Temporal resolutions of time-reversal and passive-phase conjugation for underwater acoustic communications

In this paper, we study the temporal resolution of a time-reversal or passive-phase conjugation process as applied to underwater acoustic communications. Specifically, we address 1) the time resolution or the pulse width of a back-propagated time-compressed pulse as compared with the original transmitted pulse; 2) the effectiveness of temporal focusing as measured by the peak-to-sidelobe ratio of the back-propagated or phase-conjugated pulse (both pulse elongation and sidelobe leakages are causes of intersymbol interference and bit errors for communications); 3) the duration of temporal focusing or the temporal coherence time of the underwater acoustic channel; and 4) the stability of temporal focusing as measured by the phase fluctuations of successive pulses (symbols). Binary phase-shift keying signals collected at sea from a fixed source to a fixed receiver are used to extract the above four parameters and are compared with simulated results. Mid-frequency (3-4-kHz) data were collected in a dynamic shallow-water environment, exhibiting high temporal fluctuations over a scale of minutes. Despite this, the channel is found to be highly coherent over a length of 17 s. As a result, only one probe signal is used for 17 s of data. The bit error rate and variance of the symbol phase fluctuations are measured as a function of the number of receivers. They are of the same order as that calculated from the simulated data. The agreement suggests that these two quantities could be modeled for a communication channel with high coherence time. The phase variance can be used to determine the maximum data rate for a phase-shift keying signal for a given signal bandwidth and a given number of receivers.