A dual form adaptive filter

A structure for adaptive arrays (or filters) is proposed and analyzed. It is based on a dual solution of the constrained Wiener filtering problem that arises in broadband linearly constrained adaptive arrays. The primary advantage of the dual solution is that the update equations of the adaptive algorithm involve the Lagrange multipliers of the constrained optimization problem. Hence, the dimension of the updated vector is equal to the number of constraints, which is usually much less than the number of weights. The dual algorithm is shown to converge in the mean, and expressions are derived which quantify misadjustment. Computer simulations are presented to illustrate these analytical results