A closed approximated formed expression for the achievable residual intersymbol interference obtained by blind equalizers

In this paper I propose for the noiseless, real and independent quadrature carrier case a closed approximated formed expression for the achievable residual intersymbol interference (ISI) that depends on the step-size parameter, equalizer's tap length, input signal statistics and channel power. In addition, a new closed formed approximated expression is proposed for the above mentioned case, that indicates if the chosen blind equalization method leads to perfect equalization performance from the residual ISI point of view. This new approximated expression can be a useful tool for equalization performance comparison between blind equalizers. Since the channel power is measurable or can be calculated if the channel coefficients are given, there is no need anymore to carry out any simulation with various step-size parameters in order to reach the required residual ISI. The new approximated expression for the residual ISI is applicable for type of blind equalizers where the error that is fed into the adaptive mechanism which updates the equalizer's taps can be expressed as a polynomial function of the equalized output. It should be pointed out that Godard's algorithm for example, belongs to the mentioned type of blind equalizers.