Sparsity-Based Adaptive Beamforming for Coherent Signals With Polarized Sensor Arrays

Tianpeng Liu, Yun Cheng, Junpeng Shi, Zhen Liu, Yongxiang Liu

Abstract: A sparsity-based adaptive beamforming (ABF) method is introduced to effectively process coherent signals with polarized sensor arrays (PSA). This method exploits the spatial sparsity of observed signals by transforming it into row-sparsity within a waveform-polarization composite matrix through data reorganization. This row-sparsity is subsequently cast as an $\ell _{2,1}$ norm minimization problem, characterized by a gridless and compact mathematical expression with a Hermitian Toeplitz matrix. Then, a matrix factorization-based gradient descent (GD) algorithm is introduced to effectively resolve this optimization problem. The experimental evaluations demonstrate that the GD algorithm significantly outperforms the MOSEK solver in terms of computational efficiency. Further comparative analysis demonstrates that the proposed method outperforms the existing techniques, especially in contexts of low signal-to-noise ratio (SNR), with a moderate increase in computational runtime.