Sparsity-Based Adaptive Beamforming for Non-Uniform Linear Arrays in Multipath Environment

Multipath signals are commonly encountered in complex electromagnetic environments, resulting in the failure of traditional adaptive beamforming (ABF) due to signal cancellation. Various methods have been proposed to tackle this problem, but most of them are subject to multiple restrictions such as specific array geometries or requirements for prior knowledge. To bypass these restrictions, we introduce an ABF method for non-uniform linear arrays in multipath environment. Firstly, we design a sparsity-induced decorrelation method that extends the compact formulation for the
$\ell _{2,1}$
mixed-norm to a gridless manner by Jacobi-Anger approximation. For computational efficiency, this convex problem is solved in two steps: offline calculations and online iterations, so as to yield a Toeplitz matrix. Next, we extract the direction-of-arrivals (DoAs) and
$\ell _{2}$
norms of the signals, by which a matching scheme is proposed to reconstruct the desired and interference-plus-noise covariance matrices. Additionally, we provide a novel proof for the compact formulation, and present an alternative approach for DoA estimation through analysis of the dual problem in the generalized formulation. The superiority of our method over competing approaches is validated through simulations and experimental data.