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A criterion for selecting a finite set of transmitter signals for a continuous communication channel is proposed. The "optimum" signal sets using this criterion are selected to maximize the minimum divergence between hypothesis pairs being tested at the receiver. The resulting signal sets have the property that the error probability using these signals is less than the error probability for any other choice of signals for some a priori message statistics. The signal selection procedure may be applied without a knowledge of the a priori message statistics and does not require an evaluation of error probabilities. Four examples of signal selection are included to illustrate the procedure.
T. Grettenberg (1963) studied this question.