous-time analog, then the modulation is called analog modulation.
Common analog modulation techniques:
A. AM: Amplitude modulation : Message is carried in A(t). S(t) = A(t) cos(ct + 0).
B. FM: Frequency modulation: Message is carried in (t). S(t) = A0 cos((t) + 0).
C. PM: Phase modulation
: Message is carried in (t). S(t) = A0 cos(ct + (t)).
2. Digital Modulation: When the information-bearing message signal is
discrete-time digital, then the modulation is called digital modulation.
Common digital modulation techniques:
A.
B.
C.
D.
ASK: Amplitude Shift Keying : Message signal changes the carriers amplitude.
FSK: Frequency Shift Keying: Message signal changes the carriers frequency.
PSK: Phase Shift Keying
: Message signal changes the carriers phase.
QAM: Quadrature Amplitude Modulation. A combination of ASK and PSK.
3. For Binary (2-level) Digital Modulation (M = 2):
A. BASK: Binary Amplitude Shift Keying.
B. BFSK: Binary Frequency Shift Keying.
C. BPSK: Binary Phase Shift Keying.
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Types of Digital-to-Analog Modulations
si(t )
A (t ) cos(2f t (t ))
Time-varying
Amplitude
Time-varying
Frequency
Time-varying
Phase
Digital-to-Analog
Modulation Techniques
Bit rate is the number of bits transmitted per second: Rb = kRs .
Baud rate is the number of signal elements transmitted per second: Rs = Rb/k .
In the analog transmission of digital data, if a signal unit is composed of k bits, then the
bit rate is k times higher than baud rate. Baud rate determines the channel bandwidth
required to transmit the modulated signal.
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Digital Bandpass Modulation Techniques
In digital communications, the modulating baseband message signal: m(t) is a
binary or M-ary digital data stream. The carrier is usually a sinusoidal signal.
Voltage
1. Baseband digital message signal: m(t)
Digital
Signal
Tb
0
Time
2. Analog sinusoidal carrier signal:
A. Carrier signal: Ac cos( 2fct + c )
Carrier
Signal
Time
3. ASK: Amplitude Shift Keying.
A. Message signal changes the
carriers amplitude : Ai(t).
ASK
Signal
Time
4. FSK: Frequency Shift Keying.
A. Message signal changes the
carriers frequency : fi (t) .
FSK
Signal
Time
PSK
Signal
Time
5. PSK: Phase Shift Keying.
A. Message signal changes the
carriers phase : i(t) .
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Types of Digital Modulation Techniques
1. Amplitude Shift Keying: ASK
A. On-Off Keying: OOK.
B. Binary Amplitude Shift Keying: BASK.
2. Frequency Shift Keying: FSK
A. Binary Frequency Shift Keying: BFSK.
B. 4-level Frequency Shift Keying: 4-FSK.
3. Phase Shift Keying: PSK
A.
B.
C.
D.
Digital signal with two signal levels
Binary Phase Shift Keying: BPSK.
Quadrature Phase Shift Keying: QPSK, DQPSK, OQPSK, /4-QPSK.
8-Level Phase Shift Keying: 8-PSK.
16-Level Phase Shift Keying: 16-PSK.
4. Quadrature Amplitude Modulation: QAM
A. 16-QAM
B. 64-QAM
C. 128-QAM
D. 265-QAM
E. etc. . . .
5. Continuous Phase Modulation: CPFSK
A. Minimum Shift Keying: MSK
B. Gaussian MSK: GMSK
Digital signal with four signal levels
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Multi-level Signaling: Digital Mary Modulation
1. In general, multi-level (M-ary) digital communication is used to design a
communication system that is more bandwidth efficient. With M-ary
signaling, digital inputs with more than two modulation levels are allowed on
the transmitters input.
2. The data is transmitted in the form of symbols, each symbol is represented
by k bits, so there are M = 2k different signal levels in M-ary modulation.
3. In M-ary data transmission, one of M possible signals is transmitted during
each signaling interval: Ts , where: Ts = kTb and Tb = bit time interval.
