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

TL;DR

The paper addresses sum-rate maximization in multi-user VLC when peak amplitude constraints are present by jointly optimizing probabilistic constellation shaping (PCS) and precoding. It proposes two suboptimal routes—a Firefly Algorithm (FA) for a general PCS+precoding design and a low-complexity alternating-optimization (AO) scheme with Zero-Forcing (ZF) precoding—along with a robust end-to-end autoencoder (AE) approach to cope with channel uncertainty. Results show meaningful gains over uniform signaling (e.g., about 0.4 bits/s/Hz at A/σ = 60 dB for 8- and 16-PAM) and demonstrate the robustness of the AE design under CSI errors, with FA often delivering better performance at the cost of higher computation. The work highlights the practical viability of PCS in MU-VLC and offers a robust learning-based pathway to handle real-world channel variations.

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.

Figures (10)

• Figure 1: Multi-user VLC system with precoding and PCS.
• Figure 2: End-to-end system architecture.
• Figure 3: Maximal sum-rate versus $A/\sigma$.
• Figure 4: Optimal symbol distributions and comparison of user’s achievable rate with different schemes and $A/\sigma$ values.
• Figure 5: Sum-rate versus the number of users with 9 LED layout, PCS 4-PAM and $A / \sigma = 60$ dB.