Problem 23

A consideration in the design of signal sets is insensitivity to channel disturbances in addition to additive, white Gaussian noise. One type of channel encountered often is the fading channel. Here the signal portion of the received waveform is subjected to a gain which changes randomly from bit interval to bit interval. Assume a binary signal set is used and messages are equally likely.

1.

Assume the channel gain is always a positive number. Find the property the binary signal set must possess so that the minimum probability of error receiver need not require knowledge of the channel gain to function properly.

2.

Which of the commonly used signal sets (antipodal, orthogonal, on-off-keying) satisfy this criterion?

3.

Assume the channel gain to be either plus or minus one in each bit interval; this gain changes randomly from bit interval to bit interval. Among those signal sets chosen in part (b), find a signal set that can be used over such a channel and demonstrate a receiver for this signal set.

4.

Compute the minimum probability of error obtained with the channel described in part (c) using your signal set and receiver.