This paper proposes a nested generalized sidelobe canceller (NGSC) for typical array signal processing tasks, including source counting, localization, and signal separation. Multiple blocking matrices are arranged in a nested structure to successively eliminate dominant sources until the remaining signal is predominantly incoherent noise. The microphone signals are dereverberated using a multichannel weighted prediction error algorithm. In source counting, the number of sound sources is determined by tracking the average power of the blocked signal. In source localization, the direction-of-arrival (DOA) is estimated via cosine similarity in conjunction with the golden section search. In signal separation, the estimated DOA enables speech separation in a linearly constrained minimum variance beamformer with postfiltering (LCMV-PF). Monte Carlo simulations are performed to compare the proposed NGSC approach with four baselines, minimum description length, second order statistic of the eigenvalue, multistage Wiener filtering, and multiple signal classification. The results show that NGSC achieves at least 28.80% higher source counting accuracy with a 1.04° lower root mean square degree error than the baselines. The signal-to-distortion ratio achieved by LCMV-PF is 1.52 dB higher than that achieved by the linearly constrained minimum power beamformer and the multichannel Wiener filter.
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