CRLB Optimization for O-RIS-Assisted VLP Systems
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摘要: 针对智能超表面(reconfigurable intelligent surface, RIS)辅助的室内可见光定位(visible light positioning, VLP)系统性能优化问题，本文分别研究了近场与远场下针对系统克拉美罗下届(Cramer-Rao lower bound, CRLB)优化方法。通过优化RIS配置，以提升系统定位精度与整体定位性能公平性。在远场信道模型假设下，可将RIS方向优化问题建模为接收功率最大化问题，并应用一种结合粒子群优化与N步迭代的定位算法，在接收机位置未知的情况下实现了RIS方向的动态最优调整。在近场信道模型假设下，可将RIS单元与发光二极管(light-emitting diode, LED的分配问题构建为马尔可夫决策过程，并设计一种基于经验回放与知识利用的强化学习方法进行求解，在最小化CRLB的同时，兼顾不同区域用户的定位公平性。仿真结果表明，所提算法在两种模型下均能有效提升系统定位精度，且在近场模型中显著改善了全域定位性能。Abstract:
Objective With the rapid development of indoor location-based services, Visible Light Positioning (VLP) has emerged as a promising high-accuracy positioning technology. The integration of Optical Reconfigurable Intelligent Surfaces (O-RIS) into VLP systems can effectively enhance signal coverage and improve positioning performance. However, optimizing the positioning accuracy and fairness across different user areas in RIS-assisted VLP systems remains a challenging issue. This study focuses on optimizing the Cramer-Rao Lower Bound (CRLB) of the system under both near-field and far-field channel models, aiming to enhance overall positioning precision and fairness through RIS configuration. Methods Under the far-field channel model assumption, the RIS orientation optimization problem is formulated as a received power maximization problem. A positioning algorithm combining Particle Swarm Optimization (PSO) and N-step iteration is proposed to dynamically adjust the RIS orientation optimally without prior knowledge of the receiver’s position. Under the near-field channel model assumption, the allocation problem between RIS elements and LEDs is constructed as a Markov Decision Process (MDP). A reinforcement learning method based on experience replay and knowledge utilization is designed to solve this problem, aiming to minimize the CRLB while ensuring positioning fairness for users in different regions. Results and Discussions Simulation results demonstrate that the proposed algorithms effectively enhance system positioning performance under both models. In the far-field model, the PSO-based iterative algorithm achieves dynamic optimization of RIS orientation, significantly improving positioning accuracy ( Fig. 3 ). Under the near-field model, the reinforcement learning approach not only minimizes the CRLB but also considerably improves positioning fairness across the entire area, with a noticeable reduction in performance disparity among users in different zones (Fig. 5 ,Fig. 6 ). Comparative experiments show that the proposed methods outperform conventional RIS configuration strategies in terms of both average positioning error and fairness index (Table 1 ).Conclusions This paper investigates CRLB optimization methods for O-RIS-assisted VLP systems under near-field and far-field channel models. In the far-field scenario, a PSO-based iterative algorithm is proposed to optimize RIS orientation, enhancing positioning accuracy without requiring prior receiver location information. In the near-field scenario, a reinforcement learning-based approach is designed to optimize RIS element–LED allocation, which effectively minimizes the CRLB and improves positioning fairness across the whole area. Simulation results validate the effectiveness of the proposed algorithms in both models. Future work may consider more practical channel impairments and multi-user scenarios to further improve the robustness and scalability of the system. -
表 1 基于MERAC的强化学习算法
算法1 基于MERAC的智能资源分配 输入：信道增益$ H_{i,k}^{\text{ref}} $ RIS单元数$ {N}_{\text{R}} $ LED灯个数$ {N}_{L} $ 学习速率因子$ {\beta }_{a} $和$ {\beta }_{c} $，折扣参数$ \gamma $ 初始化：初始化分配矩阵$ \text{G} $，$ {\text{s}}_{0} $，$ {\text{Q(s}}_{\text{t}}{\text{,a}}_{\text{t}}) $ 1：For t=1:T 2：在状态$ {s}_{t} $基于$ {\text{π} }_{t}({s}_{t},{a}_{t}) $选择一个动作$ a_{t}^{na} $。 3: 计算$ r $中的奖励$ {r}_{t} $，并更新状态$ {s}_{t+1} $; 4：找到历史学得的动作$ {a}^{er} $如果代理是新出现或表现不佳，则执行$ {a}^{er} $； 5：分别更新 9：跟新策略函数$ {\text{π} }_{t+1}({s}_{t},a_{t}^{\text{ov}}) $ End 
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