  We introduce a new linearly constrained minimum variance (LCMV) beamformer
that combines the set-membership (SM) technique with the conjugate gradient
(CG) method, and develop a low-complexity adaptive filtering algorithm for
beamforming. The proposed algorithm utilizes a CG-based vector and a variable
forgetting factor to perform the data-selective updates that are controlled by
a time-varying bound related to the parameters. For the update, the CG-based
vector is calculated iteratively (one iteration per update) to obtain the
filter parameters and to avoid the matrix inversion. The resulting iterations
construct a space of feasible solutions that satisfy the constraints of the
LCMV optimization problem. The proposed algorithm reduces the computational
complexity significantly and shows an enhanced convergence and tracking
performance over existing algorithms.
