An Information Theoretic Take on Time Reversal for Nonstationary Channels

It has been shown that time-reversal (TR) techniques focus energy back to the dominant scatters, lead to super-resolution focusing, and gains in detection. Time reversal has so far mainly been studied when the channel remains invariant between the initial and time-reversed signal transmission times. In this letter, we relax this assumption and study the benefits of TR over time-varying channels. To do so, we compare a time-reversed and a non time-reversed system by comparing the mutual information between the channel impulse response and channel outputs given the transmitted signals. We present analytical results for a simple scalar problem which illustrates the impact of nonstationary channels on TR, and for general channels, numerically evaluate the difference in mutual informations, which demonstrate that, if the channels are nonstationary yet correlated, TR may still provide mutual information gains over non time-reversed systems.