High-order optimum hexagonal constellations
C.D. Murphy · 2002
Bandwidth-limited high-rate digital communications systems use large constellations such as M-ary QAM, M/spl isin/{64, 128, 256, 512, 1024}. These square or cross-shaped constellations, though easy to implement, do not pack the symbols together as efficiently as possible, and besides are symmetric when the symbols are equiprobable and independent, so that no channel information is available from blind third-order statistics of the channel outputs. We develop high-order "optimum" hexagonal constellations, some of which are naturally asymmetric, and all of which can be modified to be asymmetric without exceeding the peak and average power levels of the corresponding M-ary QAM constellations.