  In this work, we propose an adaptive set-membership constant modulus (SM-CM)
algorithm with a generalized sidelobe canceler (GSC) structure for blind
beamforming. We develop a stochastic gradient (SG) type algorithm based on the
concept of SM filtering for adaptive implementation. The filter weights are
updated only if the constraint cannot be satisfied. In addition, we also
propose an extension of two schemes of time-varying bounds for beamforming with
a GSC structure and incorporate parameter and interference dependence to
characterize the environment which improves the tracking performance of the
proposed algorithm in dynamic scenarios. A convergence analysis of the proposed
adaptive SM filtering techniques is carried out. Simulation results show that
the proposed adaptive SM-CM-GSC algorithm with dynamic bounds achieves superior
performance to previously reported methods at a reduced update rate.
