1. Digital Communication
Simulation in
Digital Communication
By: Dr. Uri Mahlab

2. Baseband Digital Transmission
chapter # 5
Baseband Digital Transmission
By: Dr. Uri Mahlab

3. Binary Signal Transmission
Binary data consisting of a sequence of 1’s and 0’s.
Tb - Bit time interval

4. AWGN - Channel +
AWGN
Noise PSD

5. +
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.

6. Optimum Receiver for the AWGN Channel

7. Signal Correlator
Output
data
Sampling
@ t=Tb

8. detector
Output data

9. Determine the correlator outputs at the sampling instants.
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 A t A-
Figure 5.2: Signal waveforms s0(t) and s1(t) for a binary communication system
Determine the correlator outputs at the sampling instants.
Answer
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10. 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. t
Output of correlator 0 t
Output of correlator 1 t
Output of correlator 1 t
Output of correlator 0
(b)
(a)
Figure 5.3:Noise-free correlator outputs.(a) s0(t) was transmitted.(b) s1(t) was transmitted.

11. r Probability density function p(r0|0) and p(r1|0)r
Probability density function p(r0|0) and p(r1|0)
when s0(t) is transmitted

12. 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;

13. The matched filter output at the sampling instant t=Tb is
identical to the output of the signal correlator.

14. 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 A t A-
Answer
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15. t A t A A-
Figure 5.5:Impulse responses of matched filters for signals s0(t) and s1(t).
(a)
(b)
Figure 5.6:Signal outputs of matched filters when s0(t) is transmitted

16. 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.

17. 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 r0>r1 and that a 1 was transmitted when r0>r1 . Determine the probability of error. A A t t A-
Answer
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18. 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.

19. 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.
Uniform random number generator
Binary data source
detector
Output data
Compare
Error counter
Gaussian random number generator
Figure 5.8: Simulation model for Illustrative
Answer
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21. Other Binary Signal Transmission Methods

22. Antipodal signal If one signal waveform is negative of the other.
Antipodal Signal for Binary Signal Transmission
Antipodal signal If one signal waveform
is negative of the other.

23. A t A-
(a) A pair of antipodal signal A t A-
(b) Another pair of antipodal signal

24. The received signal is
Matched filter demodulator
Correlator demodulator

25. probability density function for the input to the detectorr
probability density function for the input to the detector

26. For antipodal signal we have :
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 :

27. 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.
Uniform random
number generator
Binary data
source
Compare
Error counter
detector r n
Gaussian random
Output data
Figure 5.13: Model of binary communication system employing antipodal signal
Answer
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28. On-Off Signal for Binary Signal Transmission
Binary information sequence may also be
transmitted by use of ON-OFF signals
The received signal is:

29. r
Figure 5.15: The probability density function for the received signal at the output of te correlator for on-off signal.

30. Probability density function for ON-OFF signalsr
Probability density function for ON-OFF signals

31. For antipodal signal we have : For On-OFF signal we have :
The Detector
For antipodal signal we have :
For On-OFF signal we have :

32. Example 5.6:use Monte Carlo simulation to estimate and plot the performance of a binary communication system employing on-off signaling
Uniform random
number generator
Binary data
source
Compare
Error counter
detector r n
Gaussian random
Output data
Answer
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33. Signal Constellation diagrams
for Binary Signals
(a)
(b)
(b)
Figure 5.17: signal point constellation for binary signal.(a) Antipodal signal.(b) On-off signals.(c) Orthogonal signals.

34. 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.
Answer
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35. Receiver signal points at input to the selector for orthogonal
signals

36. Multiamplitude Signal transmission
Transmitting multiple bits per signal waveform
Symbol = several bits in a single waveform

37. Signal Waveforms with Four Amplitude LevelsT t T T T t t
Figure 5.19: Multi amplitude signal waveforms.
-3d d d d

38. Optimum receiver for AWGN Channel
Signal correlator

39. 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.

40. 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.
Uniform RG
Gaussian random
Number Generator
compare
Error counter
detector
Mapping to
Amplitude levels + X Am r
Figure 5.22: Block diagram of four level PAM for Monte Carlo Simulation
Answer
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Example 5.8:

41. Signal Waveforms with Multiple Amplitude Levels

42. Example 5.9: perform a Monte Carlo simulation of a 16-level PAM digital communication system and measure its error-rate performance.
Answer
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43. We able to transmit k=log2(M) bits of information
Multidimensional signals
Signal waveform having M=2k amplitude levels
We able to transmit k=log2(M) bits of information
per signal waveform.
Multidimensional Orthogonal signals

44. A T t T A t A T t A T t

45. M=3
M=2
Figure 5.27: Signal constellation for M=2 and M=3 orthogonal signals.

46. Optimum receiver for multidimensional orthogonal signals.
detector

47. Detector algorithm:

48. Mapping to signal points
Example 5.10: perform a Monte Carlo simulation of a digital communication system that employs M=4 orthogonal signals. The model of the system to be simulated is illustrated in Figure 5.30.
Gaussian RNG
Compare si with ^si
Error counter
Mapping to signal points
Uniform RNG
detector
Output decision
Answer
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Figure 5.30: Block diagram of system with m=4 orthogonal signals for Monte Carlo simulation

49. A t T A t T A t A- t

50. Mapping to signal points
Example 5.11: perform a Monte Carlo simulation of a digital communication system that employs M=4 orthogonal signals. The model of the system to be simulated is illustrated in Figure 5.30.
Gaussian RNG
Output decision
detector
Uniform RNG
Mapping to signal points
Gaussian RNG
Compare si with ^si
Error conter
Figure 5.30: Block diagram of system with m=4 orthogonal signals for Monte Carlo simulation
Answer
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