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

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 (US)
Title of host publication	2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010
Pages	225-230
Number of pages	6
DOIs	https://doi.org/10.1109/ISSPIT.2010.5711782
State	Published - 2011
Externally published	Yes
Event	10th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010 - Luxor, Egypt Duration: Dec 15 2010 → Dec 18 2010

Other

Other	10th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010
Country/Territory	Egypt
City	Luxor
Period	12/15/10 → 12/18/10

Keywords

Adaptive algorithms
Indefinite quadratic forms
Tracking performance

ASJC Scopus subject areas

Information Systems
Signal Processing

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10.1109/ISSPIT.2010.5711782

Cite this

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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 = "2011",

doi = "10.1109/ISSPIT.2010.5711782",

language = "English (US)",

isbn = "9781424499908",

pages = "225--230",

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

note = "10th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010 ; Conference date: 15-12-2010 Through 18-12-2010",

}

Moinuddin, M, Al-Naffouri, TY & Sohail, MS 2011, 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, pp. 225-230, 10th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010, Luxor, Egypt, 12/15/10. 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. 2011. p. 225-230 5711782.

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.

PY - 2011

Y1 - 2011

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.

KW - Adaptive algorithms

KW - Indefinite quadratic forms

KW - Tracking performance

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U2 - 10.1109/ISSPIT.2010.5711782

DO - 10.1109/ISSPIT.2010.5711782

M3 - Conference contribution

SN - 9781424499908

SP - 225

EP - 230

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

T2 - 10th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010

Y2 - 15 December 2010 through 18 December 2010

ER -

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

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Keywords

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