Blind equalization for QAM systems based on general linearly constrained convex cost functions

Most blind QAM equalization algorithms base their parameter adaptation on the minimization of nonconvex cost functions. These cost functions may exhibit local minima which can cause undesirable convergence to equalizer parameter settings, resulting in insufficient removal of the intersymbol interference In contrast, this work considers the minimization of a special convex cost function of the equalizer output in combination with an arbitrary non-degenerate linear constraint. We establish the property that the cost minimization in the space of the equalizer parameters is achieved on a compact set that contains at least one ideal zero-ISI equalizer parameter setting. Generically this compact set consists of a single point reflecting an ideal global convergence result, implying zero intersymbol interference. Further, through general abstract methods we demonstrate that this desirable convergence property is largely independent of the input constellation geometry and independent of the linear constraint chosen. The methods are developed for and motivated by the important classes of QAM constellations used in practice.