Output SNR of time-reversal based underwater acoustic communications

While one generally expects the output signal-to-noise ratio (OSNR) to increase with the number of receivers and decrease with increasing channel estimation error, to determine their exact relationship for a given channel, a channel model is normally required as the OSNR is dependent on the number of tap coefficients which are different for different channels having different multipath spread. This paper shows, supported by experimental data from different oceans, that the increase of OSNR with the number of diverse (or effective) receivers, and the decrease of OSNR with the channel estimation (data estimation) error follow a universal relationship using the time-reversal or correlation-based equalizer, despite the fact that the channels have very different properties. The reason is due to the fact that the OSNR is a function of the q function, the autocorrelation of the received impulse responses summed over all receiver channels, and the q function is approximately the same for all the data.