Iterative Refinement Methods for Time-Domain Equalizer Design
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Iterative Refinement Methods for Time-Domain Equalizer Design ¨ Guner Arslan,1 Biao Lu,2 Lloyd D. Clark,3, 4 and Brian L. Evans5 1 Silicon
Laboratories, Corporate Headquarters, 7000 West William Cannon Drive, Austin, TX 78735, USA Sugar Land Product Center, 110 Schlumberger Drive, Sugar Land, TX 77478, USA 3 Schlumberger Austin Systems Center, 8311 N FM 620 Road, Austin, TX 78726, USA 4 TICOM Geomatics, 9130 Jollyville Road, Austin, TX 78759, USA 5 Department of Electrical and Computer Engineering, The University of Texas, Austin, TX 78712-1084, USA 2 Schlumberger
Received 1 December 2004; Revised 23 May 2005; Accepted 2 August 2005 Commonly used time domain equalizer (TEQ) design methods have been recently unified as an optimization problem involving an objective function in the form of a Rayleigh quotient. The direct generalized eigenvalue solution relies on matrix decompositions. To reduce implementation complexity, we propose an iterative refinement approach in which the TEQ length starts at two taps and increases by one tap at each iteration. Each iteration involves matrix-vector multiplications and vector additions with 2 × 2 matrices and two-element vectors. At each iteration, the optimization of the objective function either improves or the approach terminates. The iterative refinement approach provides a range of communication performance versus implementation complexity tradeoffs for any TEQ method that fits the Rayleigh quotient framework. We apply the proposed approach to three such TEQ design methods: maximum shortening signal-to-noise ratio, minimum intersymbol interference, and minimum delay spread. Copyright © 2006 G¨uner Arslan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Multicarrier modulation is a widely used modulation method for reliable high-speed communication. Discrete multitone (DMT) modulation is a popular variant of multicarrier modulation that has been standardized for asymmetric and very high-speed digital subscriber loops (ADSL and VDSL, resp.) [1]. In these applications, a guard sequence known as the cyclic prefix is prepended to each symbol to help the receiver eliminate intersymbol interference (ISI) and perform symbol recovery. A DMT symbol consists of N samples, and the cyclic prefix is a copy of the last ν samples of the symbol. The length of the channel impulse response has to be less than or equal to (ν + 1) samples in order for all ISI to be eliminated. Using a cyclic prefix, however, reduces the channel throughput of a DMT transceiver by a factor of ν/(N + ν). Therefore, it is desirable to choose ν as small as possible. The ADSL and VDSL standards set ν to be N/16. In the field, however, ADSL and VDSL channel impulse responses can exceed N/16 samples. It is up to the equalizer in the receiver to shorten the channel impulse response and to correct for frequency distortion in the short
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