Signaling constellations for fading channels

The performances of various coherent 8-ary and 16-ary modulations in additi ve white Gaussian noise (AWGN) and slowly fading channels are analyzed. New expressions for the exact symbol error rates (SER) in fading with diversit y combining are derived for any two-dimensional signaling format having pol ygonal decision boundaries. Maximal ratio combining, equal gain combining, and selection combining are considered. The SER formulas obtained make it p ossible for the first time to optimize parameters of various constellations precisely and to determine which constellation has the lowest probability of error. For example, a star constellation such as that specified in the C CITT V.29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0.63 dB power in AWGN without sa crificing the phase error tolerance, while maintaining the same error rate. The sensitivity of each constellation to phase error is presented and comp arisons are made. Six 8-ary signal sets and 11 16-ary signal sets are exami ned using the new symbol error probability formulas to determine best signa l sets for fading channels.