Error Probability in a Channel with Fading and Signallike Noise

It is shown that for a channel without fading there always exists an additive Gaussian noise for which the error probability for optimum reception of multifrequency signals is uniquely determined by the ratio of signal power to noise power and, when there is fading and arbitrary Gaussian noise in the channel, the error probability can be made arbitrarily small when the number of harmonic components of the signals is increased; this is accounted for by the random nature of the signal under fading.