Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input

Muhammad Moinuddin; Tareq Y. Al-Naffouri; Muhammad S. Sohail

doi:10.1109/ISSPIT.2010.5711782

Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input

Muhammad Moinuddin^*
, Tareq Y. Al-Naffouri
, Muhammad S. Sohail

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

This work presents exact tracking analysis of the E-normalized least mean square (ε-NLMS) algorithm for circular complex correlated Gaussian input. The analysis is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form [∥u_i∥D₁²][ε+∥u _i∥D₂²]^-1. The CDF is then used to derive the first and second moments of these variables. These moments in turn completely characterize the tracking performance of the ε-NLMS algorithm in explicit closed form expressions. Consequently, new explicit closed-form expressions for the steady state tracking excess mean square error and optimum step size are derived. The simulation results of the tracking behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ε.

Original language	English
Title of host publication	2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010
Publisher	IEEE Computer Society
Pages	225-230
Number of pages	6
ISBN (Print)	9781424499908
DOIs	https://doi.org/10.1109/ISSPIT.2010.5711782
State	Published - 2010

Publication series

Name	2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010

Keywords

Adaptive algorithms
Indefinite quadratic forms
Tracking performance

ASJC Scopus subject areas

Information Systems
Signal Processing

Access to Document

10.1109/ISSPIT.2010.5711782

Cite this

Moinuddin, M., Al-Naffouri, T. Y., & Sohail, M. S. (2010). Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input. In 2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010 (pp. 225-230). Article 5711782 (2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010). IEEE Computer Society. https://doi.org/10.1109/ISSPIT.2010.5711782

Moinuddin, Muhammad ; Al-Naffouri, Tareq Y. ; Sohail, Muhammad S. / Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input. 2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010. IEEE Computer Society, 2010. pp. 225-230 (2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010).

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title = "Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input",

abstract = "This work presents exact tracking analysis of the E-normalized least mean square (ε-NLMS) algorithm for circular complex correlated Gaussian input. The analysis is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form [∥ui∥D12][ε+∥u i∥D22]-1. The CDF is then used to derive the first and second moments of these variables. These moments in turn completely characterize the tracking performance of the ε-NLMS algorithm in explicit closed form expressions. Consequently, new explicit closed-form expressions for the steady state tracking excess mean square error and optimum step size are derived. The simulation results of the tracking behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ε.",

keywords = "Adaptive algorithms, Indefinite quadratic forms, Tracking performance",

author = "Muhammad Moinuddin and Al-Naffouri, \{Tareq Y.\} and Sohail, \{Muhammad S.\}",

year = "2010",

doi = "10.1109/ISSPIT.2010.5711782",

language = "English",

isbn = "9781424499908",

series = "2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010",

publisher = "IEEE Computer Society",

pages = "225--230",

booktitle = "2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010",

address = "United States",

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Moinuddin, M, Al-Naffouri, TY & Sohail, MS 2010, Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input. in 2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010., 5711782, 2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010, IEEE Computer Society, pp. 225-230. https://doi.org/10.1109/ISSPIT.2010.5711782

Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input. / Moinuddin, Muhammad; Al-Naffouri, Tareq Y.; Sohail, Muhammad S.
2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010. IEEE Computer Society, 2010. p. 225-230 5711782 (2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input

AU - Moinuddin, Muhammad

AU - Al-Naffouri, Tareq Y.

AU - Sohail, Muhammad S.

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N2 - This work presents exact tracking analysis of the E-normalized least mean square (ε-NLMS) algorithm for circular complex correlated Gaussian input. The analysis is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form [∥ui∥D12][ε+∥u i∥D22]-1. The CDF is then used to derive the first and second moments of these variables. These moments in turn completely characterize the tracking performance of the ε-NLMS algorithm in explicit closed form expressions. Consequently, new explicit closed-form expressions for the steady state tracking excess mean square error and optimum step size are derived. The simulation results of the tracking behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ε.

AB - This work presents exact tracking analysis of the E-normalized least mean square (ε-NLMS) algorithm for circular complex correlated Gaussian input. The analysis is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form [∥ui∥D12][ε+∥u i∥D22]-1. The CDF is then used to derive the first and second moments of these variables. These moments in turn completely characterize the tracking performance of the ε-NLMS algorithm in explicit closed form expressions. Consequently, new explicit closed-form expressions for the steady state tracking excess mean square error and optimum step size are derived. The simulation results of the tracking behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ε.

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KW - Indefinite quadratic forms

KW - Tracking performance

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T3 - 2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010

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Moinuddin M, Al-Naffouri TY, Sohail MS. Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input. In 2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010. IEEE Computer Society. 2010. p. 225-230. 5711782. (2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010). doi: 10.1109/ISSPIT.2010.5711782

Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input

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