4. There are many different Mary modulation techniques, some of these
techniques modulate one carrier parameter, like: Amplitude, or Phase, or
Frequency:
A. Mary ASK: Mary Amplitude Shift Keying: M-ASK or M-PAM.
1) The carrier signals amplitude takes on M different levels.
2) Used in baseband transmission: Pulse Amplitude Modulation (PAM) and in
bandpass transmission: ASK.
B. Mary PSK: Mary Phase Shift Keying: M-PSK.
1) The carrier signals phase takes on M different levels.
C. Mary FSK: Mary Frequency Shift Keying: M-FSK.
1) The carrier signals frequency takes on M different levels.
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Modulation in Wireless Applications
1. Analog FM: AMPS Advanced Mobile Phone System at 850 MHz.
2. GMSK: Gaussian Minimum Shift Keying:
A.
B.
C.
D.
E.
GSM Global System for Mobile Communications at 900 MHz.
DCS1800 - Digital Cellular System at 1800 MHz (USA)
PCS1900 Personal Communication System at 1900 MHz (USA)
DECT Digital European Cordless Telephone at 1880 1900 MHz (Europe)
CT2 Cordless Telephone 2 (Canada)
3. /4-DQPSK: /4 Differential Quadrature Phase Shift Keying
A. IS-54 at 900 MHz/IS-136 at 2 GHz (North America)
B. PDC Personal Digital Cellular at 800 & 1500 MHz/PHS (Japan)
4. QPSK(FL)/DQPSK(RL): IS-95 (North America Digital Cellular):
A. Data Rate = 48kb/s; Bandwidth = 30kHz
B. Bandwidth efficiency = 48/30 = 1.6bits/sec/Hz
5. BPSK, QPSK, OFDM: IEEE802.11 at 2.4 GHz & 5 GHz (ISM band).
6. GFSK: Bluetooth at 2.4 GHz (Industrial-Scientific-Medical band).
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Modulation Formats in Cable
Modulation
Description
Use
Comments
AM, FM, PM
Amplitude Modulation
Frequency Modulation
and Phase Modulation
Radio, Citizens Band,
Cable
Low Spectral Efficiency.
PAL, NTSC
Phase Alternate Line,
National Television
System Committee
Commercial Television and
Cable
Low Spectral Efficiency.
Noise viewable by
users.
QPSK, BPSK,
FSK
Quadrature Phase Shift
Keying, Binary Phase
Shift Keying, Frequency
Shift Keying
Cable modem return path,
DVB-S, Telemetry channels
Robust in poor signalto-noise.
VSB
Partially-suppressed carrier Vestigial
Sideband
North American broadcast
digital television
Good performance in
multi-path conditions.
QAM
Quadrature Amplitude
Modulation
Digital cable broadcast,
DVB-C, Cable modems
Requires good signalto-noise.
S-CDMA
Synchronous Code
Division Multiple Access
DOCSIS 2.0 return path
Good performance in
poor signal-to-noise.
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Performance Advantages of Digital Transmission
When compared to Analog Modulation
1. Digital transmission produces fewer data errors than analog transmission:
A. Data integrity & noise immunity: Easier to detect and correct information-bearing
data errors, since transmitted data is binary (1s & 0s : only two distinct values) .
B. Error coding is used to detect and correct digital transmission errors.
C. Regenerative capability: Regenerative digital repeaters placed along the
transmission channel can detect a distorted digital signal and retransmit a new,
clean digital data signal. These repeaters minimize the accumulation of noise and
signal distortion along the transmission channel.
2. Permits higher transmission data rates: Economical to build transmission
links of very high bandwidth. Optical fiber designed for digital transmission.
3. Better spectral efficiency: Effective use of limited frequency resources
(narrow bandwidth) to send a large amount of data.
4. Security & privacy: Enables encryption algorithms in information-bearing
digital bit stream signals. Deters phone cloning and eavesdropping.
5. Easy to multiplex multiple sources of information: Voice, video and data in
a single transmission channel, since all signals are made up of 1s and 0s.
6. Easy to integrate computer/communication systems.
7. Digital equipment consumes less DC power in a smaller physical size.
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Disadvantages of Digital Transmission
When compared to Analog Modulation
Disadvantages:
1. More Bandwidth Needed:
A. Transmission of digitally encoded analog signals requires significantly
more bandwidth than simply transmitting the original analog signal.
