Convergence and Steady-State Behavior of a Hybrid Decision Feedback Equalizer

Kyu-Min KANG  Gi-Hong IM  

IEICE TRANSACTIONS on Communications   Vol.E85-B   No.12   pp.2764-2775
Publication Date: 2002/12/01
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Fundamental Theories
hybrid-type decision feedback equalizer,  phase-splitting equalizer,  LMS algorithm,  excess mean-square error (MSE),  xDSL environment,  

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In this paper, we analyze the convergence and steady-state behavior of the least mean-square (LMS) adaptive filtering algorithm for a finite-length phase-splitting hybrid-type decision feedback equalizer (H-DFE). With some approximations, we derive an iterative expression for the excess mean-square error (MSE) of the H-DFE, which is composed of three statistically dependent excess MSEs; that is, the excess MSEs of the feedforward filter (FFF), intersymbol interference predictive feedback filter (ISI-FBF), and noise predictive feedback filter (NP-FBF) taps. Computer simulation and analytical results show that the average eigenvalue of the input signal for the NP-FBF taps of the H-DFE is time-varying, whereas those for the FFF and ISI-FBF taps are fixed. Nevertheless, the H-DFE can be implemented with fixed step sizes that ensure the convergence of the LMS algorithm without performance degradation from the standpoint of convergence speed, as well as steady-state performance for digital subscriber line (xDSL) applications.