Adaptive filtering algorithm for direction-of-arrival (DOA) estimation with small snapshots.

The direction-of-arrival (DOA) estimation problem with a few noisy snapshots can be formulated as a problem of finding a joint sparse representation of multiple measurement vectors (MMV), and some algorithms based on compressive sensing (CS), such as the joint ℓ0 approximation DOA (JLZA-DOA) and Multiple Snapshot Matching Pursuit Direction of Arrival (MSMPDOA) algorithms, have recently been proposed for solving this problem. Compared with the conventional DOA methods, the CS-based methods can achieve super-resolution by using only small number of snapshots, without the necessity of an accurate initialization, with small sensitivity to the correlation of the source signals. However, these CS-based algorithms usually do not work well in low signal-noise ratio (SNR) environment. In addition, the increased number of sensors in massive multiple-input-multiple-output (MIMO) systems lead to a huge matrix, and the matrix inversion operation in each iteration of the CS-based algorithm results in a relatively high computational cost. The purpose of this paper is to propose a novel adaptive filtering algorithm, i.e., the ℓ2,0-least mean square (ℓ2,0-LMS) algorithm, which can be viewed as a generalization of the ℓ0-LMS algorithm for single measurement vector (SMV) problem. Our proposed algorithm incorporates a mixed norm (ℓ2,0-norm) to treat the joint sparsity and inherits the robustness against noise and the low complexity of the ℓ0-LMS algorithm, and can thus work well for massive MIMO systems. Numerical experiments demonstrate that the proposed algorithm can achieve much better estimation performance with a lower computational cost than the existing ones.