###### Abstract
However, all these approaches are based on the assumption of synchronous CDM (i.e., no time delays among transceivers) [19; 20; 21; 22; 23; 24; 25] or quasi-synchronous CDM (i.e., very slight time delays exist among transceivers) [26]. Ideally, for synchronized CDM systems, the cross-correlation of the orthogonal codewords is zero [27], which guarantees the perfect orthogonality between VLC and VLP signals. However, in practice, LED transmitters are typically controlled independently, leading to asynchronous VLC and VLP signal emissions. Moreover, varying distances between LED transmitters and the receiver result in differing signal propagation times. Therefore, when the CDM-based VLC and VLP signals emitted from different LED transmitters arrive at the receiver, time delays always exist among CDM transceivers. These time delays are non-negligible as compared with the chip length of a CDM codeword, leading to the scenario of asynchronous CDM (ACDM). For ACDM signals, the cross-correlation of the orthogonal codewords increases due to the chip shift, which deteriorates the orthogonality between VLC and VLP signals. This causes severe multiple access interference (MAI) during signal decoding, adversely impacting VLC and VLP performance [28; 29]. Although different schemes were proposed to alleviate the MAI of ACDM signals in radio frequency communication (RFC) systems [30; 31; 32], these schemes are mainly designed for multi-user communication and cannot support high-accurate positioning. Furthermore, given the distinct nature of the VLC channel compared to RFC channels, RFC-designed schemes are not directly applicable to VLPC systems. Therefore, few efforts have been made to improve the performance and robustness of ACDM-based VLPC systems. Motivated by this gap, our work focuses on enhancing the VLPC scheme to mitigate ACDM-induced MAI, aiming to handle significant time delays among CDM transceivers. In this paper, we present a novel solution for enhancing the performance of the ACDM-based VLPC network. Firstly, we propose a new type of orthogonal codeword called orthogonal pseudo-random code (OPRC), designed for the ACDM-based VLP system. Building on our previous conceptualization of the OPRC-VLP scheme [33], we conduct a detailed investigation into the OPRC-VLP system based on ACDM through simulationsand experiments. Next, we enhance the OPRC-VLP scheme to include VLC capabilities, resulting in the OPRC-VLPC scheme. This scheme operates within a multi-cell VLPC network, where LEDs within the same cell are managed by a unified controller to maintain synchronization, while LEDs across different cells are controlled independently, leading to asynchronous transmission. In such asynchronous settings, since the coding contains user information, differences between adjacent data bits can exacerbate MAI. Thus, a successive interference cancellation decoding (SICD) technique is introduced to reduce the influence of MAI and improve the system performance. Simulation results confirm the effectiveness of the SICD-OPRC scheme, demonstrating its capability to maintain high-quality data transmission and precise positioning in asynchronous VLPC networks. The main contributions of this paper are summarized as follows:  
1. We present the mathematical formulation for generating the OPRC and analyze its correlation functions, demonstrating that it exhibits excellent correlation properties. Specifically, its cross-correlation is always zero at any chip shift, which preserves the orthogonality during asynchronous transmissions. Results indicate that the superior correlation properties of OPRC offer greater resilience to MAI compared to OZCZ codes as proposed in [26]. 2. Comprehensive simulations and experiments are conducted for the OPRC-VLP scheme in ACDM-based systems. The utilization of OPRC enables clear differentiation of VLP signals from individual LEDs at the receiver, free from MAI. Thus, the OPRC-VLP scheme achieves sub-centimeter precision positioning without synchronization between transmitters, both in simulation and experiment.