## 3 ACDM-Based VLP System by Using OPRC
### Simulation and Experimental Results  
We begin by assessing the PCCF and PACF values of the OPRC codes \(\mathbf{S_{1}}\) and \(\mathbf{S_{2}}\) under different code chip offsets, as illustrated in Figure 3. It can be observed that the employed OPRC exhibits zero-valued PCCF and multiple-valued PACF characteristics, which are crucial for maintaining the orthogonality of VLP signals during asynchronous transmission. Next, we execute a series of simulations and experiments to test the VLP performance based on OPRC using \(\mathbf{S_{1}}\) and \(\mathbf{S_{2}}\). The tests are categorized into three groups. Specifically, in Groups 1 and 2, we activate transmitters \(Tx_{1}\) and \(Tx_{2}\) separately to analyze the received signal characteristics from individual sources. For Group 3, we successively activate \(Tx_{1}\) and \(Tx_{2}\) to evaluate the performance of the OPRC-VLP scheme under asynchronous transmission. The RSS measurements for \(Tx_{1}\) and \(Tx_{2}\) at various locations are recorded, and the outcomes are depicted in Figure 4. Here, the \"Group3-\(Tx_{1}\)\" and \"Group3-\(Tx_{2}\)\" curves represent the RSS fluctuations for each transmitter at different measurement points during the Group 3 test. From Figure 4, we observe discrepancies between the normalized RSS obtained from simulations and experiments. Both setups use LED lamps with power parameters set at 3 W. However, in the actual experiment, the power of \(Tx_{1}\) slightly exceeds 3 W due to variations in LED quality, while the power of \(Tx_{2}\) is slightly below 3 W. This leads to slightly higher normalized RSS measurements for \(Tx_{1}\) and slightly lower ones for \(Tx_{2}\) compared to the simulation results. Additionally, the ideal Lambertian model does not perfectly match the real radiation of the LEDs, and human measurement errors during the experiment may have exacerbated the numerical differences between simulation and experimental results. Despite these discrepancies, the overall trends remain consistent: both the simulated and measured normalized RSS values peak near \(\pm\)13.5 cm, close to the LED positions, and then gradually decrease on either side. Notably, our comparative analysis demonstrates that, despite asynchronous signal transmission in the Group 3 test, we can accurately extract the RSS of \(Tx_{1}\) and \(Tx_{2}\) from the composite VLP signal in both simulation and experiment. The measurements closely match the single-source tests in Groups 1 and 2, thus strongly supporting the capability of the OPRC-VLP strategy to efficiently differentiate and precisely extract the VLP signals of individual LED transmitters during signal superposition and asynchronous transmission. Figure 3: Correlation values at different chip shifts for (a) \(\mathbf{S_{1}}\); and (b) \(\mathbf{S_{2}}\). After determining the RSS of each LED, we further calculate the corresponding signal transmission distances using Equation (13). However, due to inherent noise, the measured distances inevitably diverge from theoretical expectations. To quantify this discrepancy, we introduce the signal transmission distance error (STDE), defined as the absolute value of the difference between measured and theoretical distances. Figure 5a,b illustrates the STDE distributions across various measurement points for the three test groups. Owing to the perfect correlation properties of the OPRC, the STED measurements for \(Tx_{1}\) and \(Tx_{2}\) in Group 3 align closely with the individual test results from Group 1 and Group 2. This consistency confirms the results observed in the RSS patterns. Importantly, in areas close to the LEDs where the RSS is higher, the noise effect diminishes, leading to reduced STDE values. Additionally, given \(Tx_{1}\)'s higher luminous intensity compared to \(Tx_{2}\), the STDE for \(Tx_{1}\) is generally smaller. This observation further confirms the negative correlation between signal strength and measurement error. Based on the estimated signal transmission distances, Figure 5c illustrates the distribution of positioning errors.