Accelerating ray tracing simulation using tensor completion for 3D radio map

Abstract

We proposed a ray-tracing (RT) acceleration method using the tensor completion technique for a three-dimensional (3D) radio map. Internet of things (IoT) has become widespread recently, and analysis of indoor radio wave propagation has become important in optimizing the installation location of the IoT devices. Generally, RT is used for radio wave propagation analysis. However, RT is timeconsuming to simulate. The simulation time required for RT is even larger when calculating the receiving points in 3D space with many objects. Hence, in the proposed method, we reduced the number of receiving points at which the RT calculation is performed, and we interpolated by tensor completion the received power not calculated by RT.

Acceleration of Tensor Interpolation-Based Radio Map Estimation

“…The results of comparing the MAE of the proposed method and the existing method [2] ("SPC") for each iteration are shown in Fig. 3.…”

“…The existing method [2], based on the tensor interpolation method SPC [5], was applied to the missing 3D radio map X calculated using RT. However, this method does not consider radio propagation characteristics such as path loss, shadowing, and fading.…”

“…The maximum number of iterations for both methods was 5,000. Interpolations using the existing method [2] and the proposed method were performed using MATLAB R2019b. We used a computer with an Intel Core i9-9820X 3.30 GHz CPU, and 64 GB RAM for the RT simulation.…”

“…RT can be accelerated by reducing the number of receiver points to be calculated and estimating the received power at the remaining receiver points using interpolation, thereby reducing the simulation time. This study proposes a method that considers a 3D radio map as a tensor and uses smooth PARAFAC tensor completion (SPC) [2], a tensor interpolation using rank minimization based on PARAFAC decomposition. However, because interpolation by rank minimization is iterative, the number of iterations directly influences the acceleration of the interpolation.…”

“…This motivated us to apply SPC, which is also based on a rank minimization approach, for fading fluctuations in a 3D instead of a 2D radio map. In our previous study [2], we proposed the application of SPC to estimate 3D radio maps, in which the partially obtained radio map was fed into the SPC algorithm. However, in the proposed method, we assumed that the 3D radio map is the sum of two tensors.…”