Transient analysis of data-normalized adaptive filters

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability, of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model provides information about the mean-square deviation and mean-square error performance of the filters. In addition to deriving earlier results in a unified manner, the approach leads to stability and performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and does not require an explicit recursion for the covariance matrix of the weight-error vector.

[1]  N. Bershad.  Behavior of the ε-normalized LMS algorithm with Gaussian inputs , 1987, IEEE Trans. Acoust. Speech Signal Process..

[2]  Ali H. Sayed,et al.  A feedback analysis of the tracking performance of blind adaptive equalization algorithms , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[3]  Ali H. Sayed,et al.  A time-domain feedback analysis of filtered-error adaptive gradient algorithms , 1996, IEEE Trans. Signal Process..

[4]  Robert Price,et al.  A useful theorem for nonlinear devices having Gaussian inputs , 1958, IRE Trans. Inf. Theory.

[5]  Ali H. Sayed,et al.  Time-domain feedback analysis of adaptive gradient algorithms via the small gain theorem , 1995, Optics & Photonics.

[6]  B. Widrow,et al.  Stationary and nonstationary learning characteristics of the LMS adaptive filter , 1976, Proceedings of the IEEE.

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

[8]  Arie Feuer,et al.  Convergence and performance analysis of the normalized LMS algorithm with uncorrelated Gaussian data , 1988, IEEE Trans. Inf. Theory.

[9]  Teresa H. Y. Meng,et al.  Normalized data nonlinearities for LMS adaptation , 1994, IEEE Trans. Signal Process..

[10]  Tareq Y. Al-Naffouri,et al.  Mean-square analysis of normalized leaky adaptive filters , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

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

[12]  Ehud Weinstein,et al.  Convergence analysis of LMS filters with uncorrelated Gaussian data , 1985, IEEE Trans. Acoust. Speech Signal Process..

[13]  Ali H. Sayed,et al.  A unified approach to the steady-state and tracking analyses of adaptive filters , 2001, IEEE Trans. Signal Process..

[14]  Ali H. Sayed,et al.  On the convergence of blind adaptive equalizers for constant modulus signals , 2000, IEEE Trans. Commun..

[15]  E. Eweda,et al.  Analysis and design of a signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data , 1990 .

[16]  P. Maher,et al.  Handbook of Matrices , 1999, The Mathematical Gazette.

[17]  V. J. Mathews,et al.  Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm , 1987, IEEE Trans. Acoust. Speech Signal Process..

[18]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[19]  Neil J. Bershad,et al.  Analysis of the normalized LMS algorithm with Gaussian inputs , 1986, IEEE Trans. Acoust. Speech Signal Process..

[20]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[21]  Richard W. Harris,et al.  A variable step (VS) adaptive filter algorithm , 1986, IEEE Trans. Acoust. Speech Signal Process..

[22]  Teresa H. Y. Meng,et al.  The optimum scalar data nonlinearity in LMS adaptation for arbitrary IID inputs , 1992, IEEE Trans. Signal Process..

[23]  Ali H. Sayed,et al.  A feedback approach to the steady-state performance of fractionally spaced blind adaptive equalizers , 2000, IEEE Trans. Signal Process..

[24]  H. Luetkepohl.  The Handbook of Matrices , 1996 .

[25]  Markus Rupp,et al.  The behavior of LMS and NLMS algorithms in the presence of spherically invariant processes , 1993, IEEE Trans. Signal Process..

[26]  Ali H. Sayed,et al.  Ability of adaptive filters to track carrier offsets and channel nonstationarities , 2002, IEEE Trans. Signal Process..

[27]  Ralph K. Cavin,et al.  Analysis of error-gradient adaptive linear estimators for a class of stationary dependent processes , 1982, IEEE Trans. Inf. Theory.

[28]  Ali H. Sayed,et al.  Robustness issues in adaptive filtering , 1998 .

[29]  Tareq Y. Al-Naffouri,et al.  Transient analysis of adaptive filters with error nonlinearities , 2003, IEEE Trans. Signal Process..

[30]  Ali H. Sayed,et al.  Transient behavior of affine projection algorithms , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[31]  Neil J. Bershad.  On the optimum data nonlinearity in LMS adaptation , 1986, IEEE Trans. Acoust. Speech Signal Process..

[32]  Leonid G. Kazovsky,et al.  Adaptive filters with individual adaptation of parameters , 1986 .