2. Circuit complexity:
A. Analog signals must be converted to digital pulses prior to transmission
and converted back to their original analog form at the receiver: Additional
encoding/decoding circuitry needed.
3. Synchronization:
A. Requires precise time synchronization between the clocks in the
transmitter and in the receiver.
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Digital Bandpass Modulation Process
Overview
1. Digital Modulation involves translating the baseband digital message signal: m(t),
to a bandpass analog signal: s(t), at a carrier frequency: fc , that is very high
compared to the digital baseband frequency: fb. The choice of carrier frequency
allows placement of the composite modulated signal in a desired frequency band
for signal processing. Modulation allows many signals with different carrier
frequencies to share the frequency spectrum.
2. Digital Modulation is achieved by switching or keying (i.e.: varying) the
amplitude, phase and/or frequency of a high-frequency sinusoidal analog carrier
signal: s(t) in accordance with the incoming information-bearing digital baseband
message signal: m(t) , a time sequence of symbols or pulses, thereby resulting in
a bandpass modulated signal that is transmitted by the sender over a channel.
Modulated signals propagate well through the atmosphere.
3. Changes in the amplitude, phase and/or frequency of the carrier signal are used
to represent a digital state of the modulating digital baseband signal.
4. Using this technique, digital or analog data is encoded into a digital signal.
5. A bandpass carrier signal modulated by baseband digital data has the form:
si(t )
A (t ) cos(2f t (t ))
where digital data bits are encoded in discrete time-varying amplitude Ai(t) (= ASK),
discrete time-varying phase: i(t) (= PSK), or discrete time-varying frequency: i =
2(fc - fi )t (= FSK), which remain constant over a data bit time interval: Tb .
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Basic Digital Communications System
Source
bits
Channel
bits
Passband
Analog In:
Audio
Video
A/D
Anti-alias
lowpass filter
Data
Source
Nyquist
sampling
Source Encoder
Channel
Encoder
FEC
ARQ
Block
Convolution
Bandpass
Modulator
ASK
FSK
PSK
Binary
Mary
Pulse
shaping
filter
ISI
Baseband
Digital input
Multiple
Access
FDMA
TDMA
CDMA
Tx
Analog
Waveforms Communications
Transmit
Digital
output
Channel:
Receive
User
Audio
Video
D/A
Low pass
filter
Path Loss
Noise
Distortion
Interference
Baseband
Source Decoder
Analog Out:
Transmit
Channel
Bandpass
Filter
Quantization
noise
Channel
bits
Channel
Decoder
Rx
Regenerate
Demodulator
& Detect
FEC
Matched filter
Envelope
Decision threshold Coherent
ARQ
Timing recovery
Block
Carrier recovery
Source Convolution
bits
Multiple
Access
Receive
Channel
Bandpass
Filter
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Building a Digital Communications System
1. Source Encoder: Samples and quantizes a time- & amplitude-varying analog
signal, and converts the samples into a digital binary bit stream of 1s and 0s,
then encodes it into a shorter digital signal (reduces the redundancy or reduces
the bandwidth requirement: data compression). Goal: Minimize signal distortion.
2. Channel Encoder: Accepts the digital signal and encodes it into a longer digital
signal by introducing redundant data bits in the information sequence for the
purpose of combating the effects of noise and interference in the transmission
channel, thereby minimizing transmission errors.
3. Modulator: Converts the digital information data sequences into high frequency
carrier waveforms that are compatible with the characteristics of the transmission
channel. Varies the amplitude, phase and/or frequency of the carrier waveform.
4. Transmission: Carrier modulated digital symbols are transmitted towards the
desired destination, using a certain physical medium (Guided: cable, optical fiber
and Unguided: wireless).
5. Channel estimation: Generally, transmission channels may introduce distortion
to the source signal, and the characteristics of the channel distortion need to be
estimated or identified at the receiver end, in order to reduce or eliminate the
distortion and recover the original signal. This is called channel estimation or
identification.
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BER: An Introduction
1.
