An approximated expression for the convergence time of adaptive blind equalizers

In this paper, closed-form approximated expressions are proposed for the convergence time (or number of iterations required for convergence) and for the Intersymbol Interference (ISI) as a function of time valid during the stages of the iterative deconvolution process. The new derivations are valid for the noiseless, real and two independent quadrature carrier case and 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 order three of the equalized output like in Godard's algorithm. Up to now, the equalizer's performance (convergence time and ISI as a function of time) could be obtained only via simulation when the channel coefficients were known. The new proposed expressions are based on the knowledge of the initial ISI and channel power (which is measurable) and eliminate the need to carry out any more the above mentioned simulation.