This paper studies the performance of a randomly RIS-assisted multi-target localization system, in which the configurations of the RIS are randomly set to avoid high-complexity optimization. We first focus on the scenario where the number of RIS elements is significantly large, and then obtain the scaling law of Cram\'er-Rao bound (CRB) under certain conditions, which shows that CRB decreases in the third or fourth order as the RIS dimension increases. Second, we extend our analysis to large systems where both the number of targets and sensors is substantial. Under this setting, we explore two common RIS models: the constant module model and the discrete amplitude model, and illustrate how the random RIS configuration impacts the value of CRB. Numerical results demonstrate that asymptotic formulas provide a good approximation to the exact CRB in the proposed randomly configured RIS systems.

翻译：本文研究了随机配置RIS辅助多目标定位系统的性能，其中RIS的配置被随机设定以避免高复杂度优化。首先聚焦于RIS单元数量显著庞大的场景，推导了特定条件下克拉美-罗界的标度律，该标度律表明CRB随RIS维度增加呈三阶或四阶递减。其次，将分析扩展至目标和传感器数量均较庞大的大规模系统。在此设定下，探讨了两种常见RIS模型（恒定模数模型与离散幅度模型），并阐明随机RIS配置对CRB数值的影响。数值结果表明，所提出的渐近公式能有效近似随机配置RIS系统中精确CRB的取值。