Question

4.27. In a binary communication system the transmitter uses the following two signals to represent two equally likely hypotheses: S1(t) = { A, 0 <= t <= T/4 0, T/4 < t <= T/2 A, T/2 < t <= T, S2(t) = { 0, 0 <= t <= T/4 A, T/4 < t <= T, where A is some given constant. The signals are corrupted by additive white Gaussian noise with power spectral density of N0/2 Watts/Hz. The optimal receiver decides which of the two hypotheses was sent at time t = T. a) Plot the two signals. b) Draw a detailed block diagram of the optimal receiver. c) Find the probability of error of this receiver. d) Suppose that the decision is made at t = T/2. What is now the probability of error of the receiver? e) Compare the results in c) and d) and explain.

          4.27. In a binary communication system the transmitter uses the following two signals to represent two equally likely hypotheses:
S1(t) = {
A, 0 <= t <= T/4
0, T/4 < t <= T/2
A, T/2 < t <= T,
S2(t) = {
0, 0 <= t <= T/4
A, T/4 < t <= T,
where A is some given constant. The signals are corrupted by additive white Gaussian noise with power spectral density of N0/2 Watts/Hz.
The optimal receiver decides which of the two hypotheses was sent at time t = T.
a) Plot the two signals.
b) Draw a detailed block diagram of the optimal receiver.
c) Find the probability of error of this receiver.
d) Suppose that the decision is made at t = T/2. What is now the probability of error of the receiver?
e) Compare the results in c) and d) and explain.

4.27. In a binary communication system the transmitter uses the following two signals to represent two equally likely hypotheses:
S1(t) =
A, 0 <= t <= T/4
0, T/4 < t <= T/2
A, T/2 < t <= T,
S2(t) =
0, 0 <= t <= T/4
A, T/4 < t <= T,
where A is some given constant. The signals are corrupted by additive white Gaussian noise with power spectral density of N0/2 Watts/Hz.
The optimal receiver decides which of the two hypotheses was sent at time t = T.
a) Plot the two signals.
b) Draw a detailed block diagram of the optimal receiver.
c) Find the probability of error of this receiver.
d) Suppose that the decision is made at t = T/2. What is now the probability of error of the receiver?
e) Compare the results in c) and d) and explain.

Added by Katrina A.

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