On globally convergent blind equalization for QAM systems

A globally convergent blind equalization algorithm for QAM systems based on the minimization of a linearly-constrained convex function of the equalizer output is presented. Geometric methods are employed to establish a framework in which a proof of global convergence readily follows. The analysis assumes an arbitary linear constraint on the equalizer parameters and an arbitrary QAM constellation with minor assumptions on its distributional properties. Minimization is shown to occur either uniquely in the generic case or non-uniquely on a compact set in the equalizer parameter space that contains at least one open-eye solution. The framework also provides insight into the case of non-unique minimization and serves as a basis for strategies to avoid such behaviour