Probe timing optimization for time-reversal underwater communications

Passive Time Reversal (pTR) is one of the variants of time reversal applicable to digital underwater communications. In passive time reversal a probe-signal is transmitted ahead of the data-signal in order to estimate the channel impulse response for later use as a replica signal in a time reversal mirror fashion. In practice the received probe-signal must be captured in a time-window and, after correlation with the transmitted probe-signal, give a noisy estimation of the channel impulse response. Therefore, the output Signal to Noise Ratio (SNR), the Inter-Symbolic Interference (ISI) and the detection rate of passive time reversal will strongly depend on the starting time and duration of such time-window. Typically the beginning and the duration of that time-window should depend on the travel time and the dispersion of the acoustic channel. In this paper, the maximization of the pTR output SNR relative to the probe time-window is derived in closed form. It will be shown that the probe timing that gives the lower detection error rate can be predicted using closed form metrics for the pTR output SNR and ISI. Theoretical results are found to be in full agreement with simulations and with results obtained on experimental data taken during the INTIFANTE'00 sea trial.