DOA Estimation With Small Snapshots Using Weighted Mixed Norm Based on Spatial Filter

$\ell _{2,1}$
-norm penalized compressive sensing (CS) is utilized to improve the performance of DOA estimation with small snapshots recently. However, the existing CS-based methods are not robust to the noise. In this article, we propose a CS-based DOA estimation using a novel weighted
$\ell _{2,1}$
-norm penalty. A spatial filter which can roughly “clean up” or eliminate the signals coming from the directions of the true sources is constructed. Thus, the space spectrum of the spatial filter can work as a weighting matrix to adjust the sparse penalty automatically. A new weighted
$\ell _{2,1}$
-norm penalty based on this spatial filter is then proposed for DOA estimation. Simulation results demonstrate the effectiveness and efficiency of the proposed algorithm.