Solve the following problem:
A binary digital communication system employs the signals
s0(t) = 0 0 ≤ t ≤ T
s1(t) = A 0 ≤ t ≤ T
for transmitting the information. This is called on-off signaling. The demodulator cross correlates the received signal r(t) with s(t) and samples the output of the correlator at t + T .
a. Determine the optimum detector for an AWGN channel and the optimum threshold, assuming that the signals are equally probable.
b. Determine the probability of error as a function of the SNR. How does on-off signaling compare with antipodal signaling?