Time-frequency localization issues in the context of sparse process modeling

Abstract

Practical applications in acoustics such as shallow water acoustic communications often involve non-stationary processes that follow a time-varying sparse support. A classic example is acoustic scatter due to multiple reflections at the moving ocean surface and sea bottom, localized in the time-frequency domain as the sparsely distributed and time-varying Delay-Doppler spread function. In this work, we connect time-frequency localization of non-stationary processes with related issues in adaptive sparse sensing in the context of modeling and tracking the Delay-Doppler spread function. To this end, we provide an overview of methodological advances in adaptive sparse sensing techniques, and compare them over experimental field data collected as 15 m depth, 200 m range and moderate to rough sea conditions. We also comment on other adaptive techniques, such as least-squared error minimization algorithms, and discuss their extensions to the sparse sensing domain. We also explore the uncertainty principle underlying time-frequency representations, particularly in terms of how it influences the related and occasionally competing challenges to sparse process modeling: (i) restricted isometry criteria (RIP) for precise sparse reconstruction and (ii) choice of temporal window to localize the non-stationary Delay-Doppler spread function.