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This paper proposes a robust reduced-rank scheme for adaptive beamformingbased on joint iterative optimization (JIO) of adaptive filters. The novelscheme is designed according to the constant modulus (CM) criterion subject todifferent constraints, and consists of a bank of full-rank adaptive filtersthat forms the transformation matrix, and an adaptive reduced-rank filter thatoperates at the output of the bank of filters to estimate the desired signal.We describe the proposed scheme for both the direct-form processor (DFP) andthe generalized sidelobe canceller (GSC) structures. For each structure, wederive stochastic gradient (SG) and recursive least squares (RLS) algorithmsfor its adaptive implementation. The Gram-Schmidt (GS) technique is applied tothe adaptive algorithms for reformulating the transformation matrix andimproving performance. An automatic rank selection technique is developed andemployed to determine the most adequate rank for the derived algorithms. Thecomplexity and convexity analyses are carried out. Simulation results show thatthe proposed algorithms outperform the existing full-rank and reduced-rankmethods in convergence and tracking performance.

Adaptive Reduced-Rank Constrained Constant Modulus Beamforming Algorithms Based on Joint Iterative Optimization of Filters