Single-snapshot DoA estimation using adaptive elastic net in the complex domain

The elastic net (EN) is a popular regularization and variable selection method that overcomes the shortcomings of Lasso such as poor recovery in the face of high mutual coherence. In this paper, we develop an efficient algorithm to solve the weighted EN criterion for complex-valued measurements applying the cyclic coordinate descent approach. We illustrate that usage of smartly chosen adaptive (i.e., data-dependent) weights revamps the algorithm to overcome the shortcomings of naive (non-weighted) EN and enhances the exact recovery. Usefulness of the proposed algorithm is illustrated for compressed beamforming (CBF) with the single-snapshot DoA (direction-of-arrival) estimation, in a demanding multi-source scenario that contains closely spaced sources having large variation in source powers. Accurate DoA's estimation performance and error plummet by the proposed algorithm validates its application and advocates its potential usage in other signal processing problems.