Conventional beamforming (CBF) is widely used in underwater acoustic applications due to its simplicity and robustness. Under certain circumstances, incoherent noise is the main disturbance for hydrophone arrays and can lead to a serious decline in the signal power estimation accuracy and signal detection ability of CBF. Since incoherent noise contamination is concentrated along the diagonal of the covariance matrix, we propose to improve the performance of CBF by reducing the diagonal as much as possible to suppress the incoherent noise until the output spatial spectrum becomes sparsest. Mathematically, the denoising problem is convex; hence, it can be solved with guaranteed efficiency and convergence properties. The proposed denoising algorithm is named the sparsity-optimization-based diagonal denoising (SO-DD) algorithm, and its capability is investigated and compared with the recently developed positive-semidefinite-constrained diagonal denoising (PSC-DD) algorithmvia simulation and experiments. The results suggest that both SO-DD and PSC-DD work well under ideal conditions where noise is perfectly incoherent, while SO-DD performs more reliably when noise is partially coherent due to limited sampling and the existence of coherent noise component in practice.
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