Time-domain equalisation for discrete multi-tone transceivers: new results and performance analysis

The time-domain equaliser (TEQ) is a commonly used device to shorten the channel impulse response in a discrete multitone (DMT) receiver. Many methods have been proposed to design the TEQ with a capacity maximisation criterion. An implicit assumption used by existing methods is that circular convolution can be conducted for the noise signal and the TEQ. This assumption is not valid because the noise vector, observed in a DMT symbol, does not have a cyclic prefix. A similar assumption is also made for the residual inter-symbol interference (ISI) signal. Because of these invalid assumptions, the TEQ-filtered noise and residual ISI powers in each subcarrier were not properly evaluated. As a result, optimum solutions derived are not actually optimal. This paper attempts to resolve this problem. We first analyse the statistical properties of the TEQ-filtered noise signal and the residual ISI signal in detail, and derive precise formulae for the calculation of the TEQ-filtered noise and residual ISI powers. Then, we re-formulate the capacity maximisation criterion to design the true optimum TEQ. Simulations show that the proposed method outperforms the existing ones, and its performance closely approaches the theoretical upper bound.