Optimizing Constellations for Noncoherent Optical Communication Systems

We optimize modulation formats for the additive white Gaussian noise channel with a nonnegative input constraint, also known as the intensity-modulated direct-detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical, average optical, and peak power. The nonnegativity input signal constraint is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some remarkably dense packings are found, which yield more power-efficient modulation formats than previously known. For example, at a spectral efficiency of 1.5 bit/s/Hz, the modulation format optimized for average electrical power has a 2.55 dB average electrical power gain over the best known format to achieve a symbol error rate of 10−6. The corresponding gains for average and peak optical power are 1.35 and 1.72 dB, respectively. The penalty of using modulation formats optimized for peak power in systems which are average-power limited is less than vice versa. We also evaluate the modulation formats in terms of their mutual information to predict their performance in the presence of capacity-achieving error-correcting codes, and finally show numerically and analytically that the optimal modulation formats for reliable transmission in the wideband regime have only one nonzero point.