Fast azimuth–frequency sparse beamforming with adaptive filtering for tonal enhancement under low signal-to-noise ratio conditions

Enhancing weak tonal signals under low signal-to-noise ratio (SNR) conditions is a fundamental yet challenging problem in underwater acoustic signal processing. In this paper, a sparse fast azimuth–frequency beamforming with adaptive filtering (SFAFBF-AF) method is proposed for robust tonal enhancement using array measurements. The proposed method exploits the sparsity of tonal signals in the joint azimuth–frequency domain to achieve improved resolution. By introducing a whitening transformation, the sparse azimuth–frequency spectrum can be efficiently recovered using a closed-form soft-thresholding operator, thereby avoiding computationally expensive iterative sparse optimization. A simple adaptive filtering is then employed to suppress nonstationary noise components that are unstable over time while further reinforcing temporally stable tonal structures, leading to high enhancement gain. Owing to this design, SFAFBF-AF achieves a favorable balance between performance and computational efficiency. It provides high enhancement gain and good angular resolution while maintaining a relatively fast computation speed. Simulations and experiments demonstrate that the proposed method outperforms conventional wideband beamforming and other reference approaches, particularly for weak or closely spaced tonal targets under low-SNR conditions.