An Incomplete Factorization Preconditioner for LMS Adaptive Filter

In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

• Shazia Javed
• Noor Atinah Ahmad

• Autocorrelation matrix
• Cholesky's factor
• eigenvalue spread
• Markov input.

[1] B. Farhang-Boroujeny, Adaptive filters: theory and applications, John
Wiley & Sons, Inc.,1998.
[2] S. Haykin, Adaptive Filter Theory, 2nd edition, Prentice Hall,1991.
[3] F. Beaufays, Transform-Domain Adaptive Filters: An Analytical Approach,
IEEE transactions on signal processing, 1995.
[4] N. A. Ahmad, Comparative study of iterative search method for adaptive
filtering problems, International Conference on Applied mathematics,
2005.
[5] M. Benzi, Preconditioning Techniques for Large Linear Systems: A
Survey, Journal of Computational Physics, Elsevier, 2002.
[6] S. Narayan, , A. Peterson, and M. Narasimha, Transform domain LMS
algorithm, Acoustics, Speech and Signal Processing, IEEE Transactions
on, 1983.
[7] J. Benesty and et al., A Nonparametric VSS NLMS Algorithm, Signal
Processing Letters, IEEE, 2006.
[8] E. Kreyszig, Introductory functional analysis with applications, Vol. 1,
wiley, 1989.
[9] Y. Saad, Iterative methods for sparse linear systems, Vol. 1. 2nd ed,
SIAM, 2003.