Doppler compensation in underwater channels using time-reversal arrays

This work addresses the problem of compensating for differential Doppler shifts due to source motion in a time-reversal mirror. Time reversal is a feedback wave focusing technique that can be used in poorly-characterized media, and is quite appealing in bidirectional underwater communications as it allows multipath to be transparently canceled in highly dispersive channels. Under simplifying assumptions, it is shown that time-reversed focusing occurs even when the source moves uniformly, although this induces fluctuations in the envelope of the regenerated signal due to differential Doppler. The proposed technique for Doppler compensation builds on the representation of time-varying pulse shapes using delay-Doppler spread functions. By inverting these functions in both delay and Doppler at each transducer, the mirror is able to project signals that converge on the source and are devoid of Doppler shifts when observed in its moving reference frame.