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This paper studies the performance of a randomly RIS-assisted multi-targetlocalization system, in which the configurations of the RIS are randomly set toavoid high-complexity optimization. We first focus on the scenario where thenumber of RIS elements is significantly large, and then obtain the scaling lawof Cram\'er-Rao bound (CRB) under certain conditions, which shows that CRBdecreases 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 andsensors is substantial. Under this setting, we explore two common RIS models:the constant module model and the discrete amplitude model, and illustrate howthe random RIS configuration impacts the value of CRB. Numerical resultsdemonstrate that asymptotic formulas provide a good approximation to the exactCRB in the proposed randomly configured RIS systems.

Asymptotic CRB Analysis of Random RIS-Assisted Large-Scale Localization Systems