Convergence and steady-state behavior of a hybrid decision feedback equalizer

Abstract

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) [1]. 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.