Multidimensional Constellation Design Based on Geometric Shaping for MISO VLC With Per-LED Optical Power Constraints

Visible light communication (VLC) integrates illumination and communication, offering significant potential for 6G mobile communications. In 6G communications, reliability and low latency are critical. To meet these demands, finite blocklength codewords are employed for data transmission. For indoor VLC scenarios, multiple light-emitting diodes (LEDs) serve as transmitters, with each transmitter operating under distinct optical power constraints tailored to user requirements. In this paper, a multidimensional constellation design based on geometric shaping is proposed for multi-input single-output (MISO) VLC with per-LED optical power constraints. This design employs truncated cubic shaping to design the equivalent transmitted signal and decomposes it into transmitted signals using a partition-based greedy decomposition. The proposed scheme designs signals in the finite blocklength regime while adhering to per-LED optical power constraints. Simulation results for indoor MISO VLC systems demonstrate the advantages of the proposed scheme over benchmark schemes and quantify the performance gains as well as the gap to the Shannon limit.