Optimum linear transmission of analog data for channels with feedback

With feedback, the transmission of analog data over a channel can be regarded as a stochastic-control problem. Restricting ourselves to linear receiver operations and an average power constraint, we take this approach to find minimum mean-square error signals for multiplicative and additive noise channels with noiseless feedback and for additive noise channels with noisy feedback. Our solution for the additive Gaussian noise channel with noiseless feedback achieves the theoretical minimum mean-square error. For the noisy feedback problem, we use the result that the optimum signals are the minimum mean-square error estimates of the optimum noiseless feedback signals. This control-theoretic approach requires knowledge of only the first and second moments of all random variables and extends easily to multidimensional cases and to wide-sense Markov noise processes.