Hankel Meets NOMP: Matrix Pencil and Newtonized Orthogonal Matching Pursuit for Robust Beamforming via Interference-Plus-Noise Covariance Matrix Reconstruction

Abstract

Beamforming based on interference-plus-noise covariance matrix (INCM) reconstruction is a cornerstone of robust adaptive beamforming. Conventional Capon type and maximum entropy type methods typically require numerical integration, leading to stability issues and integration errors. Sparse recovery-based approaches, while avoiding integration, suffer from high computational cost due to the need for overcomplete dictionaries. To address these issues, this article proposes a parameter estimation-based INCM reconstruction method that requires neither numerical integration nor the construction of an overcomplete dictionary. First, the matrix-pencil method based on Hankel matrix is employed to extract the powers and directions-of-arrival regarding the signal of interest and interference sources, serving as a coarse support set estimate for the subsequent Newtonized Orthogonal Matching Pursuit (NOMP) stage. This approach effectively circumvents the computational redundancy typically associated with constructing overcomplete dictionaries for coarse estimation; subsequently, Newton refinement is applied to correct the estimated directions and the corresponding powers are re-estimated by nonnegative least squares. We achieve a seamless integration of the matrix-pencil method and NOMP within the unified framework of INCM reconstruction. Simulation comparisons against state-of-the-art algorithms and other seminal methods within the INCM domain demonstrate the superiority and efficacy of our proposed method. Our research is expected to stimulate renewed interest among researchers in the INCM field regarding the application of parameter estimation techniques, such as the matrix-pencil method and NOMP.