Dual forms for constrained adaptive filtering

A new structure for constrained adaptive filtering is proposed. It is based on a “dual” solution of the constrained minimization problems that arise in optimal broadband adaptive array processing. The dual solution is unique in the sense that its update equations involve the Lagrange multipliers rather than the adaptive filter weights. The dual approach is shown to be applicable to two types of adaptive filtering (or beamforming) problems. One is the linearly constrained power minimization beamformer and the other is the norm constrained robust beamformer. In each case, the equations defining the dual structure are derived, and the convergence of the resulting iteration is analyzed. Simulation results are included to illustrate the performance of the dual algorithms compared with the primal methods. It is shown that the convergence and computational complexity of the dual algorithms are similar to that of RLS-type algorithms