A Closed-Form Approximated Expression for the Residual ISI Obtained by Blind Adaptive Equalizers with Gain Equal or Less than One

In this paper we propose for the real and two independent quadrature carrier cases, a closed-form approximated expression for the achievable residual Inter-Symbol Interference (ISI). The expression depends on the step-size parameter, equalizer’s tap length, equalized output gain, input signal statistics, channel power and SNR. This expression is valid for blind adaptive equalizers where the error fed into the adaptive mechanism, which updates the equalizer‘s taps, can be expressed as a polynomial function of order three of the equalized output, and where the gain between the input and equalized output signal is less than, or equal to one, as in the case of Godard (gain= 1) and WNEW (gain < 1) algorithm. Since the channel power is measurable, or can be calculated if the channel coefficients are given, there is no need for simulation with various step-size parameters to reach the required residual ISI. In addition, we show two new equalization methods (gain dependent) which have improved equalization performance compared to Godard and WNEW.