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A robust generalized sidelobe canceller is proposed to combat direction of arrival (DOA) mismatches. To estimate the interference-plus-noise (IPN) statistics characteristics, conventional signal of interest (SOI) extraction methods usually collect a large number of segments where only the IPN signal is active. To avoid that collection procedure, we redesign the blocking matrix structure using an eigenanalysis method to reconstruct the IPN covariance matrix from the samples. Additionally, a modified eigenanalysis reconstruction method based on the rank-one matrix assumption is proposed to achieve a higher reconstruction accuracy. The blocking matrix is obtained by incorporating the effective reconstruction into the maximum signal-to-interference-plus-noise ratio (MaxSINR) beamformer. It can minimize the influence of signal leakage and maximize the IPN power for further noise and interference suppression. Numerical results show that the two proposed methods achieve considerable improvements in terms of the output waveform SINR and correlation coefficients with the desired signal in the presence of a DOA mismatch and a limited number of snapshots. Compared to the first proposed method, the modified one can reduce the signal distortion even further.