Abstract
From classical fixed-time signal-detection theory, it is known that the basis for optimum receiver design is likelihood ratio. For composite-signal hypothesis problems, the optimum receiver forms a total likelihood ratio that is an average over all the various possible signals that could be transmitted in the observation interval. When the transmitted signal is composed of one of a finite class of waveforms that is repetitively generated by a random independent trigger process, the various possible signals that could occur grow with time so that a classic nonsequential realization requires a growing memory size that is impractical to implement. In problems of this type, the optimum reciever can be realized in an equivalent sequential fashion that is an adaptive realization. Using adaptive realizations, the receiver can be realized with a memory size that remains fixed in size. [This work supported by the U. S. Office of Naval Research, Code 468.]
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