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The following signal set is used to transmit equally likely messages
over an additive white Gaussian noise channel with spectral height
Thus, this 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
- Assume that the energy of the transmitted signal can never
exceed . Is it possible to modify the above signal set in such a
way that the probability of error is reduced without exceeding the
limit on the signal energy? Explain why or why not.
Dr. Bernd-Peter Paris