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Binary Digital Communications 631
FIGURE 12.16
Model of binary data communications system
In practice the signal waveforms transmitted over the channel are
corrupted by additive noise and other types of channel distortions that
ultimately limit the performance of the communications system. As a
measure of performance, we normally use the average probability of error,
which is often called the bit error rate.
12.7.1 PROJECT 12.7: BINARY DATA COMMUNICATIONS SYSTEM
The purpose of this project is to investigate the performance of a binary
data communications system on an additive noise channel by means of
simulation. The basic configuration of the system to be simulated is shown
in Figure 12.16. Five MATLAB functions are required.
1. A binary data generator module that generates a sequence of independent
binary digits with equal probability.
2. Amodulator module that maps a binary digit 1 into a sequence of
M consecutive +1’s, and maps a binary digit 0 into a sequence of M
consecutive −1’s. Thus the M consecutive +1’s represent a sampled
version of the rectangular pulse.
3. A noise generator that generates a sequence of uniformly distributed
numbers over the interval (−a, a). Each noise sample is added to a
corresponding signal sample.
4. A demodulator module that sums the M successive outputs of the
noise corrupted sequence +1’s or −1’s received from the channel. We
assume that the demodulator is time synchronized so that it knows the
beginning and end of each waveform.
5. A detector and error-counting module. The detector compares the output
of the modulator with zero and decides in favor of 1 if the output
is greater than zero and in favor of zero if the output is less than zero.
If the output of the detector does not agree with the transmitted bit
from the transmitter, an error is counted by the counter. The error rate
depends on the ratio (called signal-to-noise ratio) of the size of M to
the additive noise power, which is P n = a 2 /3.
The measured error rate can be plotted for different signal-to-noise
ratios, either by changing M and keeping P n fixed or vice versa.
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