DUAL FORMS FOR CONSTRAINED ADAPTIVE FILTERING

In this paper, a new structure for constrained adaptive filtering is p roposed. It is based on a ''dual'' solution of the constrained minimiz ation problems that arise in optimal broadband adaptive array processi ng. The dual solution is unique in the sense that its update equations involve the Lagrange multipliers rather than the adaptive filter weig hts. In this paper, the dual approach is shown to be applicable to two types of adaptive filtering (or beamforming) problems. One is the lin early constrained power minimization beamformer and the other is the n orm constrained robust beamformer. In each case, the equations definin g 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 method s. It is shown that the convergence and computational complexity of th e dual algorithms are similar to that of RLS-type algorithms.