Application of time-series algebra to the adaptive equalisation of band-limited waveform-transmission systems

Using time-series algebra, the operation of adaptive equalisers for both minimum-mean-signal-error and minimum-mean-square-error criteria are considered, and the convergence properties of the iterative procedures generally used are discussed. It is pointed out that, in any practical situation, the control criterion and the iterative algorithm to be used, must be selected to provide the desired performance over the range of situations likely to be encountered. The effect of the equaliser on the regenerator-input signal/noise ratio is also considered, and this, together with the economic need to minimise the equaliser length, is shown to lead to a requirement to select the reference sampling point accordingly. One selection algorithm is described, and its operation is demonstrated in an example.