A class of discrete-time detection problems is formulated and a general recursive formula for the likelihood ratio is obtained. The result is analogous to the general likelihood-ratio formula or "estimator-correlator" receiver which has been derived in continuous time for a number of detection problems. As in the continuous-time versions, a conditional-mean estimate again plays a central role in the receiver structure.
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S.C. Schwartz (1977) studied this question.
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