where is an integer, is used to transmit one of two equally-likely messages over an additive, white Gaussian noise channel with spectral height .

- Draw a block diagram of the optimum receiver.
Can this receiver be implemented using only
*one*correlator. - Compute the probability of error for this receiver.
- Now, the signals

are added to the above signal set. Each signal is then used to transmit one of four equally likely messages. Draw a block diagram of the optimum receiver for this*quaternary*signal set in additive white Gaussian noise. - Compute the resulting probability of error.

*Hint:* Remember that the likelihood ratio test

can also be written as

2003-01-28