Optimizing Constellations for Single-Subcarrier Intensity-Modulated Optical Systems

TL;DR

This paper develops optimized modulation formats for intensity-modulated direct-detection optical channels, achieving significant power efficiency improvements through sphere packing within a conical signal space constraint.

Contribution

It introduces a novel sphere packing approach in conical signal space for designing power-efficient modulation formats for optical systems, surpassing previous methods.

Findings

Achieved up to 2.55 dB power gain at 1.5 bit/s/Hz.

Dense packings outperform known formats in power efficiency.

Optimal wideband modulation has only one nonzero point.

Abstract

We optimize modulation formats for the additive white Gaussian noise channel with nonnegative input, 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 nonnegative constraint on the input to the channel is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some 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 formats optimized for average and peak optical power are 1.35 and 1.72 dB, respectively. Using modulation formats optimized for peak power in average-power limited systems results in a smaller power penalty than when using formats optimized for average power in peak-power limited systems. 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.