Sparse broadband acoustic response estimation via a gaussian mixture model with application to m-ary orthogonal signaling

Abstract

Shallow water acoustic response functions at high frequencies and large bandwidths exhibit spatio- temporal variability that depends greatly on the propagation media's volume and boundary conditions as well as system source-receiver motion. For this reason practical acoustic systems invariably must operate without perfect knowledge of the space-time state of the ocean media. Considered here is a Gaussian mixture assignment over Doppler and channel bandwidth employed to describe the amplitude and phase of such acoustic response functions over signal duration and bandwidth that can serve in many scenarios to replace recursive least squares and Kalman-like algorithms. The mixtue Gaussian model of channel dynamics allows for the accurate and adaptive description of the response function. The model is flexible and naturally accommodates varying degrees of observed channel spar- sity. Posterior expectations are derived and shown to be soft shrinkage operators over Doppler-channel frequency. The model allows for novel and accurate estimates regarding the aggregate acoustic path dilation process that serve to replace conventional phase locked loops. This adaptive filtering scheme with aggregate path dilation estimation and compensation is tested on M-ary orthogonal signals at both 1 and 2 bits per symbol during the Unet08 acoustic communication experiments. These tests took place in the downward refracting, lossy bottom environment of St. Margaret's Bay Nova Scotia off of the R/V Quest. Receiver algorithms based on this approach were applied to a single element acoustic time series and empirical bit error rates demonstrate a 4 dB improvement over rank based maximal path combining methods. For a single hydrophone at 2 bits per symbol a bit error rate of less than 10-4 is observed at received SNR < -10 dB corresponding to an SNR/bit < 14 dB.