Simplified fixed and adaptive beamforming methods beyond the generalized sidelobe canceler

The generalized sidelobe canceler (GSC) is a widely used beamforming framework in acoustic signal processing, where constrained optimization is reformulated through a two-path structure consisting of a fixed upper-path beamformer and an adaptive lower path. From a beampattern perspective, this paper revisits the conventional GSC and reveals key limitations caused by mismatches between the upper- and lower-path beampatterns, which can lead to noise amplification and reduced interference suppression, particularly in broadband scenarios. To address these issues, we propose modified GSC-based beamforming designs in which the conventional blocking matrix is replaced by a null beamformer. By increasing beampattern similarity in both magnitude and phase, the proposed structure enables more effective signal subtraction. Based on this formulation, we develop two variants: a fixed beamforming approach that eliminates the adaptive filter in the lower path and an adaptive approach that uses a single adaptive filter with a modified update rule. Simulation results demonstrate improved convergence, robustness, and interference suppression compared to the conventional GSC. The matlab implementation is publicly available at https://github.com/PhanLeSon03/FBSS_ABSS.git.