Transmitted-reference techniques for random or unknown channels

In this paper, a particular approach to the problem of communicating in certain random or unknown channels is considered. A particular set of signals is chosen, each member of which is partitioned into a known reference or sounding signal and a message signal. The channel is assumed to be linear, and is divided into a multiplicative and an additive portion. The multiplicative portion is assumed to have the same response to both message and reference components, while the additive noises associated with these components are assumed to be independent. The channel outputs and the additive noises are further assumed to be Gaussian. Under these circumstances, the optimum receiver is shown to cross-correlate the message portion of the received signal with a filtered version of the posterior mean of the channel output, which is merely a filtered combination of the prior mean and the perturbed reference signal. This is an interesting extension of the optimum receiver for known signals in additive Gaussian noise. Several special cases are considered which yield additional insight into the operation of the optimum receiver.