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Various structures have recently been obtained for optimally demodulating analog signals transmitted over a noisy, randomly fading channel. Their performance, in a least mean-signal error sense, is evaluated in this paper. In the case of the optimum linear filter for AM (or equivalent baseband) signals, as the carrier-to-noise ratio increases indefinitely, an irreducible error is found. The Cramèr-Rao (lower) bound on the error is found and indicates, however, that the fading error can be reduced to zero by use of a nonlinear receiver. An analysis of the maximum a posteriori receiver, utilizing estimates of the channel fading characteristics, does in fact indicate that for this nonlinear receiver, the fading error can be made to approach zero. Similar considerations are found to apply in the case of PM signals.