Solve the following problem:
Suppose that the binary signal ±sl(t) is transmitted over a fading channel and the received signal is
r1(t) = ±as1(t) + z(t), 0 ≤ t ≤ T
where z(t) is zero-mean white Gaussian noise with autocorrelation function
![1959_autocorrelation function.jpg](https://secure.tutorsglobe.com/CMSImages/1959_autocorrelation function.jpg)
The energy in the transmitted signal is ε = 1/2 ∫T0 |s1(t)|2 dt .The channel gain α is specified by the probability density function
p(α) = 0.1δ(α) + 0.9δ(α - 2)
a. Determine the average probability of error Pb for the demodulator that employs a filter matched to s1(t).
b. What value does Pb approach as E/N0 approaches infinity?
c. Suppose that the same signal is transmitted on two statistically independently fading channels with gains a1 and a2, where
p(αk) = 0.1δ(αk) + 0.9δ(αk - 2), k= 1,2
The noises on the two channels are statistically independent and identically distributed. The demodulator employs a matched filter for each channel and simply adds the two filter outputs to form the decision variable. Determine the average Pb.
d. For the case in (c) what value does Pb approach as E/N0 approaches infinity?