By choosing a particular equalizer it is useful to know in advance if the chosen
equalizer leads to perfect equalization performance. In this chapter, we explain
how we can know without carrying out any simulation, if the chosen equalizer
leads to perfect equalization performance for the real valued and two independent
quadrature carrier case. We derive in this chapter for the real valued and two
independent quadrature carrier case, some conditions on the input constellation
statistics for which perfect equalization performance is obtained for type of blind
equalizers where the error that is fed into the adaptive mechanism which updates
the equalizer's taps is expressed as a polynomial function of order three. We show
also that perfect equalization performance can not be obtained for type of blind
equalizers where the error that is fed into the adaptive mechanism which updates
the equalizer's taps is expressed as a polynomial function of order three, when
dealing with the noiseless and 16QAM constellation input case.
Keywords: Blind deconvolution, perfect equalization, intersymbol interference (ISI), convolu-
tional noise, convolutional noise power, residual ISI, step-size parameter, equalizer's
tap-length, mean square error (MSE), polynomial function of order three
