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A novel approach to linearly constrained minimum variance (LCMV) beamforming based on reduced-rank processing is proposed. The method is based on a constrained joint iterative optimisation of an adaptive projection matrix and a reduced-rank filter according to the minimum variance criterion. We derive LCMV expressions for the design of the projection matrix and the reduced-rank filter and present low-complexity adaptive algorithms for their efficient implementation. Simulations show that the proposed scheme outperforms the full-rank and existing reduced-rank methods with low complexity.