Generalized Widely Linear Robust Adaptive Beamforming: A Sparse Reconstruction Perspective

Widely linear (WL) robust adaptive beamforming exhibits superior performance by effectively leveraging the additional noncircularity information. However, existing studies focus solely on the noncircular (NC) impinging interferences, often overlooking main-lobe interferences and suffering from high computational complexity. To tackle these challenges, this article introduces a generalized WL sparse reconstruction (GWLSR) beamforming framework that addresses the general scenario where the impinging interferences consist of mixed circular and NC signals from a sparse reconstruction perspective. The framework considers two variants, GWLSR(1) and GWLSR(2), to accommodate circular and NC signal of interest, respectively. Within this framework, we can estimate the power of a larger number of interferences in the general scenario, supported by a root finding-based approach for direction-of-arrival (DOA) and NC phase (NCP) estimation. We then reconstruct the conjugate augmented interference-plus-noise covariance by leveraging the estimated DOAs, NCPs, and power associated with the interferences. The proposed beamformers are computational efficient as all the involved procedures can be formulated using close-form expressions. In addition, they can effectively suppress main-lobe interferences. Simulation examples are provided to illustrate the advantages of the proposed beamformers.