  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.
