Adaptive beamforming by constrained parallel projection in the presence of spatially-correlated interferences

The contribution of this paper is twofold. We first clarify geometrically an inherent difference in convergence speed between two adaptive algorithms, projected-NLMS (PNLMS) and constrained-NLMS (CNLMS), both of which are widely used for linearly constrained adaptive filtering problems. A simple geometric interpretation suggests that CNLMS converges faster than PNLMS especially in the challenging situations of the adaptive beamforming where there exist spatially-correlated interferences (i.e., interferences that have small angular separation with the desired signal). To enhance the advantage of CNLMS in convergence speed while keeping linear computational complexity, we then propose an efficient adaptive beamformer that utilizes multiple data at each iteration by extending the constrained parallel projection algorithm to complex cases. The simulation results demonstrate that the proposed beamformer exhibits even faster convergence than the constrained affine projection algorithm (CAPA) as well as CNLMS.