Analog communication over randomly-time-varying channels

The problem of analog communication over a randomly-time-varying channel is considered. An analog source generates a message which is assumed to be a sample function from a Gaussian random process. The message is passed through a linear realizable system before modulation. (This corresponds to the pre-emphasis network in FM.) The output of this system is the modulating signal for a no-memory modulator which, in general, will be nonlinear. The modulated signal is transmitted over a time-varying channel We restrict ourselves to Gaussian multiplicative channels. At the channel output, noise is added. The specific problem of interest is to find the optimum estimate of the message. The principle results are: begin{enumeratge} item An integral equation whose solution is the optimum estimate. item A feedback demodulator whose output is the optimum estimate over a certain range of signal-to-noise ratios. item A proof that the optimum demodulator corresponds to a joint channel and message estimator. This result is the continuous analog of the estimator-correlator result in digital systems. Some related problems and possible extensions are discussed briefly. end{enumerate}