Adaptive set membership constant modulus algorithm with a generalized sidelobe canceler based on dynamic bounds for beamforming

• Adaptive set-membership CM beamforming algorithm with a GSC structure is proposed.
• SG algorithm using the concept of SM filtering with the GSC structure is devised.
• We propose an extension of two schemes of time-varying bounds for beamforming.
• A convergence analysis of the proposed adaptive techniques is carried out.

In this study, 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 to facilitate an 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 where we incorporate parameter and interference dependency 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 technique was performed. The simulation results showed that the proposed adaptive SM-CM-GSC algorithm with dynamic bounds delivered superior performance compared with previously reported methods and at a reduced update rate.