Problem 29

The following signal set is being used to transmit equally likely signals over an AWGN channel.

$$\begin{array} {cc} s_1(t) = 0\;\; \mbox{for all $t$} & s_2... ...\leq t \leq T$}\\ 0 & \mbox{else}\end{array}\right.\end{array}$$

1.

Draw and accurately label the signal constellation for this signal set in signal space.

2.

Compute the smallest prabability of error that can be obtained with this signal set.

3.

The quantity E may not be known at the receiver. Is this quantity necessarily used by the receiver achieving the minimum probability of error? If not, demonstrat the receiver; If so, modify the signal set so that the probability of error remains the same and E does not have to be known.