These signals are used to transmit equally-likely bits over a channel which adds white Gaussian noise of spectral height to the signal.

- Assuming
, show that the ``correlation
coefficient'' of the signals and , defined as

is given approximately by

where is the duration of a bit interval. - What is the minimum value of the frequency shift for which the signals are orthogonal?
- Draw a block diagram of the receiver which attains the minimum probability of error.
- Compute the minimum probability of error as a function of .
- What is the value of that minimizes the probability of error?

*Hint:* You may need these equations:

2003-01-28