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The generalized eigenspace-based beamformer (GEIB) is presented here, which utilizes the eigenstructure of the correlation matrix to enhance the performance of the linearly constrained minimum variance beamformer (LCMVB). The weight vector of the GEIB is found by projecting the LCMVB weight vector onto a vector subspace constructed from the eigenstructure of the correlation matrix. The GEIB and the LCMVB have the same responses to the desired signal and the interferers. However, the weight vector of the GEIB has a smaller norm and generates a lower output noise power. An additional advantage of the GEIB is that the linear constraints can be treated flexibly, i.e. each linear constraint can be chosen to be preserved or not preserved. The cost of preserving a linear constraint is to get more output noise power. In addition to developing the GEIB, we discuss the effects of imposing linear constraints on the …