  In this work a constrained adaptive filtering strategy based on conjugate
gradient (CG) and set-membership (SM) techniques is presented for adaptive
beamforming. A constraint on the magnitude of the array output is imposed to
derive an adaptive algorithm that performs data-selective updates when
calculating the beamformer's parameters. We consider a linearly constrained
minimum variance (LCMV) optimization problem with the bounded constraint based
on this strategy and propose a CG type algorithm for implementation. The
proposed algorithm has data-selective updates, a variable forgetting factor and
performs one iteration per update to reduce the computational complexity. The
updated parameters construct a space of feasible solutions that enforce the
constraints. We also introduce two time-varying bounding schemes to measure the
quality of the parameters that could be included in the parameter space. A
comprehensive complexity and performance analysis between the proposed and
existing algorithms are provided. Simulations are performed to show the
enhanced convergence and tracking performance of the proposed algorithm as
compared to existing techniques.
