  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.
