Constrained Adaptive Beamforming Using Smoothed Gradient Estimates
Henry L. Cox, R.M. Zeskind, G.M. Skarda · 2005
Multiple linear equality constraints are used in adaptive beamformers to control mainlobe shape, and a quadratic inequality constraint is effective in insuring robustness in the face of imprecise knowledge and tolerance errors. However, their use in recursive adaptive beamforming algorithms requires significant added computations at each time step. Indeed, the computational load associated with computing constraints is the dominant load in computing updated weights, and can be the dominant load in the entire beamforming operation. This paper examines efficient computation of constraints. A modified algorithm is introduced in which the weights are updated less frequently, reducing the cost of implementing constraints. The updated weights are based on a smoothed gradient estimate obtained by averaging over the intervening samples since the previous weight update. The underlying concept is not only to step less frequently and with less randomness, but also to use a larger step size to offset the reduced frequency of weight updating. The performance of the modified algorithm is compared with the standard algorithm, and shown to give approximately the same performance with greatly reduced computations.