Time reversal communication over doubly spread channels.

Conventional time reversal can mitigate multipath delay dispersion by temporal focusing. But it is not applicable to time-varying channels with a Doppler spread. Although recently time reversal communication has been adapted to time-variant channels, the modified technique requires frequent channel updates to track channel variations and cannot handle large Doppler spread, which means that it cannot achieve frequency focusing. In this paper, two time reversal receivers for underwater acoustic communications over doubly spread channels are proposed. The proposed approach, which can be interpreted as time-frequency channel matching, is based on the channel spreading function rather than impulse response adopted by the existing techniques; this leads to much less frequent channel updates. Unlike existing methods that only correct a single Doppler shift, the proposed approach uses a rake-like structure to compensate for multiple Doppler shifts and hence can eliminate severe Doppler spread induced by temporal channel variations. Simulation results verify the effectiveness of the proposed approach, indicating that it can simultaneously counteract delay and Doppler spreads, achieving both temporal and frequency focusing.