CONVERGENCES OF ADAPTIVE BLOCK SIMULTANEOUS-ITERATION METHOD FOR EIGENSTRUCTURE DECOMPOSITION

Eigenstructure decomposition of data correlation matrices is of basic interest in many modern signal processing problems. In practical situa tions, often the data environment is changing or nonstationary, and th us it may be advantageous to use adaptive algorithms to obtain the des ired eigenvectors and eigenvalues. Recently, we have shown the adaptiv e block simultaneous iteration method (SIM) has an efficient implement ation using a systolic processor array architecture for evaluating som e or all of the eigenvectors of the data correlation matrix. In this p aper, the convergence and optimality properties of this adaptive algor ithm are considered. We first review the basic properties of the adapt ive SIM algorithm and consider its application to the MUSIC direction- of-arrival problem. Then we discuss the convergence in the mean and th e asymptotic convergence of the adaptive SIM eigendecomposition soluti ons to the true solutions, based upon two standard assumptions in the analysis of adaptive algorithm. Furthermore, we consider the optimalit y of the algorithm under the minimum variance criterion. We show the a symptotic equivalence of the Kalman algorithm approach and the adaptiv e SIM algorithm approach in estimating the smallest eigenvector using a transversal filter. Our analytical results on the adaptive SIM algor ithm confirm and extend various optimality results reported by Karhune n based on simulation results.