An approach to blind equalization of non-minimum phase systems

Blind equalization of systems which contain a nonminimum phase component is a difficult task. Minimizing the energy (l₂ minimization) of the equalizer output (under a fixed tap constraint) cannot be guaranteed to open the eye (to reliably unscramble the message) because it tends to converge to an equalizer setting that contains a reflection of the unstable zeros inside the unit circle. It is shown that, in at least one simple setup involving a mixture of minimum and nonminimum phase elements, an l_∞ minimization of the equalizer output is the appropriate criterion which should be minimized in order to successfully open the eye. Utilizing a finite impulse response equalizer constrained to have a unity coefficient on the center tap, it is shown that for a large enough dimension (depending on the closeness of the zeros of the channel to the unit circle) the eye will be opened. There is no simple (gradient) scheme to exactly implement the l_∞ minimization. The use of a gradient l_p scheme for large p is proposed