Dimension-Reduced Direction-of-Arrival Estimation Based on $\ell_{2,1}$ -Norm Penalty

Abstract

Multiple measurement vectors (MMVs) are regarded as jointly sparse when their elements share a common sparsity pattern. Direction-of-arrival (DOA) estimation with a small number of noisy snapshots can be modeled as an MMV problem and solved by compressive sensing-based algorithms. However, all these algorithms have to search the potential DOAs or areas actually containing sources over the entire range of interest which requires a rather heavy computational cost. In this paper, we propose a new algorithm with a pre-estimation to reduce the dimensionality of the measurement matrix for DOA estimation with a small number of noisy snapshots. In the first stage, the range of interest is divided into a relatively low-resolution grid, and the conventional beam former is used to quickly identify the candidate or potential areas where true sources may exist. In the second stage, the candidate areas obtained in the first stage are divided into a denser sampling grid, and the $\ell _{2,1}$ -norm penalty is used to solve the MMV problem. The uniform linear array case (1-D DOA) and uniform plane array case (2-D DOA) are considered in this paper. Simulation results demonstrate the effectiveness and efficiency of the proposed algorithm.