Multi-user Visible Light Communications with Probabilistic Constellation Shaping and Precoding

TL;DR

This paper introduces a joint probabilistic constellation shaping and precoding method for multi-user visible light communication channels, significantly improving sum-rate performance and robustness under channel uncertainties.

Contribution

It presents a novel joint design framework combining PCS and precoding, including a low-complexity alternating optimization and a robust autoencoder-based approach for VLC systems.

Findings

Achieves up to 19.2% higher sum-rate at 60 dB SNR with 16-PAM.

Demonstrates robustness of the autoencoder-based design under channel uncertainty.

Provides insights into optimal symbol distributions for joint design approaches.

Abstract

This paper proposes a joint design of probabilistic constellation shaping (PCS) and precoding to enhance the sum-rate performance of multi-user visible light communications (VLC) broadcast channels subject to signal amplitude constraint. In the proposed design, the transmission probabilities of bipolar $M$-pulse amplitude modulation ($M$-PAM) symbols for each user and the transmit precoding matrix are jointly optimized to improve the sum-rate performance. The joint design problem is shown to be a complex multivariate non-convex problem due to the non-convexity of the objective function. To tackle the original non-convex optimization problem, the firefly algorithm (FA), a nature-inspired heuristic optimization approach, is employed to solve a local optima. The FA-based approach, however, suffers from high computational complexity. Thus, using zero-forcing (ZF) precoding, we propose a low-complexity design, which is solved using an alternating optimization approach. Additionally, considering the channel uncertainty, a robust design based on the concept of end-to-end learning with autoencoder (AE) is also presented. Simulation results reveal that the proposed joint design with PCS significantly improves the sum-rate performance compared to the conventional design with uniform signaling. For instance, the joint design achieves $\mathbf{17.5\%}$ and $\mathbf{19.2\%}$ higher sum-rate for 8-PAM and 16-PAM, respectively, at 60 dB peak amplitude-to-noise ratio. Some insights into the optimal symbol distributions of the two joint design approaches are also provided. Furthermore, our results show the advantage of the proposed robust design over the non-robust one under uncertain channel conditions.