A method for adaptive beamforming based on an inverse QR decomposition

The inverse QR-based decomposition algorithm is applied to adaptive beamforming. The inverse QR algorithm employs orthogonal rotation operations to update the filter weights thereby preserving the inherent stability properties of the QR method for solving the recursive least squares (RLS) problem. The weight vector for the beamformer is updated in a recursive way while avoiding the highly serial backsubstitution step required in the QR algorithm for solving the RLS estimation problem. Furthermore, the inverse Cholesky factor of the inverse QR algorithm is always a full rank while the Cholesky factor of the direct QR algorithm may be of deficient rank. We have demonstrated the utility of the inverse QR algorithm in constrained (as well as unconstrained) adaptive filtering applications such as adaptive beamforming by modifying the recursive updates required in the algorithm for this application. Simulation results show that the inverse QR algorithm possesses rapid initial convergence typical of RLS-based algorithms and also maintains the long-term stability properties of the orthogonal rotation methods