mohatta2015.pdf

12 INTRODUCTION
rollo« 0.22
0.8
Ί
Γ
ΓΤ
raised cos
root-raised cos
0.6
0.4
0.2
0
-0.2
-0.4 _L _L _L _l_
-4 -3 - 2 - 1 0 1
normalized time (t/T)
Figure 1.11
liaised cosine function.
approximate the channel with a symbol-spaced channel model, especially when the
channel is highly dispersive (signal energy spread out in time due to the channel).
Consider an example in which the transmitter uses RRC pulse shaping with
rolloff 0.22. The Nyquist sampling period is 1/1.22 or 0.82 symbol periods. Thus,
for an arbitrary channel, we would need a tap spacing of 0.82'/' for smaller. As
most simulation programs work with a sampling rate that is a power of 2 times
the symbol rate, a convenient tap spacing would be 0.75T. If the channel is wellmodeled
with a single tap at delay 0, the received signal (after filtering with a RRC
filter) would give us the raised cosine function shown in Fig. 1.11. To recover the
symbol at time 0, we would sample at time 0, where the raised cosine function is
at its maximum. Notice that when recovering the next symbol, we would sample
at time 1, and the effect of the symbol at time 0 would be 0 (no ISI). In fact, we
can see that when recovering any other symbol, the effect of symbol 0 would be 0,
as the zero crossings are symbol-spaced relative to the peak.
Suppose, instead, that the channel is well-modeled by two taps 0.75T apart.
An example with path coefficients 0.5 and 0.5 is shown in Fig. 1.12 (the x axis
is normalized so that the peak occurs at time 0). Relative to Fig. 1.11, we see
that the symbol is spread out more in time, or dispersed. Hence, the channel is
considered dispersive. Observe that when recovering the next symbol at time 1,
there is ISI from symbol 0.