Mapping 3D Indoor Radio Environment With Signed Distance Fields

The 3D radio environment map is envisioned as a key component for enabling environment-aware communications in 6G. However, existing methods for radio environment mapping are typically geometry-based, effective for 2D environment with simple geometries but inadequate for complex 3D environment. In this letter, we propose using the signed distance fields (SDFs) to represent the 3D indoor radio environment, which are more expressive than the traditional geometry-based methods. To map the 3D indoor environment using SDFs, we leverage the non-line-of-sight (NLoS) paths that reflect off the environment surfaces. Given an SDF-based environment and the geometric properties (e.g., AoA and ToF) of NLoS paths estimated at the base stations (BSs), we can estimate the user equipment (UE) positions using ray tracing. The 3D reconstruction can be achieved by adjusting the SDF-based environment such that the difference between the estimated and true UE positions are minimized. Simulations show that our method is robust to noisy measurements and can achieve significantly lower reconstruction errors than the geometry-based methods.