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

Pseudo-random sequences have been used in the past as training signals for setting up automatic transversal equalizers during start-up periods. 1,2 For fast start-up, it is desirable to know how the equalizer settling time depends on the choice of the pseudo-random sequence, the channel characteristics, and the initial receiver conditions. These problems are examined in the first part of this paper for single-sideband Nyquist systems. We present basic theories from which the reader 2013 2014 T H E BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1972 can work out numerical examples of special interest. The results are compared with those obtained previously 3 for a different class of training signals (isolated test pulses). An important difference between these two cases is pointed out. When pseudo-random sequences are used, it is most convenient to adjust the equalizer tap gains to minimize the mean-square error between the equalizer output and the transmitted pseudo-random sequence. It is not immediately clear how closely this simple algorithm optimizes the data set performance for transmission of random data (because an equalizer setting optimum for pseudo-random sequence transmission is not necessarily optimum for random data transmission, particularly when pseudo-random sequences with very short periods are used for fast start-up purpose). This problem is examined in Section IV and the analysis is illustrated by examples. Section V summarizes the results of this paper. The reader mainly interested in the conclusions and their implications may read Section V next.