Sub-Optimum 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 $\frac{N_0}{2}$:

$$\begin{array} {l} s_0(t) = \left\{ \begin{array} {cl} At & \... ...2} < t \leq T$}\\ 0 & \mbox{else}\end{array}\right. \end{array}$$

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

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

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.

5.

If $g(t) = \sin(\pi \frac{t}{T})$ were used in the sub-optimum receiver, would the resulting probability of error be larger or smaller than the probability of error achieved with the g(t) in part (c)? Explain.