Joint Design of Probabilistic Constellation Shaping and Precoding for Multi-user VLC Systems

TL;DR

This paper tackles sum-rate maximization for multi-user VLC broadcast channels under LED peak constraints by jointly optimizing probabilistic constellation shaping and precoding. It introduces two methods: a Firefly algorithm to search jointly over PCS distributions and the precoding matrix, and a low-complexity alternating-optimization scheme using zero-forcing precoding. Results show substantial gains over uniform signaling and reveal how optimal symbol probabilities evolve with SNR, providing practical guidance on shaping and precoding in indoor VLC. The work demonstrates a viable path to boosting indoor VLC throughput by exploiting both probabilistic shaping and spatial degrees of freedom with manageable complexity tradeoffs.

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 non-convex problem due to the non-convexity of the objective function. To tackle the problem, the firefly algorithm (FA), a nature-inspired heuristic optimization approach, is employed to solve a local optima to the original non-convex optimization problem. The FA-based approach, however, suffers from high computational complexity. Therefore, we propose a low-complexity design based on zero-forcing (ZF) precoding, which is solved using an alternating optimization (AO) approach. Simulation results reveal that the proposed joint design with PCS significantly improves the sum-rate performance compared to the conventional design with uniform signaling. Some insights into the optimal symbol distributions of the two joint design approaches are also provided.

Figures (4)

• Figure 1: Schematic diagram of a multi-user VLC system with precoding and PCS.
• Figure 2: Maximal sum rate versus $A / \sigma$.
• Figure 3: Optimal symbol distributions of PCS 8-PAM with different $A / \sigma$.
• Figure 4: Convergence behaviors of FA and AO approach with PCS 16-PAM and $A / \sigma = 70$ dB.