Problem 3:
The following signal set is used to transmit equally likely messages
over an additive white Gaussian noise channel with spectral height
$\frac{N_0}{2}$,
$s_{i_1} = \sqrt{\frac{2E}{T}} \cdot i_1 \cdot cos(\frac{20\pi t}{T})$ for $0 \le t \le T$, $i_1 = -1, 1$.
Thus, this signal set consists of $M = 2$ signals.
(a) Draw and accurately label a block diagram for the optimum
receiver for this signal set.
(b) Draw and accurately label the signal constellation in an appropriately chosen signal space and indicate the decision boundaries formed by the optimum receiver. Then, compute the
probability of error achieved by the optimum receiver.