Suboptimum Receivers

A binary communication system employs the following signals to communicate two equally likely messages over an additive white Gaussian noise channel with spectral height $\frac{N_0}{2}$:

$$\begin{array} {c} s_0(t) = \left\{ \begin{array} {cl} A \sqr... ...$0 \leq t < T$}\\ 0 & \mbox{else}\end{array}\right. \end{array}$$

1.

Draw a block diagram of the optimum receiver.

2.

Compute the probability of error achieved by your receiver from part (a).

3.

Consider now the following suboptimum receiver:

where g(t) is given by

$$g(t) = \left\{ \begin{array} {cl} 1 & \mbox{for $0 \leq t < ... ... $\frac{T}{2} \leq t < T$}\\ 0 & \mbox{else.}\end{array}\right.$$

Find the distribution of R for both cases, s₀(t) was transmitted and s₁(t) was transmitted.

4.

Find the probability of error of the suboptimum receiver and compare with that of the optimum receiver.

Hint: $\sin^2 x = \frac{1}{2}(1-\cos 2x).$