Three-Dimensional Modulation Formats with Constant Power for Optical Communications

In this paper, a new method of constructing three-dimensional modulation formats with constant power is introduced. Constellations designed by the method have slightly larger minimum Euclidean distances (MEDs) than the conventional ones. No repetitive algorithm to maximize MED is used so that the new method has little computational complexity. Since signal points in the new formats are distributed regularly and symmetrically, an error control coding with systematic set-partition is applicable. We also present theoretical symbol error probability (SEP) of the new constellations in an additive white Gaussian noise environment, and demonstrate that the theoretical results are accurate. As the new modulation formats have almost the same or slightly lower SEPs than the conventional ones, they are appropriate for implementing a highly reliable optical communication system.