- Draw a block diagram of the optimum receiver and compute the probability of error for this receiver.
- Assume now that the signal experiences an unknown phase shift
during transmission, i.e., if is transmitted the received
signal is

Compute the probability of error that your receiver from part (a) achieves in this situation. - Illustrate the effect of the unknown phase shift in a suitably chosen signal space, i.e., sketch the location of signals and in signal space as a function of for .
- Based on your observations from part (c), what is the decision boundary associated with the optimum receiver for distinguishing between and for unknown . It is sufficient to indicate this decision boundary in signal space and describe it in words. You do not have to write down the decision rule.
- Draw the block diagram of a receiver that implements the decision boundary you determined above.

2003-01-28