Linearly Constrained Adaptive Filtering Algorithms Designed Using Control Liapunov Functions

The standard conjugate gradient (CG) method uses orthogonality of the residues to simplify the formulas for the parameters necessary for convergence. In adaptive filtering, the sample-by-sample update of the correlation matrix and the cross-correlation vector causes a loss of the residue orthogonality in a modified online algorithm, which, in turn, results in loss of convergence and an increase of the filter quadratic mean error. This paper extends a recently proposed optimality and convergence proof of the degenerated CG method to the case of linearly constrained adaptive filtering, and proposes a constrained Steepest Descent (CSD) method. Keywords— Linearly constrained adaptive filtering algorithms, single-user DS-CDMA, control Liapunov function, conjugate gradient method, steepest descent method.