Direction-of-Arrival Estimation for Correlated Sources and Low Sample Size

In this paper, we study the problem of recovering the direction-of-arrival in difficult scenarios of highly correlated source signals and only few available snapshots. Recently, the partial relaxation framework has been proposed as an optimizationbased technique that accounts for the existence of multiple signals while performing the estimation task through a simple spectral search. Its performance is superior to conventional methods but tends to deteriorate drastically when the source signals are highly correlated due to information loss associated with the relaxation. On the other hand, from a compressed sensing point of view, the recently proposed sparse row-norm reconstruction method formulates the parameter estimation problem as a compact $\ell_{2,1}$ -mixed-norm minimization problem. One of its prominent advantages is its robustness under highly correlated sources and a low number of snapshots; an intrinsic bias induced by the $\ell_{1}$ -norm approximation, however, affects the estimation performance. In this paper, we propose a method that integrates the $\ell_{2,1}$ -mixed-norm minimization formulation into the spectral search of the partial relaxation estimators. Simulation results show that the proposed estimator has superior error performance in difficult scenarios and alleviates the disadvantages of both methods.