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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
, and .
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 now that signal is removed from the above signal
set. Draw and accurately label the new signal constellation in an
appropriately chosen signal space and indicate the new optimum
- Can you still express the resulting probability
of error in terms of the Q-function? If your answer is yes, compute
of error; if it is no, explain why not and indicate whether the
probability of error of the reduced signal set is larger or smaller
than that of the original set.
Dr. Bernd-Peter Paris