Robust adaptive modified Newton algorithm for generalized eigendecomposition and its application

Authors:
Jian Yang;Feng Yang;Hong-Sheng Xi;Wei Guo;Yanmin Sheng
Affiliations:
Laboratory of Network Communication System and Control, Department of Automation, University of Science and Technology of China, Hefei, Anhui, China;Laboratory of Network Communication System and Control, Department of Automation, University of Science and Technology of China, Hefei, Anhui, China;Laboratory of Network Communication System and Control, Department of Automation, University of Science and Technology of China, Hefei, Anhui, China;Laboratory of Network Communication System and Control, Department of Automation, University of Science and Technology of China, Hefei, Anhui, China;Laboratory of Network Communication System and Control, Department of Automation, University of Science and Technology of China, Hefei, Anhui, China
Venue:
EURASIP Journal on Advances in Signal Processing
Year:
2007

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Abstract

We propose a robust adaptive algorithm for generalized eigendecomposition problems that arise in modern signal processing applications. To that extent, the generalized eigendecomposition problem is reinterpreted as an unconstrained nonlinear optimization problem. Starting from the proposed cost function and making use of an approximation of the Hessian matrix, a robust modified Newton algorithm is derived. A rigorous analysis of its convergence properties is presented by using stochastic approximation theory. We also apply this theory to solve the signal reception problem of multicarrier DS-CDMA to illustrate its practical application. The simulation results show that the proposed algorithm has fast convergence and excellent tracking capability, which are important in a practical time-varying communication environment.