where the symbols and can take on values from the set and is an even integer. Hence, this signal set contains signals.

The second signal set uses orthogonal carriers to transmit one of signals
of the form

where the bits are drawn from the alphabet .

- Consider the QAM signal set with and the orthogonal signal set with
, such that both signal sets consist of 4 signals. For each signal set
determine
- the amplitudes and such that the average signal energy equals unity,
- orthonormal basis functions for depicting the constellation in an appropriate signal space; draw the signal space diagrams,
- the minimum probability of error for this signal set.

- Repeat part (a) for the signal sets with 16 signals resulting when and .
- Compare the probability of error for the two types of constellations with equal numbers of signals as and increase. I.e., consider the case of 64 signals (, ), 256 signals (, ), etc. You do not need to compute explicitly but you should be as specific as possible.
- Compare the bandwidth requirements for the two types of constellations with equal numbers of signals as and increase.

2003-01-28