CONSTELLATION SHAPING FOR WIRELESS OPTICAL INTENSITY CHANNELS

Abstract

As the demand for high-speed, power-efficient optical communication systems continues to grow, constellation shaping has emerged as a key technique for improving spectral efficiency or transmission reliability. This thesis investigates the application of constellation shaping in indoor visible light communication systems operating in high signal-to-noise ratio (SNR) regimes and employing intensity modulation/direct detection (IM/DD) optical channels, which provide a cost-effective alternative to coherent optical communication. Unlike conventional schemes based on equiprobable signaling, constellation shaping modifies the probability distribution of transmitted symbols to reduce the average transmission power and approach channel capacity while maintaining a fixed data rate.

Two primary approaches for approaching the channel capacity are investigated: geometric constellation shaping (GCS) and probabilistic constellation shaping (PCS). GCS involves selecting signal points from a multidimensional lattice code while confining them within an optimal shaping region, thereby inducing a Maxwell–Boltzmann (MB) distribution, which maximizes entropy under non-negativity and average power constraints. In contrast, PCS directly assigns the MB distribution to a lower-dimensional constellation. Theoretical analysis demonstrates that both approaches achieve the same ultimate shaping gain at the expense of an increased constellation expansion ratio (CER) and peak-to-average power ratio (PAPR), thereby validating their effectiveness for IM/DD optical channels.

This thesis extends prior work by generalizing the dimensionality of the constituent constellations. Although increasing the dimensionality introduces a trade-off that enables higher data rates at the expense of reduced shaping gain, an analytical framework is developed to evaluate these trade-offs in practical IM/DD systems. In addition, shaping codes originally developed for coherent optical systems, such as constant composition distribution matching (CCDM) and enumerative sphere shaping (ESS), are adapted to the constraints of IM/DD channels. In particular, enumerative cone shaping (ECS), which is a modification of ESS tailored to IM/DD channels, is fully implemented for both one-dimensional PAM constellations and three-dimensional raised-QAM constellations, achieving approximately 92\% and 89\% of the theoretical shaping gain, respectively. By contrast, CCDM is formulated analytically without a full implementation.

The results of this thesis provide valuable insights for the design of band-limited indoor optical wireless communication systems, particularly visible light communication (VLC) systems, which represent a promising complementary solution to traditional radio-frequency (RF) systems in addressing the growing global demand for higher data rates.