Constrained adaptive filtering algorithms based on conjugate gradient techniques for beamforming

This article proposes constrained adaptive algorithms based on the conjugate gradient (CG) method for adaptive beamforming. The proposed algorithms are derived for the implementation of the beamformer according to the minimum variance and constant modulus criteria subject to a constraint on the array response. A CG-based weight vector strategy is created for enforcing the constraint and computing the weight expressions. The devised algorithms avoid the covariance matrix inversion and exhibit fast convergence with low complexity. A complexity analysis compares the proposed algorithms with the existing ones. The convergence properties of the CCM criterion are studied, conditions for convexity are established and a convergence analysis for the proposed algorithms is derived. Simulation results are conducted for both stationary and non-stationary scenarios, showing the convergence and tracking ability of the proposed algorithms.