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Approximation of locally optimum detector nonlinearities

The problem of finding a detector nonlinearity that maximizes the efficacy (or asymptotic processing gain) over a class of suboptimal nonlinearities is considered. It is shown that this efficacy maximization problem is essentially the same as the problem of finding the minimum-mean-square-error approximation to the locally optimal detector nonlinearity. This result is compared with some intuitive ideas about suboptimal detection.