A stochastic analysis of the NLMS algorithm implemented in finite precision

Author

Bershad, Neil J. ; Bermudez, José C M

fYear

2010

fDate

7-10 Nov. 2010

Firstpage

1625

Lastpage

1629

Abstract

Quantization effects in the NLMS algorithm are investigated for a white Gaussian data model. Nonlinear recursions are derived for the weight mean error and mean-square deviation (MSD) that include the effects of various quantization operations in the implementation of the algorithm. The nonlinear recursion for the MSD is solved numerically and shown in excellent agreement with Monte Carlo simulations, supporting the theoretical model assumptions. The theory is extended to tracking a Markov channel and accurately predicts the tracking behavior as well. For the white data case, the excess mean square-error (EMSE) is simply related to the MSD. The tradeoff between the number of bits in the quantizers, steady-state EMSE, and algorithm convergence rate is studied using these results.

Keywords

Markov processes; Monte Carlo methods; convergence; mean square error methods; quantisation (signal); Markov channel; Monte Carlo simulation; NLMS algorithm; convergence rate; excess mean square-error; finite precision; mean-square deviation; nonlinear recursion; quantization effect; steady-state EMSE; stochastic analysis; tracking behavior; weight mean error; white Gaussian data model; Algorithm design and analysis; Analytical models; Approximation algorithms; Least squares approximation; Mathematical model; Prediction algorithms; Signal processing algorithms;

fLanguage

English

Publisher

ieee

Conference_Titel

Signals, Systems and Computers (ASILOMAR), 2010 Conference Record of the Forty Fourth Asilomar Conference on

Conference_Location

Pacific Grove, CA

ISSN

1058-6393

Print_ISBN

978-1-4244-9722-5

Type

conf

DOI

10.1109/ACSSC.2010.5757813

Filename

5757813