Coprime array‐adaptive beamforming via atomic‐norm‐based sparse recovery

Abstract

Abstract Coprime arrays (CPAs) have been found to be an effective configuration for adaptive beamforming (ABF). However, most ABF methods for CPAs are embedded with the spatial spectrum estimation technique, and therefore they usually deteriorate in the case of low signal‐to‐noise ratio (SNR), especially without prior information of interferences. To address this issue, a robust ABF method for CPAs via atomic‐norm‐based sparse recovery is proposed. This method begins with initialised virtual array interpolation to avoid aperture loss caused by ‘holes’, which is subsequently transformed to a matrix completion and denoising issue via a Toeplitz step. With the matrix’s Hermitian Toeplitz structure and the intrinsic sparsity of interferences, sparse recovery for the interference covariance matrix is introduced by subtracting the target signal and noise from the received signal and implemented by atomic‐norm minimisation. Concretely, this non‐convex process is decomposed into two convex steps and solved iteratively. Unlike previous methods, this method can interpolate the virtual array and estimate the steering vector of the target and the noise power simultaneously; consequently, the interference‐plus‐noise covariance matrix is reconstructed with merely some trivial entry selections without the need for the spatial spectrum. Furthermore, the optimality conditions and boundedness in this method are proven theoretically. Simulation results demonstrate the effectiveness of the proposed method and its advantages over previous methods under those non‐ideal conditions.

Keywords

• Toeplitz matrices
• iterative methods
• covariance matrices
• array signal processing
• minimisation
• signal denoising