Problem 15

The following signal set is used to transmit three equally-likely symbols.

The channel adds white Gaussian noise of spectral height $\frac{N_0}{2}$ to the transmitted signal.

1. Draw and accurately label a block diagram of the optimum receiver, i.e., the receiver that minimizes the probability of a wrong decision.
2. Find the appropriate signal space and indicate the decision regions of the optimum receiver.
3. Compute the minimum probability of error attainable with this signal set.
4. Repeat part (b) under the assumption that the amplitude of signal $s_1(t)$ is increased to $\sqrt{2}$.
5. Find another signal set with $s_0(t) = A \cos(2\pi f t)$ that achieves the same performance as the signal set sketched above.