Adaptive reduced-rank least squares beamforming algorithm based on the set-membership framework

This paper presents a new adaptive algorithm for the linearly constrained minimum variance (LCMV) beamformer design. We incorporate the set-membership filtering (SMF) mechanism into the reduced-rank joint iterative optimization (JIO) scheme to develop a constrained recursive least squares (RLS) based algorithm called JIO-SM-RLS. The proposed algorithm inherits the positive features of reduced-rank signal processing techniques to enhance the output performance, and utilizes the data-selective updates (around 10-15%) of the SMF methodology to save the computational cost significantly. An effective time-varying bound is imposed on the array output as a constraint to circumvent the risk of overbounding or underbounding, and to update the parameters for beamforming. The updated parameters construct a set of solutions (a membership set) that satisfy the constraints of the LCMV beamformer. Simulations are performed to show the superior performance of the proposed algorithm in terms of the convergence rate and the reduced computational complexity in comparison with the existing methods.