Block noncoherent detection of hexagonal QAM

We consider block noncoherent detection of hexagonal quadrature amplitude modulation (QAM). We focus on hexagonal constellations generated from a Voronoi code. We find that these constellations are particularly well suited to noncoherent detection because they avoid most of the identifiability problems that occur with more traditional constellations. We describe a fast, approximate, noncoherent detection algorithm with statistical performance that is almost indistinguishable from an optimal, brute force approach, but with significantly smaller computational requirements. The performance is close to that of coherent detection when the block length is sufficiently large.