Ill-Convergence of Godard Blind Equalizers in Data Communication Systems

Godard algorithms form an important class of adaptive blind channel equalization algorithms for QAM transmission. In this paper, the existence of stable undesirable equilibria for the Godard algorithms is demonstrated through a simple AR channel model. These undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function, and thus permit the ill-convergence of the Godard algorithms which are stochastic gradient descent in nature. Simulation results confirm predicted misbehavior. For channel input of constant modulus, it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization. A criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached.