Estimation of the conditional variance of a broadband source signal employing a repetition code through shallow water waveguides

A repetition code can be employed as a computationally fast suboptimal means to exploit available time-bandwidth product for improved bit error rate performance. Applications include synthetic aperture communications. Underwater acoustic response functions can vary over the duration of the transmission and thereby degrade system performance. A measure of precision of estimation of the source signal is the source posterior variance given the receiver pressure field time series. Presented here is the computation of the covariance of a source signal accounting for the covariance of the acoustic response function. A Gibbs sampling scheme is employed as a computational method to computing these variances to an acceptable precision. The resulting posterior variance as a function of SNR gives insight into the contributing phenomena that impart ambiguity in synthetic aperture communications through underwater acoustic channels. The method is tested on the very shallow water environment of Keyport WA at a center frequency of 20 kHz.