On-Off-Keying

The following signal set is used to transmit equally likely messages over an additive white Gaussian noise channel with spectral height $\frac{N_0}{2}$:

$$\begin{array} {cc} s_0(t) = \left\{ \begin{array} {cl} \frac... ...d{array}\right. & s_1(t) = 0 \; \mbox{ for all $t$.}\end{array}$$

1.

Draw a block diagram of the receiver which achieves the minimum probability of error for this signal set. (2 pts.)

2.

What is the probability of error achieved by your receiver from part (a)? (2 pts.)

3.

Consider the following receiver

Compute the probability of error achieved by this receiver as a function of the amplifier gain $\alpha$. (3 pts.)

4.

For what value of $\alpha$ is the probability of error minimized? Compare with the result from part (b). (3 pts.)