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This paper presents reduced-rank linearly constrained minimum variance (LCMV)beamforming algorithms based on joint iterative optimization of filters. Theproposed reduced-rank scheme is based on a constrained joint iterativeoptimization of filters according to the minimum variance criterion. Theproposed optimization procedure adjusts the parameters of a projection matrixand an adaptive reducedrank filter that operates at the output of the bank offilters. We describe LCMV expressions for the design of the projection matrixand the reduced-rank filter. We then describe stochastic gradient and developrecursive least-squares adaptive algorithms for their efficient implementationalong with automatic rank selection techniques. An analysis of the stabilityand the convergence properties of the proposed algorithms is presented andsemi-analytical expressions are derived for predicting their mean squared error(MSE) performance. Simulations for a beamforming application show that theproposed scheme and algorithms outperform in convergence and tracking theexisting full-rank and reduced-rank algorithms while requiring comparablecomplexity

Adaptive Reduced-Rank LCMV Beamforming Algorithms Based on Joint Iterative Optimization of Filters: Design and Analysis