The Tap-Length Associated with the Blind Adaptive Equalization/Deconvolution Problem

Abstract

The step-size parameter and the equalizer’s tap length are the system parameters in the blind adaptive equalization design. Choosing a large step-size parameter causes the equalizer to converge faster compared with applying a smaller value for the step size parameter. However, a higher step-size parameter leaves the system with a higher residual inter-symbol-interference (ISI) than does a lower step-size parameter. The equalizer’s tap length should be set large enough to compensate for the channel distortions. However, since the channel parameters are unknown, the required equalizer’s tap length is also unknown. The system parameters are usually designed via simulation trials, in such a way that the equalizer’s performance from the residual ISI point of view reaches a system desired residual ISI level. Recently, a closed-form approximated expression was derived for the residual ISI as a function of the system parameters, input sequence statistics and channel power. This expression was obtained under the assumption having a value for the equalizer’s tap length that is sufficient to compensate for the channel distortions. Based on this approximated expression, the outcome from the step-size parameter multiplied by the equalizer’s tap length can be derived when the residual ISI is given. By choosing a step-size parameter, we automatically have also the value for the equalizer’s tap length which might now not be large enough to compensate for the channel distortions and thus leaving the system with a higher residual ISI than the required one. In this work, we derive an expression that sets a condition on the equalizer’s tap length based on the input sequence statistics, on the chosen equalizer’s characteristics and required residual ISI. In addition, highlights are supplied on how to set the equalizer’s tap length for different channel cases based on this new derived expression. The findings are accompanied by simulation results.