In millimeter-wave (mmWave) cellular systems, reconfigurable intelligent surfaces (RISs) are foreseeably deployed with a large number of reflecting elements to achieve high beamforming gains. The large-sized RIS will make radio links fall in the near-field localization regime with spatial non-stationarity issues. Moreover, the discrete phase restriction on the RIS reflection coefficient incurs exponential complexity for discrete beamforming. It remains an open problem to find the optimal RIS reflection coefficient design in polynomial time. To address these issues, we propose a scalable partitioned-far-field protocol that considers both the near-filed non-stationarity and discrete beamforming. The protocol approximates near-field signal propagation using a partitioned-far-field representation to inherit the sparsity from the sophisticated far-field and facilitate the near-field localization scheme. To improve the theoretical localization performance, we propose a fast passive beamforming (FPB) algorithm that optimally solves the discrete RIS beamforming problem, reducing the search complexity from exponential order to linear order. Furthermore, by exploiting the partitioned structure of RIS, we introduce a two-stage coarse-to-fine localization algorithm that leverages both the time delay and angle information. Numerical results demonstrate that centimeter-level localization precision is achieved under medium and high signal-to-noise ratios (SNR), revealing that RISs can provide support for low-cost and high-precision localization in future cellular systems.

翻译：在毫米波蜂窝系统中，可重构智能表面预计将部署大量反射单元以实现高波束赋形增益。大规模RIS会使无线链路落入近场定位区域，伴随空间非平稳性问题。此外，RIS反射系数的离散相位约束导致离散波束赋形呈现指数级复杂度。如何在多项式时间内找到最优的RIS反射系数设计仍是一个开放性问题。为解决这些问题，我们提出了一种可扩展的分区远场协议，同时考虑了近场非平稳性与离散波束赋形。该协议利用分区远场表示逼近近场信号传播，继承成熟远场模型的稀疏性以促进近场定位方案。为提升理论定位性能，我们提出快速无源波束赋形算法，该算法能最优求解离散RIS波束赋形问题，将搜索复杂度从指数阶降至线性阶。进一步地，通过利用RIS的分区结构，我们引入一种结合时延与角度信息的两阶段粗到精定位算法。数值结果表明，在中高信噪比条件下可实现厘米级定位精度，揭示了RIS可为未来蜂窝系统提供低成本高精度定位支持。