By: Dr. Uri Mahlab

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Simulation in Digital Communication
By Dr. Uri Mahlab
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chapter 5 Baseband Digital Transmission
By Dr. Uri Mahlab
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Binary Signal Transmission
Binary data consisting of a sequence of 1s and
0s.

• Tb - Bit time interval

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AWGN - Channel

AWGN
Noise PSD
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Receiver

• The receiver task is to decide whether a O or 1
  was transmitter
• The receiver is designed to minimize the error
  probability.
• Such receiver is called the Optimum receiver.

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Optimum Receiver for the AWGN Channel
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Signal Correlator
Output data
Sampling _at_ tTb
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detector
Output data
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Example 5.1 suppose the signal waveforms s0(t)
and s1(t) are the ones shown in figure 5.2, and
let s0(t) be the transmitted signal. Then, the
received signal is
Figure 5.2 Signal waveforms s0(t) and s1(t) for
a binary communication system
Determine the correlator outputs at the sampling
instants.
Answer ip_05_01
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Figure 5.3 illustrates the two noise-free
correlator outputs in the interval
for each of the two cases-I.e., when
s0(t) is transmitted and when s1(t) is
transmitted.
(b)
(a)
Figure 5.3Noise-free correlator outputs.(a)
s0(t) was transmitted.(b) s1(t) was transmitted.
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0
r
Probability density function p(r00) and p(r10)
when s0(t) is transmitted
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Matched Filter

• Provides an alternative to the signal correlator
• for demodulating the received signal r(t).
• A filter that is matched to the signal waveform
  s(t)
• has an impulse response

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The matched filter output at the sampling instant
tTb is identical to the output of the signal
correlator.
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Example 5.2 Consider the use of matched filters
for the demodulation of the two signal waveforms
shown in the figure and determine the outputs
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A
0
A-
Figure 5.5Impulse responses of matched filters
for signals s0(t) and s1(t).
0
0
(a)
(b)
Figure 5.6Signal outputs of matched filters when
s0(t) is transmitted
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The Detector
The detector observes the correlator or the
matched filter output r0 and r1 and decided on
whether the transmitted signal waveform is s1(t)
or s0(t), which corresponding to 1 or 0,
respectively. The optimum detector is defined
the detector that minimizes the probability of
error.
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Example 5.3 Let us consider the detector for
the signals shown in Figure 5.2 which are equally
probable and have equal energies. The optimum
detector for these signals compares r0 and r1 and
decides that a 0 was transmitted when r0gtr1 and
that a 1 was transmitted when r0gtr1 . Determine
the probability of error.
A
A
t
0
t
0
A-
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Monte Carlo Simulation Communication System
Monte Carlo computer simulations are usually
performed in practice to estimate the
probability of error of a digital communication
system, especially in cases where the analysis
of the detector performance is difficult to
perform.
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Example 5.4 use Monte Carlo simulation to
estimate an plot Pe versus SNR for a binary
communication system that employs correlators or
matched filters. The model of the system is
illustrated in figure 5.8.
Figure 5.8 Simulation model for Illustrative
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Other Binary Signal Transmission Methods
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Antipodal Signal for Binary Signal Transmission
Antipodal signal If one signal waveform is
negative of the other.
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(b) Another pair of antipodal signal
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The received signal is
Matched filter demodulator
Correlator demodulator
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0
r
probability density function for the input to the
detector
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The Detector
The detector observes the correlator or the
matched filter output r0 and r1 and decided on
whether the transmitted signal waveform is s1(t)
or s0(t), which corresponding to 1 or 0,
respectively. The optimum detector is defined
the detector that minimizes the probability of
error.
For antipodal signal we have
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Example 5.5 use Monte Carlo simulation to estime
and plot the error probability performance of
binary communication system. The model of the
system is illustrated in Figure 5.13.
Figure 5.13 Model of binary communication system
employing antipodal signal
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On-Off Signal for Binary Signal Transmission
Binary information sequence may also be
transmitted by use of ON-OFF signals
The received signal is
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r
0
Figure 5.15 The probability density function for
the received signal at the output of te
correlator for on-off signal.
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0
r
Probability density function for ON-OFF signals
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The Detector
For antipodal signal we have
For On-OFF signal we have
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Example 5.6use Monte Carlo simulation to
estimate and plot the performance of a binary
communication system employing on-off signaling
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Signal Constellation diagrams for Binary Signals
Figure 5.17 signal point constellation for
binary signal.(a) Antipodal signal.(b) On-off
signals.(c) Orthogonal signals.
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Example 5.7 The effect of noise on the
performance of a binary communication system can
be observed from the received signal plus noise
at the input to the detector. For example, let us
consider binary orthogonal signals, for which the
input to the detector consists of the pair of
random variables (r0,r1), where either.
The noise random variables n0 and n1 re
zero-mean, independent Gaussian random variables
with variance .as in Illustrative Problam 5.4
use Monte Carlo simulation to generate 100
samples of (r0,r1) for each value of 0.1,
0.3, and 0.5, and plot these 100 samples
for each on different two-dimensional plots.
The energy E of the signal may by normalized to
unity.?
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Receiver signal points at input to the selector
for orthogonal signals
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Multiamplitude Signal transmission
Transmitting multiple bits per signal waveform
Symbol several bits in a single waveform
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Signal Waveforms with Four Amplitude Levels
T
t
0
t
Figure 5.19 Multi amplitude signal waveforms.
00 01 11
10
-3d -d 0 d
3d
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Optimum receiver for AWGN Channel
Signal correlator
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The detector
Observes the correlator output r and decides
which of the four PAM signals was transmitted in
the signal interval. The optimum amplitude
detector computes the distances
The detector selects the amplitude
corresponding to the smallest distance.
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Example 5.8 Perform a Monte Carlo simulation of
four - level PAM communication system that
employs a signal correlator, followed by an
amplitude detector. The model for the system to
be simulated is shown in Fig 5.2.
Figure 5.22 Block diagram of four level PAM for
Monte Carlo Simulation
Example 5.8
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Signal Waveforms with Multiple Amplitude Levels
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Example 5.9 perform a Monte Carlo simulation of
a 16-level PAM digital communication system and
measure its error-rate performance.
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Multidimensional signals
Signal waveform having M2k amplitude levels
We able to transmit klog2(M) bits of
information per signal waveform.
Multidimensional Orthogonal signals
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M3
M2
Figure 5.27 Signal constellation for M2 and M3
orthogonal signals.
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Optimum receiver for multidimensional orthogonal
signals.
detector
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Detector algorithm
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Example 5.10 perform a Monte Carlo simulation of
a digital communication system that employs M4
orthogonal signals. The model of the system to be
simulated is illustrated in Figure 5.30.
Figure 5.30 Block diagram of system with m4
orthogonal signals for Monte Carlo simulation
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Example 5.11 perform a Monte Carlo simulation of
a digital communication system that employs M4
orthogonal signals. The model of the system to be
simulated is illustrated in Figure 5.30.
Output decision
0
detector
Mapping to signal points
Uniform RNG
Compare si with si
Figure 5.30 Block diagram of system with m4
orthogonal signals for Monte Carlo simulation