Two-Stage Beamtraining With Geometry-Aware Codebooks for Precise Positioning in Multi-RIS Systems

Existing Reconfigurable Intelligent Surface (RIS) beamtraining designs often prioritize communication metrics while neglecting geometric factors. This leads to inefficient initial access and poor positioning accuracy, which in turn hinders the fine beam alignment that relies on location priors. To resolve this dilemma, this paper proposes a two-stage beamtraining framework enabled by a novel geometry-aware codebook. First, a multi-RIS Cramér-Rao Lower Bound (CRLB) is derived to quantify positioning limits. Guided by this, a geometry-aware transformer-based network is developed to generate codebooks to optimize spatial beam allocation, by jointly minimizing region-averaged CRLB and maximizing achievable rate. This codebook facilitates the two-stage beamtraining process: an initial scan yields reliable Time-of-Arrival (ToA) and Angle-of-Arrival (AoA) measurements for coarse positioning, which are then utilized to compute precise phase shifts for fine alignment. Extensive simulations under the considered sub-6 GHz multi-RIS setting demonstrate that the proposed framework significantly outperforms state-of-the-art methods in both positioning accuracy and communication rates, with over 80% of realizations achieving sub-meter positioning accuracy after two-stage refinement.