Tracking time varying multipath phase at very low signal to noise ratios

Abstract

Diverse acoustic environments support multipath propagation. Estimating the arrival gains allows receiver structures to coherently combine acoustic energy for improved reception. In the case of mobile acoustic sources and receivers or dynamic boundaries, the amplitudes and phases of those arrivals are time varying such that estimation is made more difficult and typically entails some kind of phase tracking loop. This can be challenging as trackers are often formed as recursions in time employing previous observations to predict the phase at present, updating each phase estimate with the most recent observation. At extremely low SNR, recursive tracking can suffer loss of lock. Since a great deal of information about the instantaneous phase is contained in observations before and after it is judicious to seek estimators that exploit all of the observations in the signalling interval to infer the time varying response phase. Presented here is a scheme for simultaneous time varying phase estimation from the reception of a long duration, high time-bandwidth product transmission. In this approach, the phase process is derived from a minimum mean square error estimate of the sparse acoustic time varying response under an assumed sparse mixture model prior over Doppler and frequency. Demonstrations in shallow water at less than −12 dB received signal to noise ratio are presented.