2.
3.
4.
5.
6.
7.
8.
Bit Error Rate is a major indicator of the health of the communication system.
As data is transmitted some of the bits may not be received correctly.
The more bits that are incorrect, the more the signal will be affected.
Its important to know what portion of the bits are in error.
Need to know how much margin the system has before failure.
Good signal: BER < 10-10 .
Threshold for visible degradation: BER ~ 10-6 .
Example:
A. A 256QAM channel transmits at a symbol rate of 5M symbols per second.
B. Bit rate = 8 bits per symbol X 5M symbol per second = 40M bits per second.
C. Error Incident = Bit rate X BER = Errors Per Second.
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Bit Rates of Digital Transmission Systems
System
Bit Rate
Observations
Telephone
twisted pair
33.6-56 kbps
4 kHz telephone channel
Ethernet
twisted pair
10 Mbps, 100 Mbps
100 meters of unshielded
twisted copper wire pair
Cable modem
500 kbps-4 Mbps
Shared CATV return channel
ADSL twisted
pair
64-640 kbps in,
1.536-6.144 Mbps out
2.4 GHz radio
2-11 Mbps
28 GHz radio
1.5-45 Mbps
5 km multi-point radio
Optical fiber
2.5-10 Gbps
1 wavelength
Optical fiber
>1600 Gbps
Many wavelengths
Coexists with analog
telephone signal
IEEE 802.11 wireless LAN
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Examples of Transmission Channels
Channel
Bandwidth
Bit Rates
Telephone voice channel
3 kHz
33 kbps
Copper pair
1 MHz
1-6 Mbps
500 MHz (6 MHz channels)
30 Mbps/ channel
300 MHz (11 channels)
54 Mbps / channel
Many TeraHertz
40 Gbps / wavelength
Coaxial cable
5 GHz radio (IEEE 802.11)
Optical fiber
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ASK: Amplitude Shift Keying
One dimensional linear modulation
1. Binary (2-level) ASK: BASK
(1-bit: 2 signal levels)
Binary Data
BASK
signal
2. 4-level ASK: 4-ASK
(2-bits: 4 signal levels)
Binary Data
4-ASK
signal
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ASK: Amplitude-Shift Keying
Basis of operation
1. When the baseband signal modulates the amplitude of the carrier signal, the process is
called amplitude modulation. For digital baseband signals, it is called Amplitude Shift
Keying : ASK . Also referred to as PAM: Pulse Amplitude Modulation.
2. Amplitude-Shift Keying (ASK) is a form of digital modulation that represents digital data
solely as variations in the amplitude of a carrier signal.
3. In ASK, the amplitude of the carrier signal is changed between two (or more) levels by the
digital information message signal: m(t) to represent a binary bit 0 or a binary 1 . The
carrier signals center frequency: fc and phase: c remain constant.
4. For binary ASK (BASK) , binary digit 1 is represented by the presence of the carrier signal,
at constant amplitude, during a bit period: Tb , while binary bit 0 is the absence of the carrier
during a bit period. If Tb indicates the time duration of one information bit, the two time-limited
modulated signals can be expressed as:
2 Ei(t)
s( t )ASK Ac m( t ) cos 2 fc t c Tb cos ( 2f ct c) for a binary 1 ; m(t) 1
0
for a binary 0 ; m(t) 0
5. Carrier frequency: fc = nc/Tb, Hertz, for some fixed integer: nc .
6. On-Off Keying (OOK) is also called Amplitude Shift Keying (ASK), which consists of keying
(i.e.: switching) a carrier sinusoid on and off with a uni-polar binary signal.
7. Since noise affects the amplitude of a signal, ASK is highly susceptible to noise interference,
fading, and electromagnetic induction. ASK is also most susceptible to the effects of nonlinear devices, which compress and distort the signals amplitude. It is rarely used on its own.
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BASK: Binary Amplitude Shift Keying
Tb
2Tb
3Tb
4Tb
5Tb
Implementation of Binary ASK:
Amplitude
Digital signal
Message
m(t)
Time
C(t)
Time
ASK
signal
SASK(t)
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Power Spectral Density of Bandpass Binary ASK
Assumes baseband rectangular pulses:
Pv ( f )
1
Pg f f o Pg f f o
4
Eb sin(( f fo) / Rb )
8Rb ( f fo) / Rb
2fb = 2Rb
Energy per bit: Eb = P Tb , watts-second.
