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In this paper, we present a novel blocking matrix and fixed beamformer design for a generalized sidelobe canceler for speech enhancement in a reverberant enclosure. They are based on a new method for estimating the acoustical transfer function ratios in the presence of stationary noise. The estimation method relies on solving a generalized eigenvalue problem in each frequency bin. An adaptive eigenvector tracking utilizing the power iteration method is employed and shown to achieve a high convergence speed. Simulation results demonstrate that the proposed beamformer leads to better noise and interference reduction and reduced speech distortions compared to other blocking matrix designs from the literature.