Robust Adaptive Beamforming Based on a Gradient Projection Method

Recently, adaptive beamforming has been widely used in wireless communications, microphone array speech processing and so on. One of the adaptive beamforming methods is directionally constrained minimization of power. However, this method is known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated [5]. To resolve this disadvantage, some methods have been proposed [7, 8, 10], whereas these methods does not sufficiently exploit the degree of freedom of the step parameter in the recursive rule, or take relatively large computational complexity. In this paper, we propose an algorithm of robust adaptive beamforming. First, we apply a gradient projection method to the minimization problem with linear constraints and derive a generalized recursive rule. We next present the convergence condition of the recursive rule and propose a design method of the step parameter in the recursive rule such that the convergence condition is approximately satisfied. Finally, we show that the proposed algorithm gives more robust performance than the conventional algorithm. Notation: For a complex matrix A, AT , Ā and A∗ stand for the transpose, complex conjugate and complex conjugate transpose of A, respectively.