ZHI Yongfeng, LI Ru, LI Huxiong. A New Affine Projection Algorithm and Its Statistical Behavior[J]. Chinese Journal of Electronics, 2013, 22(3): 537-542.
Citation: ZHI Yongfeng, LI Ru, LI Huxiong. A New Affine Projection Algorithm and Its Statistical Behavior[J]. Chinese Journal of Electronics, 2013, 22(3): 537-542.

A New Affine Projection Algorithm and Its Statistical Behavior

Funds:  This work is supported by the National Natural Science Foundation of China (No.61201321), and the Basic Research Foundation of Northwestem Polytechnical University (No.JC20100217).
  • Received Date: 2012-10-01
  • Rev Recd Date: 2012-12-01
  • Publish Date: 2013-06-15
  • An Affine projection algorithm with Direction error (AP-DE) is presented by redefining the iteration error. Under a measurement-noise-free condition, the iteration error is directly caused by the direction vector. A statistical analysis model is used to analyze the AP-DE algorithm. Deterministic recursive equations for the mean weight error and for the Mean-square error (MSE) in iteration direction are derived. We also analyze the stability of MSE in iteration direction and the optimal step-size for the AP-DE algorithm. Simulation results are provided to corroborate the analytical theory.
  • loading
  • S. Haykin, Adaptive Filter Theory, Prentice-Hall, Upper Saddle River, USA, 1991.
    K. Ozeki, T. Umeda, “An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties”, Electronics and Communication in Japan, Vol.67-A, No.5, pp.19-27, 1984.
    S.G. Kratzer, D.R. Morgan, “The partial-rank algorithm for adaptive beamforming”, Proc. of SPIE International Society for Optical Engineering, San Diego, CA, USA, pp.9-14, 1985.
    S.G. Sankaran, A.A. (Louis) Beex, “Normalized LMS algorithm with orthogonal correction factors”, Proc. of 31th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, pp.1670-1673, 1997.
    D.R. Morgan, S.G. Kratzer, “On a class of computationally efficient, rapidly converging, generalized NLMS algorithms”, IEEE Signal Processing Letters, Vol.3, No.8, pp.245-247, 1996.
    S.G. Sankaran, A.A. (Louis) Beex, “Fast generalized affine projection algorithm”, International Journal of Adaptive Control and Signal Processing, Vol.14, No.6, pp.623-641, 2000.
    S.L. Gay, S. Tavathia, “The fast affine projection algorithm”, Proc. of International Conference on Acoustics, Speech and Signal Processing, Detroit, MI, USA, pp.3023-3026, 1995.
    F. Albu, C. Kotropoulos, Z. Cernekova, I. Pitas, “New affine projection algorithms based on Gauss-Seidel method”, Proc. of International Symposium on Signals, Circuits and Systems, Iasi, Romania, pp.565-568, 2005.
    H.X. Wen, L.D. Chen, Z.F. Cai, “An improved affine projection algorithm and its application in network echo cancellation”, Acta Electronica Sinica, Vol.40, No.6, pp.1229-1234, 2012. (in Chinese)
    F. Bouteille, P. Scalart, M. Corazza, “Pseudo affine projection algorithm new solution for adaptive identification”, Proc. of Eurospeech, Vol.1, pp.427-430, 1999.
    M. Rupp, “A family of adaptive filter algorithms with decorrelating properties”, IEEE Transactions on Signal Processing, Vol.46, No.3, pp.771-775, 1998.
    S.G. Sankaran, A.A. (Louis) Beex, “Convergence behavior of affine projection algorithms”, IEEE Transactions on Signal Processing, Vol.48, No.4, pp.1086-1096, 2000.
    T.K. Paul, T. Ogunfunmi, “On the convergence behavior of the affine projection algorithm for adaptive filters”, IEEE Transactions on Circuits and Systems-I: Regular Papers, Vol.58, No.8,pp.1813-1826, 2011.
    D.T.M. Slock, “On the convergence behavior of the LMS and the normalized LMS algorithms”, IEEE Transactions on Signal Processing, Vol.41, No.9, pp.2811-2825, 1993.
    H.C. Shin, A.H. Sayed, “Mean-square performance of a family of affine projection algorithms”, IEEE Transactions on Signal Processing, Vol.52, No.1, pp.90-102, 2004.
    S.J.M.D. Almeida, J.C.M. Bermudez, N.J. Bershad, “A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs”, IEEE Transactions on Circuits and Systems-I: Regular Papers, Vol.52, No.7, pp.1394-1405, 2005.
    S.J.M.D. Almeida, J.C.M. Bermudez, N.J. Bershad, “A stochastic model for a pseudo affine projection algorithm”, IEEE Transactions on Signal Processing, Vol.57, No.1, pp.107-118, 2009.
    M. Rupp, “Pseudo affine projection algorithms revisited: robustness and stability analysis”, IEEE Transactions on Signal Processing, Vol.59, No.5, pp.2017-2023, 2011.
    S. Zhang, Y.F. Zhi, “Affine projection algorithm with regressive estimated error”, ISRN Signal Processing, doi:10.5402/2011/180624, 2011.
    A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York, USA, 1965.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (342) PDF downloads(1188) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return