In the sequel, assume that the communication channel is an additive white Gaussian noise channel with spectral height .

- One user employs the following signal set to transmit equally
likely binary symbols

Draw a block diagram of the receiver which minimizes the probability of a bit error for this signal set.

- Compute the probability of error achieved by your receiver.
- Now, a second users transmits one of the following signals with
equal probability

Both signals are transmitted simultaneously, such that the received signal is given by

(1) Find the probability of error of your receiver from part (a) for distinguishing between and if the received signal is given by (1). Which value does the probability of error approach if the amplitude of the interfering user approaches ?

- Find the minimum probability of error receiver for
distinguishing between and in the
presence of the interfering signal , i.e.,
if the received signal is given by (1).
*Note:*You do not need to find the probability of error for this receiver. - Indicate the locations of the relevant signals and the decision regions for your receiver from part (d) in a suitably chosen and accurately labeled signal space. Indicate also the decision boundary formed by the receiver from part (a).

2003-01-28