On Fast Start-Up Data Communication Systems Using Pseudo-Random Training Sequences

Abstract

This paper analyzes the start-up performance of automatic transversal equalizers when maximum-length pseudo-random sequences of short periods are selected as the training signals for fast start-up purposes. Single-sideband Nyquist systems are considered because they represent the limiting case of vestigial-sideband systems with small excess bandwidth. It is shown that the equalizer is capable of fast start-up except in some rare situations which can be avoided by using proper timing, phase, and equalizer initial settings. The results also show that the equalizer tap convergence rate is independent of the phase characteristic of the communication channel and of the choice of the pseudo-random sequences which have the same period. The equalizer is set up in the training period by minimizing the mean-square error between the equalizer output and the transmitted pseudo-random sequence, which is different from the mean-square error for random data. Surprisingly, we have found that, even for pseudo-random sequences of very short periods, this start-up algorithm results in only a slight degradation in system performance. Accordingly, good system performance can be expected immediately after the system switches from the training mode to the data mode.