Abstract
Abstract : By generalizing a trivial problem in estimation theory, some interesting results were obtained for a class of pulse amplitude modulation (PAM) communication channels. A linear channel with memory perturbed by additive noise which is uncorrelated with the signal statistics is considered. For specified second-order statistics and a mean square error criterion, the Bayes estimation rule for the specific case of zero-mean Gaussian signal and noise statistics is both the best linear estimation rule and the minimax estimation rule. This fact is used in the theoretical design of sampled-data and continuous time receivers for such PAM systems. In the continuous time case with an infinite observation interval and stationary noise statistics, the receiver designed agrees with the optimum linear receiver previously derived for this case by Tufts using a different approach. The present analysis shows that Tufts's linear receiver is also the best nonlinear receiver in the minimax sense.
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