A recursive least squares implementation for adaptive beamforming under quadratic constraint

Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. In this paper, we propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, where the amount of loading is found from the solution to a quadratic equation. Simulations under different scenarios demonstrate that this algorithm outperforms both the RLS beamformer with no quadratic constraint, and the RLS beamformer using the scaled projection technique.