Thus the signal set consists of signals.

- Draw and accurately label the signal constellation in an appropriately chosen signal space and indicate the decision boundaries formed by the optimum receiver.
- Compute the probability of error achieved by the optimum receiver.
- How many bits are sent with each transmission for this signal set?
- Define the average bit-energy as

where denotes the energy of signal and denotes the corresponding a priori probabilities. Compute the average bit-energy for this signal set. - Repeat parts (a)-(c) for the following signal set with signals:

- If both signal sets would be using the same bit-energy , which signal set yields the smaller probability of error? Explain.
- Which other very important parameter in a communication system may lead a system designer to choose the second signal set over the first signal set, particularly if the signal-to-noise ratio is large? Explain.

2003-01-28