Null-to-Null RF transmission bandwidth: Bnull = (fo + fb) (fo fb) = 2fb = 2Rb = 2/Tb.
Bandwidth with 95% of the total transmitted power: B95% = 3fb (Hz), centered at fo .
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Error Probability for M-ary Amplitude Shift Keying
In an Additive White Gaussian Noise (AWGN) channel
A. Modulated signalfor Multi - Level ASK modulation:
s( t )ASK 2 Ei ( t ) cos ( 2f ct) 6 2i 12 M Es cos ( 2f ct), where Ei Eg 2i 1 M 2
Tb
( M 1 )Tb
2
B. Probability of symbol error for coherently detected Multi - Level ASK modulation:
2(M 1 ) 2 E g
Pse, MASK
Q
No
M
2(M 1 ) ( 6 log 2 M)E (M 1 )
( 3 log 2 M)Eb
b
erfc
2
(M 2 1 )N
M
(M
1
)N
M
o
o
(M 2 1 )
where: Es ( log 2 M)Eb
Eg Average energy/symbol.
3
C. Probability of bit error (BER) for M - ary ASK :
Pse ,MASK Pse ,MASK
, where: k log 2 M
log 2 M
k
D. Binary ASK (M 2) bit error probability :
Pbe, MASK
Pbe,BASK
Es
Q Eb 1 erfc Eb
Q
N 2
2N
o
o
No
4-ASK Signal Constellation Diagram:
00
s1
3 Eg
01
11
s3
s2
Eg
Eg
10
s4
3 Eg
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1 (t )
Error Probability for M-ary Amplitude Shift Keying
In an Additive White Gaussian Noise (AWGN) channel
1. The average probability of bit error (BER) for Multi-Level Amplitude Shift
Keying (M-ASK) modulation using coherent detection is:
( 3 log 2 M)Eb
2(M 1 ) 2 E g 2(M 1 ) ( 6 log 2 M)Eb (M 1 )
erfc
2
(M 2 1 )N
M log 2 M N o M log 2 M (M 1 )N o M log 2 M
o
(M 2 1 )
where: Es ( log 2 M)Eb
Eg Average energy/symbol and k log 2 M ,bits / symbol.
3
Pbe, MASK
M
4
16
64
256
Probability of Bit Error (BER): Pbe
Pbe,4 ASK
Pbe,16 ASK
Pbe,64 ASK
Pbe,256 ASK
6 Eb
3
erfc
8
15 N o
12 Eb
15
erfc
64
255 N o
M
8
18 Eb
63
erfc
384
4 ,095 N o
32
24 Eb
255
erfc
2048
65 ,535 N o
128
512
k
3
Probability of Bit Error (BER): Pbe
Pbe,8 ASK
Pbe,32 ASK
Pbe,128ASK
Pbe,512ASK
9 Eb
7
erfc
24
63 N o
15 Eb
31
erfc
160
1,023 N o
127
erfc
896
21Eb
16 ,383 N o
27 Eb
511
erfc
4608
262 ,143 N o
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Probability of Bit Error (BER): Mary ASK
In an Additive White Gaussian Noise (AWGN) channel
Probability of symbol error for coherently detected Multi - Level ASK modulation:
2(M 1 ) 2 E g
Pse, MASK
Q
No
M
2(M 1 ) ( 6 log 2 M)E (M 1 )
( 3 log 2 M)Eb
b
erfc
2
2
M
M
(M 1 )N o
(M 1 )N o
(M 2 1 )
where: Es ( log 2 M)Eb
Eg Average energy/symbol and k log 2 M, bits/symbol.
