This dissertation was presented to the Faculty of the Graduate School of The University of Texas at Austin in partial fulfillment of the requirements for the degree of

Ph.D. in Electrical Engineering

G.DMT and G.lite Asymmetric Digital Subscriber Line (ADSL) modems and some Very-high-speed Digital Subscriber Line (VDSL) modems rely on discrete multitone modulation (DMT). In an ADSL discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Previous TEQ design methods such as minimum mean-squared error (MMSE), maximum shortening signal-to-noise ratio (MSSNR), and maximum geometric signal-to-noise ratio (MGSNR) do not directly optimize channel capacity.

In this dissertation, I develop a TEQ design method to optimize channel capacity at the output of the TEQ. First, I partition an equalized multicarrier channel into its equivalent signal, noise, and ISI paths to develop a new subchannel signal-to-noise (SNR) definition. Using the new subchannel SNR definition, I derive a nonlinear function of TEQ taps that measures channel capacity. Based on the nonlinear function, I propose the optimal maximum-channel-capacity (MCC) TEQ that achieves 99.87% of the matched filter bound on ADSL channel capacity with a 17-tap equalizer. I also derive a computationally-efficient, near-optimal minimum-ISI (min-ISI) method that generalizes the MSSNR method by weighting the ISI in the frequency domain.

The frequency domain weighting increases computational complexity for higher bit rate. Based on simulations using eight different carrier-serving-area ADSL channels, (1) the proposed methods yield higher bit rates than the MMSE, MSSNR, and MGSNR methods; (2) two-tap TEQs designed with the proposed methods yield higher bit rates than 17-tap MMSE and geometric TEQs; and (3) the min-ISI method achieves 99.99% of the bit rate of the optimal MCC method.

Most state-of-the-art ADSL transceivers use MMSE-based algorithms to design TEQs of 17-32 taps. The min-ISI TEQ gives better performance with a smaller TEQ. For example, a two-tap min-ISI TEQ requires 4 DSP MIPS and outperforms a 20-tap MMSE TEQ which requires 40 DSP MIPS. This reduction in complexity would eliminate the need for hardware acceleration for the TEQ in an ADSL transceiver.