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Sec. 7–7 Output Signal-to-Noise Ratio for PCM Systems 525
obtained from noisy signals that are present at the receiver input, the reference signals are also
noisy. Consequently, the P e will be larger than that given for the ideal case when noise-free
sync is assumed.
The third type of synchronization that is required by most digital systems is frame sync,
or word sync. In some systems, this type of sync is used simply to demark the serial data into
digital words or bytes. In other systems, block coding or convolutional coding is used at the
transmitter so that some of the bit errors at the output of the threshold device of the receiver
can be detected and corrected by using decoding circuits. In these systems, word sync is
needed to clock the receiver decoding circuits. In addition, frame sync is required in timedivision
multiplex (TDM) systems. This was described in Fig. 3–37. Higher levels of
synchronization, such as network synchronization, may be required when data are received
from several sources. For example, multiple-access satellite communication systems require
network synchronization, as illustrated in Chapter 8.
7–7 OUTPUT SIGNAL-TO-NOISE RATIO FOR PCM SYSTEMS
In the previous sections, we studied how the P e for various digital systems depends on the
energy per bit E b of the signal at the receiver input and on the level of the input noise spectrum
N 0 2. Now we look at applications of these signaling techniques where an analog
signal is encoded into a PCM signal composed of the data that are transmitted over the
digital system having a BER of P e . This is illustrated in Fig. 7–15. The digital transmitter
and receiver may be any one of those associated with the digital signaling systems studied
Analog input
signal
Low-pass filter
PCM encoder
(analog-to-digital converter) Q(x k )
x k Quantizer
Sampler
(M levels)
Encoder
PCM signal
(polar waveform)
Transmitter
s(t)
Channel
n(t)
r(t)
Receiver
Recovered
PCM
PCM decoder
(digital-to-analog converter)
y k =x k +n k
Analog sample out
(S/N) out measured here
Figure 7–15
PCM communications system.