Frequency domain interpretation of LMS convergence of a fractionally spaced equalizer

Author

Reznic, Zvi ; Johnson, C. Richard, Jr. ; De Victoria, Fernando López

Author_Institution

Sch. of Electr. Eng., Cornell Univ., Ithaca, NY, USA

Volume

3

Issue

7

fYear

1996

fDate

7/1/1996 12:00:00 AM

Firstpage

206

Lastpage

208

Abstract

In this letter, we extend results regarding the behavior of a symbol-spaced tapped-delay-line LMS-adapted equalizer in frequency domain terms to a fractionally spaced implementation. These results rely on an eigendecomposition of the autocorrelation matrix of the received signal. In fractionally spaced equalization systems, the output of the analog channel is oversampled, resulting in a cyclostationary signal. We derive its autocorrelation matrix. A symbol-spaced representation of the combined channel, equalizer and downsampling device is formed in the frequency domain, and the convergence rate of the time-domain LMS algorithm is described in the frequency domain.

Keywords

adaptive equalisers; convergence of numerical methods; correlation methods; delay lines; eigenvalues and eigenfunctions; frequency-domain analysis; least mean squares methods; matrix algebra; signal representation; signal sampling; time-domain analysis; LMS convergence; analog channel; autocorrelation matrix; cyclostationary signal; downsampling device; eigendecomposition; fractionally spaced equalizer; frequency domain interpretation; oversampling; symbol-spaced representation; symbol-spaced tapped-delay-line LMS-adapted equalizer; time-domain LMS algorithm; Autocorrelation; Convergence; Equalizers; Finite impulse response filter; Frequency domain analysis; Least squares approximation; Sampling methods; Time domain analysis; Transfer functions; USA Councils;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/97.508166

Filename

508166