Effectiveness of sparse optimization techniques against rapid fluctuations in the shallow water acoustic channel

Abstract

The shallow water acoustic channel exhibits rapid temporal fluctuations due to fluid and platform motion as well as reflection from moving surfaces. Tracking the time-varying channel delay spread effectively for subsequent equalization is an open signal processing challenge. The delay-Doppler spread function characterizes this time-variability over a selected range of Doppler frequencies but itself does not exhibit stationary behavior over longer time intervals. Typically the delay-Doppler spread function and sometimes the delay spread itself follow a sparse distribution where most of the energy is concentrated in a few significant components distributed sparsely over a larger support. A variety of sparse optimization techniques have recently been proposed in the compressive sensing literature to efficiently track sparsely distributed coefficients. However, the ill-conditioned nature of the delay-Doppler spread estimation problem, coupled with the necessity to track the complex-valued coefficients directly in real time, renders direct application of traditional sparse sensing techniques infeasible and intractable in the shallow water acoustic paradigm. The talk will provide a synopsis of well-known and recently proposed sparse optimization techniques, with focus on mixed norm algorithms, along with a comparative analysis of these techniques in the shallow water acoustic paradigm over simulated and experimental field data.