7CCSMCTH Communications Theory Homework #1
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7CCSMCTH
Communications Theory
Homework #1
1. The baseband equivalent of a channel pulse response is given as
p(t) = - sin c + 1 + sin c - sin c .
a) Find pk = p(kT) .
b) Find qk .
c) Find Q(D) .
d) Find WZFE (D) .
e) Find oZ(2)FE .
f) Find YZFE .
g) Find SNR MFB and SNR ZFE in terms of Ex and
0
.
2
2. The pulse response of a channel is described as
P(o) =〈|((1 + .9ejoT )
|l0
A binary PAM with Ex = 1 and SNR MFB = 10 dB is used on this channel.
a) Find the mean square distortion, i.e., D ms .
b) Find the approximated average probability of error Pe for the un-equalised channel using the D ms in part (a).
c) Find the signal to noise ratio for the un-equalized channel.
d) Find the filter transform, Pe and SNR ZFE for the ZFE equaliser on this channel. Compute the difference between SNR ZFE and the SNR based on the mean-square distortion computed in part (c) in dB and discus the result.
Graph for the Q-Function Values
For low values
The vertical axis: Q(x) = wjx e du
The horizontal axis: 20log10 (x)
2023-04-14