Spectral norm-based sparse arrays design: A matrix completion perspective

Abstract

A key challenge in sparse linear arrays (SLAs) is that only partial elements can be observed in a single snapshot. To address this, we employ low-rank Toeplitz matrix completion to estimate missing entries. This method is integrated into a nuclear norm minimization framework tailored for SLA sampling patterns, which directly governs the matrix recovery quality. From this perspective, we establish an empirical performance guarantee linked to the spectral norm of the sampling matrix, providing a quantitative metric for sparse array design. Arrays designed with lower spectral norms demonstrate superior recovery performance. Simulations validate this correlation and suggest using the spectral norm as a preprocessing tool for array screening, substantially reducing design iterations.