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  • Research Article
  • Open Access
  • Robust Adaptive Modified Newton Algorithm for Generalized Eigendecomposition and Its Application

    EURASIP Journal on Advances in Signal Processing20072007:038341

    • Received: 1 October 2006
    • Accepted: 16 April 2007
    • Published:


    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.


    • Nonlinear Optimization
    • Hessian Matrix
    • Stochastic Approximation
    • Adaptive Modify
    • Nonlinear Optimization Problem

    Authors’ Affiliations

    Laboratory of Network Communication System and Control, Department of Automation, University of Science and Technology of China, Hefei, Anhui, 230027, China


    1. Lu J, Plataniotis KN, Venetsanopoulos AN: Face recognition using LDA-based algorithms. IEEE Transactions on Neural Networks 2003,14(1):195-200. 10.1109/TNN.2002.806647View ArticleGoogle Scholar
    2. Fidler S, Skočaj D, Leonardis A: Combining reconstructive and discriminative subspace methods for robust classification and regression by subsampling. IEEE Transactions on Pattern Analysis and Machine Intelligence 2006,28(3):337-350.View ArticleGoogle Scholar
    3. Wong TF, Lok TM, Lehnert JS, Zoltowski MD: A linear receiver for direct-sequence spread-spectrum multiple-access systems with antenna arrays and blind adaptation. IEEE Transactions on Information Theory 1998,44(2):659-676. 10.1109/18.661511MathSciNetView ArticleGoogle Scholar
    4. Yang J, Xi H, Yang F, Zhao Y: Fast adaptive blind beamforming algorithm for antenna array in CDMA systems. IEEE Transactions on Vehicular Technology 2006,55(2):549-558. 10.1109/TVT.2005.863419View ArticleGoogle Scholar
    5. Yang B: Projection approximation subspace tracking. IEEE Transactions on Signal Processing 1995,43(1):95-107. 10.1109/78.365290View ArticleGoogle Scholar
    6. Ouyang S, Ching PC, Lee T: Robust adaptive quasi-Newton algorithms for eigensubspace estimation. IEE Proceedings: Vision, Image and Signal Processing 2003,150(5):321-330. 10.1049/ip-vis:20030767Google Scholar
    7. Hyvärinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.View ArticleGoogle Scholar
    8. Golub GH, VanLoan CF: Matrix Computations. John Hopkins University Press, Baltimore, Md, USA; 1991.Google Scholar
    9. Mathew G, Reddy VU: A quasi-Newton adaptive algorithm for generalized symmetric eigenvalue problem. IEEE Transactions on Signal Processing 1996,44(10):2413-2422. 10.1109/78.539027View ArticleGoogle Scholar
    10. Chatterjee C, Roychowdhury VP, Ramos J, Zoltowski MD: Self-organizing algorithms for generalized eigen-decomposition. IEEE Transactions on Neural Networks 1997,8(6):1518-1530. 10.1109/72.641473View ArticleGoogle Scholar
    11. Xu D, Principe JC, Wu H-C: Generalized eigendecomposition with an on-line local algorithm. IEEE Signal Processing Letters 1998,5(11):298-301. 10.1109/97.728475View ArticleGoogle Scholar
    12. Morgan DR: Adaptive algorithms for solving generalized eigenvalue signal enhancement problems. Signal Processing 2004,84(6):957-968. 10.1016/j.sigpro.2004.02.002View ArticleGoogle Scholar
    13. Rao YN, Principe JC, Wong TF: Fast RLS-like algorithm for generalized eigendecomposition and its applications. The Journal of VLSI Signal Processing 2004,37(2-3):333-344.View ArticleGoogle Scholar
    14. Yang J, Xi H, Yang F, Zhao Y: RLS-based adaptive algorithms for generalized eigen-decomposition. IEEE Transactions on Signal Processing 2006,54(4):1177-1188.View ArticleGoogle Scholar
    15. Lok TM, Wong TF, Lehnert JS: Blind adaptive signal reception for MC-CDMA systems in Rayleigh fading channels. IEEE Transactions on Communications 1999,47(3):464-471. 10.1109/26.752827View ArticleGoogle Scholar
    16. Kondo S, Milstein LB: Performance of multicarrier DS CDNA systems. IEEE Transactions on Communications 1996,44(2):238-246. 10.1109/26.486616View ArticleGoogle Scholar
    17. Proakis JG: Digital Communications. McGraw-Hill, New York, NY, USA; 1995.MATHGoogle Scholar
    18. Namgoong J, Wong TF, Lehnert JS: Subspace multiuser detection for multicarrier DS-CDMA. IEEE Transactions on Communications 2000,48(11):1897-1908. 10.1109/26.886487View ArticleGoogle Scholar
    19. Haykin S: Adaptive Filter Theory. Prentice-Hall, Upper Saddle River, NJ, USA; 2002.MATHGoogle Scholar
    20. Ljung L: Analysis of recursive stochastic algorithms. IEEE Transactions on Automatic Control 1977,22(4):551-575. 10.1109/TAC.1977.1101561MathSciNetView ArticleGoogle Scholar
    21. Kushner HJ, Clark DS: Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer, New York, NY, USA; 1978.View ArticleGoogle Scholar
    22. Morgan DR, Benesty J, Sondhi MM: On the evaluation of estimated impulse responses. IEEE Signal Processing Letters 1998,5(7):174-176. 10.1109/97.700920View ArticleGoogle Scholar
    23. Lok TM, Wong TF: Transmitter and receiver optimization in multicarrier CDMA systems. IEEE Transactions on Communications 2000,48(7):1197-1207. 10.1109/26.855527View ArticleGoogle Scholar


    © Jian Yang et al. 2007

    This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.