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EE4900/EE6720 Digital Communications Suketu Naik
EE4900/EE6720: Digital Communications
Lecture 10
Performance of
Communication System:
Bit Error Rate (BER)
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EE4900/EE6720 Digital Communications Suketu Naik
Block Diagrams of Communication System
Digital Communication System
Informatio
n (sound,
video, text,
data, …)
Transducer &
A/D ConverterModulator
Source
Encoder
Channel
Encoder
Tx RF
System
Output
Signal
D/A Converter
and/or output
transducer
DemodulatorSource
Decoder
Channel
Decoder
Rx RF
System
Channel
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EE4900/EE6720 Digital Communications Suketu Naik
Performance Metrics: Power and Bandwidth
Baseband Modulation is done before the information
(bits) is sent out using a carrier signal
Carrier signal is received (and down-converted to the
baseband signal)
Baseband signal is demodulated and information is
recovered
How do we know the performance of a modulation
scheme?
Bandwidth: measured from power spectral density of
the baseband signal, proportional to the bit rate
Power: Measured from probability of bit error (Bit
Error Rate or BER)
Trade-off between Bandwidth and Power
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EE4900/EE6720 Digital Communications Suketu Naik
EE4900/EE6720: Digital Communications
Bandwidth
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EE4900/EE6720 Digital Communications Suketu Naik
Bandwidth: PAM
To find Bandwidth, we first need the Fourier transform
of the pulse shape p(t) in continuous-time domain
Pulse shapes: NRZ, RZ, MAN, HS, SRRC
PAM Modulator
Bandwidth
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EE4900/EE6720 Digital Communications Suketu Naik
Bandwidth: QAM
To find Bandwidth, we first need the Fourier transform
of the pulse shape p(t) in continuous-time domain
Pulse shapes: NRZ, RZ, MAN, HS, SRRC
Direct Digital Synthesizer
QAM Modulator BandwidthSame Bandwidth
(shifted by Ω0)
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EE4900/EE6720 Digital Communications Suketu Naik
Bandwidth: Pulse Shapes
NRZ, RZ, MAN, and HS pulses
NRZ
HS
MAN
RZ
Frequency at which
10log10|P(f)|2<-60dB
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EE4900/EE6720 Digital Communications Suketu Naik
Bandwidth: Pulse Shapes
Continuous-time SRRC
α = Roll-off factor: indicates excess BW
α = 0: 0% excess BW
α = 0.5: 50% excess BW
α = 1: 100% excess BW
tSmaller α = Smaller
lobes in Frequency
Domain
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EE4900/EE6720 Digital Communications Suketu Naik
Bandwidth: Pulse Shapes
Discrete-time SRRCLp=3
Lp=6
Lp=12
When you truncate the pulse in
time-domain it creates side-lobes
in freq. domain
Lp=# of Symbols used to create
the SRRC pulse
Goal: -40 dB side-lobe level
Lp vs α to achieve -40 dB
attenuation in freq. domain
Decreasing α
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EE4900/EE6720 Digital Communications Suketu Naik
Bandwidth for PAM and QAM
Bandwidth is determined from Power Spectral Density
(PSD) of PAM pulse:
Eq. 6.1: PSD equation
Eq. 6.2: BW of NRZ, RZ, MAN, and HS pulses
Eq. 6.3: BW of SRRC pulse
Bandwidth is determined from Power Spectral Density
(PSD) of QAM pulse:
Eq. 6.29: PSD equation
Eq. 6.30 : BW of NRZ, RZ, MAN, and HS pulses
Eq. 6.31: BW of SRRC pulse
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EE4900/EE6720 Digital Communications Suketu Naik
EE4900/EE6720: Digital Communications
Probability of Bit Error
and Power
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EE4900/EE6720 Digital Communications Suketu Naik
Probability of Bit Error for PAM
The received baseband signal (after down-converting from the
carrier signal) is demodulated and detected (decoded)
The 1-D decision regions determine the amplitudes of the
approximated received signal
The probability of error is computed from the conditional
probabilities of error and applying the total probability theorem
Discrete-time PAM DemodulatorProbability of Error is computed
based on the decision regions
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EE4900/EE6720 Digital Communications Suketu Naik
Probability of Bit Error for 4-PAM
Decision Regions for 4-PAM (M=4)
Probability of Symbol Error, P(E), given that original
symbols were transmitted: Eq. 6.22, Eq. 6.23
Probability of Bit Error, Pb: Eq. 6.25, Eq. 6.26
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EE4900/EE6720 Digital Communications Suketu Naik
PDF for Matched Filter Output for 4-PAM
Received symbols will be shaped by randomness
introduced by noise which is defined by Gaussian R.V.
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EE4900/EE6720 Digital Communications Suketu Naik
Probability of Bit Error for M-ary PAM
Probability of Symbol Error, P(E): Eq. 6.27
Probability of Bit Error, Pb: Eq. 6.28
Probability of
Bit Error
Average Bit Energy over Noise Level
Eb/No: “ebno”
(rhymes with elbow)
is the required power
4
8
M=4
M=2
M=8
Pb is also known as
Bit Error Rate (BER)
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EE4900/EE6720 Digital Communications Suketu Naik
BER Plot for PAM
Eb/No
4
8
M=4
M=2
M=8
BER
How do we interpret the BER curves?
