Adaptive Filter-and-sum Beamforming in Spatially Correlated Noise

In this paper we propose a novel adaptation algorithm for Filterand-Sum beamforming in spatially correlated noise. Deterministic and stochastic gradient ascent algorithms are derived from a constrained optimization problem, which iteratively estimate the principal eigenvector of a generalized eigenvalue problem. The method does not require an explicit estimation of the speaker location. It is shown that the well-known Delay-and-Sum beamformer and the previously introduced Filter-and-Sum beamformer in spatially white noise are obtained as special cases. Further, bounds on the maximally achievable SNR gains are derived and it is shown that the proposed adaptation algorithm is able to approach these performance bounds.