On the mutual information of time reversal for non-stationary channels

Time-reversal (TR) techniques have been shown to lead to gains in detection and enable super-resolution focusing. These gains have thus far mainly been demonstrated for time invariant channels, where the channel remains constant between the initial and time-reversed signal transmissions. Here, we are interested in determining whether TR techniques may be beneficial in time-varying channels. We approach this problem by comparing the mutual information between the channel and the received signals over two time slots of a radar system which does / does not use TR. Besides evaluating this mutual information, and showing that for this setup it is equal to directed information which might be of interest in feedback-like channels, we also provide a low-rank interpretation of this mutual information for Gaussian channels. Numerical evaluations suggest that if the channels are non-stationary yet correlated, TR may still provide information gains over non time-reversed systems.