Limited Sampling Spatial Interpolation Evaluation for 3D Radio Environment Mapping.

The increasing densification and diversification of modern and upcoming wireless networks have become an important motivation for the development of agile spectrum sharing. Radio environment maps (REMs) are a basic tool for spectrum utilisation characterisation and adaptive resource allocation, but they need to be estimated through accurate interpolation methods. This work evaluated the performance of two established algorithms for spatial three-dimensional (3D) data collected in two real-world scenarios: indoors, through a mechanical measuring system, and outdoors, through an unmanned aerial vehicle (UAV) for measurement collection. The investigation was undertaken for the complete dataset on two-dimensional (2D) planes of different altitudes and for a subset of limited samples (representing the regions of interest or RoIs), which were combined together to describe the spatial 3D environment. A minimum error of -9.5 dB was achieved for a sampling ratio of 21%. The methods' performance and the input data were analysed through the resulting Kriging error standard deviation (STD) and the STD of the distances between the measurement and the estimated points. Based on the results, several challenges for the interpolation performance and the analysis of the spatial RoIs are described. They facilitate the future development of 3D spectrum occupancy characterisation in indoor and UAV-based scenarios.