A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs

This paper presents a new statistical analysis of the affine projection (AP) algorithm. An analytical model is derived for autoregressive (AR) inputs for unity step size (fastest convergence). Deterministic recursive equations are derived for the mean AP weight and mean-square error for large values of N (the number of adaptive taps). The value of N is also assumed large compared to the algorithm order (number of input vectors used to determine the weight update direction). The model predictions display better agreement with Monte Carlo simulations in both transient and steady-state than models previously presented in the literature. The model's accuracy is sufficient for most practical design purposes.

[1]  J.C.M. Bermudez,et al.  A stochastic model for the convergence behavior of the affine projection algorithm for Gaussian inputs , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[2]  Dirk T. M. Slock,et al.  On the convergence behavior of the LMS and the normalized LMS algorithms , 1993, IEEE Trans. Signal Process..

[3]  Kazuhiko Ozeki,et al.  An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties , 1984 .

[4]  Steve McLaughlin,et al.  A stochastic analysis of the affine projection algorithm for Gaussian autoregressive inputs , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[5]  Jacob Benesty,et al.  Acoustic signal processing for telecommunication , 2000 .

[6]  D.T.M. Stock The block underdetermined covariance (BUC) fast transversal filter (FTF) algorithm for adaptive filtering , 1992, [1992] Conference Record of the Twenty-Sixth Asilomar Conference on Signals, Systems & Computers.

[7]  Ali H. Sayed,et al.  Mean-square performance of a family of affine projection algorithms , 2004, IEEE Transactions on Signal Processing.

[8]  A. A. Beex,et al.  Convergence behavior of affine projection algorithms , 2000, IEEE Trans. Signal Process..

[9]  Steven L. Gay,et al.  The fast affine projection algorithm , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[10]  Claude Samson,et al.  Fixed point error analysis of the normalized ladder algorithm , 1983 .

[11]  Anthony G. Constantinides,et al.  Underdetermined-order recursive least-squares adaptive filtering: the concept and algorithms , 1997, IEEE Trans. Signal Process..

[12]  Markus Rupp A family of adaptive filter algorithms with decorrelating properties , 1998, IEEE Trans. Signal Process..

[13]  Simon Haykin,et al.  Adaptive filter theory (2nd ed.) , 1991 .

[14]  Gerhard Schmidt,et al.  Acoustic echo control. An application of very-high-order adaptive filters , 1999, IEEE Signal Process. Mag..

[15]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..