Fast Sparse Non-Negative Least Squares via ADMM for High Resolution DOA Estimation

High-resolution and low-complexity direction of arrival (DOA) estimation deserves a warm welcome in a real radar sensor. However, achieving this goal is nontrivial. For the DOA estimation of the uniform linear array (ULA), we offer an efficient approach to reach a good compromise between complexity, resolution and accuracy. Under the covariance fitting framework, we construct a sparse non-negative least squares (NNLS) that is solved by the alternating direction method of multipliers (ADMM) at a low-computational complexity. The regularization item involved in the ADMM procedure yields an inherent improvement on robustness. Moreover, a large-scale matrix inversion that is a computationally expensive operation in the ADMM procedure is recursively computed by exploiting the diagonal matrix property of the regularization item, resulting in a reduction on complexity. In addition, the pre-estimation of the noise variance further reduces the scale of the sparse NNLS problem and alleviates the ill-conditioning effect to some extent. Compared to several sparse covariance fitting methods, both the simulation data and the 77 GHz radar-measured data demonstrate that the proposed algorithm has the good resolution, robustness, and accuracy performance with lower computationally cost.