Sequential adaptive elastic net approach for single-snapshot source localization

This paper proposes efficient algorithms for accurate recovery of direction-of-arrivals (DoAs) 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. A complex-valued pathwise weighted elastic net (c-PW-WEN) algorithm is developed that finds solutions at the knots of penalty parameter values over a path (or grid) of elastic net (EN) tuning parameter values. c-PW-WEN also computes least absolute shrinkage and selection operator (LASSO) or weighted LASSO in its path. A sequential adaptive EN (SAEN) method is then proposed that is based on c-PW-WEN algorithm with adaptive weights that depend on 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, EN, or orthogonal matching pursuit in several challenging multiple target scenarios. The effectiveness of SAEN is more pronounced in the presence of high mutual coherence.