3
k,bits/ symbol =
1
2
3
4
5
Probability of bit error (BER)
M signal
Eb/No, dB
levels =
2
4
Eb/No Probability of Bit
8
Error:
16
32
Pbe,MASK
1.000
0.07865
0.13916
0.17295
0.17789
0.1674
1.585
0.03751
0.09756
0.14612
0.16391
0.1607
2.512
0.0125
0.05862
0.11576
0.14691
0.1523
3.981
0.00239
0.02787
0.08347
0.12667
0.1419
6.310
1.91E-04
0.00925
0.05232
0.10334
0.1292
10
10.000
3.87E-06
0.00175
0.02653
0.07781
0.114
12
15.849
9.01E-09
1.39E-04
0.00972
0.05202
0.096
14
25.119
6.81E-13
2.76E-06
0.00215
0.0291
0.0757
16
39.811
0.0E+00
6.25E-09
2.17E-04
0.0124
0.0542
18
63.096
0.0E+00
4.52E-13
6.35E-06
0.00347
0.0337
20
100.00
0.0E+00
0.0E+00
2.63E-08
5.05E-04
0.0168
22
158.49
0.0E+00
0.0E+00
4.97E-12
2.63E-05
0.006
24
251.19
0.0E+00
0.0E+00
0.0E+00
2.72E-07
0.0013
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for Multi - Level ASK :
Pse ,MASK Pse ,MASK
log 2 M
k
where: k log 2 M , bits/symbol
Pbe, MASK
The complementary error
function: erfc is built into
most spreadsheet software
programs, like: Excel.
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Probability of Bit Error (BER): M-ASK
1.E+00
Probability of Symbol Error for M - ASK :
Pse, MASK
Probability of Bit Error: Pbe,MASK
1.E-01
( 3 log 2 M)Eb
(M 1 )
erfc
2
M
(M 1 )N o
1.E-02
k = 2 bits/symbol
k = 3 bits/symbol
1.E-03
M = 32
k=5
k = 4 bits/symbol
k = 5 bits/symbol
M = 16
k=4
1.E-04
M=8
k=3
1.E-05
Probability of Bit Error (BER) for M - ASK :
M=4
k=2
Pse,MASK Pse,MASK
P
be, MASK
1.E-06
log 2 M
k
where: k log 2 M , bits/symbol.
1.E-07
10
12
14
Eb/No, dB
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20
22
24
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Eb/No = Signal energy per bit over Noise density per bit
May-2013
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Summary: Digital Modulation, Part 1
1. Digital Modulation continues to dominate the world of data & voice
communication with high throughput within a congested frequency
spectrum at affordable cost.
2. Design trade-offs for power-limited systems and bandwidth-limited
systems often narrows the choice of digital modulation techniques.
3. Amplitude Shift Keying provides a simple & cost-effective method
for communication, but is rarely used on its own, due to poor
susceptibility to noise and distortion.
4. Look for additional presentations from Atlanta RF on Digital
Modulation techniques, and visit our website: www.AtlantaRF.com
to download these and other topics on Link Budget Analysis.
Refer to background material in Atlanta RFs presentation titled: Link Budget Getting Started ,
which can be downloaded from our website: www.AtlantaRF.com.
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Atlanta RF
Services, Software & Designs
Thank You!
Contact Atlanta RF by e-mail at:
Atlanta RF Services : Services@AtlantaRF.com
Atlanta RF Software : Sales@AtlantaRF.com
Atlanta RF Designs : Designs@AtlantaRF.com
Bob Garvey
Chief Engineer
Atlanta RF, LLC
Or, contact Atlanta RF by phone at: 770-645-0315, to reach our Atlanta-area
office in Georgia, USA, and discuss our support to your current or future
projects & products.
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Presentations by Atlanta RF, LLC
Download various presentations at our website: www.AtlantaRF.com :
1.
2.
3.
4.
5.
6.
7.
8.
Satellite: LEO, MEO & GEO.
Antennas: An Overview.
Link Budget: Getting Started.
Link Budget: Digital Modulation Part 1 (Overview & M-ASK).
Link Budget: Digital Modulation Part 2 (M-FSK).
Link Budget: Digital Modulation Part 3 (M-PSK & QAM).
Link Budget: Error Control & Detection.
Multiple Access Techniques: FDMA, TDMA and CDMA.
Visit our website often as presentations are added for your viewing pleasure.
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