Third-order blind equalization properties of hexagonal constellations

Many digital communications systems use symbol constellations such as M-ary PAM, PSK, or QAM, which are simple to implement and symmetric. In a blind setting, equalization of intersymbol interference (ISI) caused by a linear channel with unknown phase characteristics requires baud-sampled statistics of at least fourth order. Disadvantages of fourth-order statistical approaches are the relatively large sample sizes needed for good estimates of the statistics and the high computational complexity of the associated equalization algorithms. Here we examine several inherently asymmetric constellations with symbols placed on a hexagonal lattice rather than on the square lattice of QAM-type constellations. These constellations have a smaller average power under minimum symbol separation constraints than several widely-used constellations. We show how to modify the constellations to provide controllable third-order properties, and demonstrate blind equalization using a low-complexity third-order algorithm