title: Broadband performance of a moving time reversing array.
abstract: Acoustic time reversal exploits reciprocity between sources and receivers to generate backward propagating waves that automatically focus at their point of origin. In underwater acoustics, an array of transducers that can both transmit and receive, referred to as a time reversing array (TRA) or time reversal mirror (TRM), generates the back-propagating waves. Such arrays have been shown to spatially and temporally focus sound in unknown complicated multipath environments, and are therefore of interest for active sonar and underwater communication applications. Although stationary vertical linear TRAs have been favored in prior studies, practical applications of acoustic time reversal in underwater environments are likely to involve towed, tilted, horizontal, or bottom-mounted arrays. In particular, array motion introduces Doppler effects and eliminates source-receiver reciprocity, two factors that potentially impact the automatic focusing capability of TRAs. This paper presents the results from a theoretical and computational investigation into how array motion and orientation influence TRA retrofocusing in the shallow ocean. Here, the TRA tow speed is assumed constant, and the array is assumed to be straight and linear (vertical, horizontal, or tilted). And, for simplicity, the TRA is assumed to respond to a stationary point source emitting a broadband pulse. When a TRA moves, the retrofocus is predicted to shift in the direction of array motion due to the translation of the array between its reception and broadcast times. In addition, the performance of a towed horizontal TRA is predicted to degrade more rapidly with towing speed than that of an equivalent (but clearly idealized) towed vertical array because of range-dependent Doppler phase differences that do not influence the vertical array. However, short tilted arrays may approach vertical array performance and appear to be a potentially versatile compromise for implementing TRA concepts in active sonar or underwater communication systems.