Identification and matching of sparse Delay-Doppler Spread Functions from high-frequency communications signals

This work proposes methods for estimating the responses of time-varying underwater acoustic channels using ℓ₂ - ℓ₁ basis pursuit and quantifying their similarity. This is motivated by problems where environmental information is to be extracted from communications signals through high-frequency ocean acoustic tomographic techniques. We view underwater channels as time-varying linear systems and characterize them by their Delay-Doppler Spread Functions (DDSF), which have many adjustable parameters but are often very sparse. Basis pursuit estimation of DDSF coefficients is achieved with either the SpaRSA or TwIST algorithms, which can efficiently handle sparse unconstrained ℓ₂ - ℓ₁ minimization even for very large problem sizes, and directly operate on the complex signals of baseband communication models. We show that these algorithms offer better performance than matching pursuit methods, in terms of DDSF estimation accuracy and computational complexity, using both simulated and real data. We examine criteria based on Euclidean distance, correlation, and Kullback-Leibler divergence for quantifying the similarity of DDSFs, as needed in the envisaged tomographic systems for matching observations and model predictions. Their performance is found to be similar, with the correlation metric showing somewhat less consistent performance than the other two in simulation. Our matching approach also enables a simplification of DDSF estimation algorithms by tolerating the inherent biasing in ℓ₂ - ℓ₁ solutions, and thereby avoiding the need for further postprocessing.