1) Find number of error bits given a certain power (Eb/No)
2) For constant power, BER increases as M increases
3) For constant BER, Power increases as M increases
Example: Pb=10-6 **
2-PAM: Eb/No=10.6 dB
4-PAM: Eb/No= 14.6 dB
8-PAM: Eb/No= 19.2 dB
** 10-6 or one in million bits is a standard
Trade-off between M
(faster transmission)
and BER
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EE4900/EE6720 Digital Communications Suketu Naik
BER Plot for PAM
Eb/No
4
8
M=4
M=2
M=8
BER
What about bandwidth?For Pb=10-6 and Rb=1 kbits/s : 2-PAM: Eb/No= 10.6 dB, BW=750 Hz
4-PAM: Eb/No= 14.6 dB, BW=375 Hz
8-PAM: Eb/No= 19.2 dB, BW=250 Hz
Bigger the M (# of
bits per symbol),
Smaller the BW,
Bigger the Power
BW
Decreases
Bigger M = Faster
Transmission
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EE4900/EE6720 Digital Communications Suketu Naik
Probability of Bit Error for QAM
The received baseband signal (after down-converting from the
carrier signal) is demodulated into I & Q signals
The 2-D decision regions determine the amplitudes of the
approximated I & Q signals
The probability of error is computed from the conditional
probabilities of error and applying the total probability theorem
Discrete-time QAM DemodulatorProbability of Error is computed
based on the decision regions
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EE4900/EE6720 Digital Communications Suketu Naik
Probability of Bit Error for 16-QAM
Decision Regions for 16-PAM (M=16)
Probability of Symbol Error, P(E), given that original symbols
were transmitted: Eq. 6.61, Eq. 6.62
Probability of Bit Error, Pb: Eq. 6.63
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EE4900/EE6720 Digital Communications Suketu Naik
Probability of Bit Error for M-ary QAM For MPSK, Probability of Bit Error, Pb: Eq. 6.72
For square MQAM, Probability of Bit Error, Pb: Ex. 6.5
For irregular MQAM, Probability of Bit Error, Pb: Eq. 6.91
Probability of
Bit Error
Average Bit Energy over Noise Level
M=64
(6 bits/symbol)
M=16
(4 bits/symbol)
M=256
(8 bits/symbol)
M=4
(2 bits/symbol)
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EE4900/EE6720 Digital Communications Suketu Naik
BER Plot for MPSK**
Which one is better?
** Recall that MPSK is a special case of MQAM
M=4
(2 bits/symbol)
M=8
(3 bits/symbol)
M=16
(4 bits/symbol)
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EE4900/EE6720 Digital Communications Suketu Naik
BER Plot
Which one is better?
4-PAM
Y-QAM
QPSK
M=4, 2 bits/symbol
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EE4900/EE6720 Digital Communications Suketu Naik
BER Plot
Which one is better?
M=8, 3 bits
CCITT V.29 (9600 bps modem)
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EE4900/EE6720 Digital Communications Suketu Naik
Measured BER Plot
How to measure BER for an actual comm. system?
1) Compare transmitted bits with received bits (from the received
symbols) and find BER. Repeat for different power levels
2) Example:
Tx: [1 0 0 1 0 1 0 0 1 1]
Rx: [1 1 0 0 0 1 0 0 1 1]
BER= Number of error bits/
Total number of bits
BER= 2/10=0.2=20%
Interpretation:
2 out of 10 bits are erroneous
20% chance of getting errors
Example: Measured BER performances of
IMDD-OOFDM** systems
** intensity-modulated and direct-detection optical OFDM
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EE4900/EE6720 Digital Communications Suketu Naik
BER Meters
Use BER Test Meters
Tektronix BitAlyzer® Bit
Error Rate Tester BA
Reach Technologies
BER Tester
Cool Low-cost
and Home-made
BER Tester
(Senior/M.S.
Project)
Example: NI’s PXI-6552 box
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EE4900/EE6720 Digital Communications Suketu Naik
Usefulness of BER
Performance Metric
Determine the integrity of the communication system
Key parameter that is used in assessing digital comm. systems
that transmit data from one location to another
Determine what degrades the digital signal: noise, interference,
changes to the propagation path, phase jitter, etc.
How to improve the communication system?
A: Reduce BER by reducing BW, increasing transmitter
power, decreasing data speed, etc.
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EE4900/EE6720 Digital Communications Suketu Naik
Usefulness of BER
Link Budget
System design: Find Eb/No (C/No) in terms of transmitter power,
distance, antenna gain, noise level, losses, etc.
Link budget equation: Eq. 6.126
Example: 3G uplink in suburban environment
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EE4900/EE6720 Digital Communications Suketu Naik
Matlab/Simulink Exercise
1) Find bandwidth of SRRC pulse
2) Find BER of either of the comm. system in Assignment 5
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EE4900/EE6720 Digital Communications Suketu Naik
Assignment 6 [10]
Simulate and generate BER plot for either of the comm.
system in Assignment 5 [10]
Submit the following:
1) BER plot:
Compare ideal BER (Formula based) with your system
Example