Objective Visible light communication (VLC), as a novel wireless communication type, seamlessly combines illumination and data transmission. It has drawn significant attention as a promising solution for indoor wireless communication because of its advantages such as license-free deployment, high data-rate capabilities, and lack of electromagnetic interference. VLC usually uses light-emitting diodes (LEDs) as transmitters and photodiodes (PDs) as receivers. In recent years, with the rapid development and wide application of LEDs, VLC has attracted extensive attention from many scholars. Phosphor-converted LEDs (pc-LEDs) and multi-color LEDs (mc-LEDs) are two typical types of LEDs used in VLC. The pc-LEDs have a competitive price and a large market share. However, their inherent modulation bandwidth is limited to the MHz range. Compared with pc-LEDs, mc-LEDs generate white light by mixing light from different LED chips and can provide higher modulation bandwidth and multiple sub-channels. Recently, multi-color VLC has been applied in various important fields like integrated sensing and communication and indoor localization. Therefore, it is essential to study transmission techniques for multi-color VLC. Existing transmission techniques for multi-color VLC systems use PDs with monochromatic filters to separate optical signals from LED chips of different colors. However, due to the limited adaptability of PDs with monochromatic filters to different light colors, it is usually necessary to use multiple PDs to receive optical signals of different colors. Moreover, the cost of PDs with monochromatic filters is also higher. Therefore, it is necessary to study the application of a regular PD without filters in multi-color VLC. Methods To simplify the communication process, VLC usually adopts intensity modulation and direct detection (IM/DD) for communication, with transmitted signals modulated on the optical intensity. Therefore, in VLC systems, the optical intensity signal should be nonnegative and its power is directly proportional to the optical intensity, which is different from conventional radio frequency (RF) communication. Based on the above practical requirements in multi-color VLC systems and the results on multi-input single-output (MISO) optical intensity channels with per-antenna power constraints, we propose an optimal constellation design based on the equivalent transmitted signal for indoor multi-color VLC. The receiver in the system uses a regular PD without monochromatic filters. First, we determine the normalized average power of each chip in the mc-LED by minimizing the total optical power while considering constraints on chromaticity, brightness, and optical intensity signals. Then, we model the system as a MISO VLC system with per-antenna power constraints. By maximizing the minimum Euclidean distance (MED) of the equiprobable equally-spaced amplitude shift keying (ASK) equivalent transmitted signal constellation and using partition-based decomposition (PBD) to decompose the equivalent transmitted signal into the transmitted signals of each LED chip, we finally obtain the optimal constellation design. Results and Discussions In this study, we simulate an indoor VLC system composed of a mc-LED and a regular PD without monochromatic filters. The transmitter used in the simulation is the Cree Xlamp MC-E RGB LED, and the receiver used is the HAMAMATSU S2386 silicon PD. The normalized channel gain of each chip is calculated using the Lambertian model [Eq. (2)]. We provide the parameters of different LED chips (Table 2) and the configuration parameters of the Lambertian model (Table 3). Also, we provide the center chromaticity coordinates and the corner coordinates of quadrangles corresponding to different correlated color temperature (CCT) values (Table 4). First, we show the optical power of the mc-LED and each chip within it under different CCT values and total luminous fluxes (Fig. 5). As shown in Fig. 5, the total optical power remains relatively constant across different CCT values under the same luminous flux. Moreover, an increase in CCT values leads to an increase in the green and blue light components, while a decrease is observed in the red light component. Then, we provide the bit error rate (BER) curves for both the proposed ASK-PBD scheme and the optimal precoding-based transmission schemes under different CCT values and total luminous fluxes (Fig. 6). As shown in Fig. 6, the proposed ASK-PBD scheme has better error performance than the optimal precoding scheme under the same conditions. Conclusions In this study, we propose an optimal constellation design based on the equiprobable equally-spaced ASK equivalent transmitted signal for the indoor multi-color VLC system. The system configuration consists of an mc-LED as the transmitter and a regular PD without monochromatic filters as the receiver. We determine the normalized average power by minimizing the total optical power while considering constraints on chromaticity, brightness, and optical intensity signal. Then, we model the system as an indoor MISO VLC system with per-antenna power constraints. Using the normalized average power and channel gain of each LED chip, we determine the optimal interval for the ASK equivalent transmitted signal. Furthermore, we decompose the equivalent transmitted signal into the transmitted signals using partition-based decomposition to obtain the optimal constellation. Simulation results of an indoor multi-color VLC system show that our proposed scheme has better error performance than the benchmark scheme under the same conditions. In conclusion, the proposed optimal constellation design is a promising alternative for multi-color VLC systems due to its cost-effectiveness and adaptability to different light wavelengths.
