Sequential adaptive elastic net approach for single-snapshot source localization

This paper proposes efficient algorithms for accurate recovery of direction-of-arrival (DoA) of sources from single-snapshot measurements using compressed beamforming (CBF). In CBF, the conventional sensor array signal model is cast as an underdetermined complex-valued linear regression model and sparse signal recovery methods are used for solving the DoA finding problem. We develop a complex-valued pathwise weighted elastic net (c-PW-WEN) algorithm that finds solutions at knots of penalty parameter values over a path (or grid) of EN tuning parameter values. c-PW-WEN also computes Lasso or weighted Lasso in its path. We then propose a sequential adaptive EN (SAEN) method that is based on c-PW-WEN algorithm with adaptive weights that depend on the previous solution. Extensive simulation studies illustrate that SAEN improves the probability of exact recovery of true support compared to conventional sparse signal recovery approaches such as Lasso, elastic net or orthogonal matching pursuit in several challenging multiple target scenarios. The effectiveness of SAEN is more pronounced in the presence of high mutual coherence.