Complexity reduction of ordinary kriging algorithm for 3D REM design

• Published in: Physical communication Vol. 55; p. 101912
• Main Authors: Maiti, Pradipta, Mitra, Debjani
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2022
• Subjects: Clustering; Elbow technique; Indoor 3D REM; Ordinary kriging; Semivariogram; Time complexity; Elbow technique; Semivariogram; Clustering; Ordinary kriging; Time complexity; Indoor 3D REM
• ISSN: 1874-4907; 1876-3219
• DOI: 10.1016/j.phycom.2022.101912

This work has investigated the feasibility of using cluster ordinary kriging (OK) interpolation to speed up indoor three-dimensional (3D) radio environment map (REM) generation time than the conventional OK-based REM generation time in two-dimensional (2D) and 3D ways mainly. The REM has been generated on the real-time received signal strength (RSS) dataset of an ultra-high frequency active television (TV) channel to explore TV grey space (TVGS) volume for cognitive access inside a six-storied office building. It can support future home networks for high-speed data-based applications. The optimal number of clusters has been found at K=4 on both 3D and 2D ways through distortion % deviation analysis. The maximum distortion % deviation = 88.74%, has been found at K=4. The exponential semivariogram model has been selected as the best-fit model after a thorough cross-validated comparative analysis of the clustered and non-clustered OK algorithms separately on residual squared error (RSE), root mean square error (RMSE) and the ratio of expected variance (EV) and kriging variance (KV) results. The RSE and RMSE are minimum, and the EV: KV ratio is in between 0.95 to 1.05 for the exponential model. Significant observation of the analysis of the results shows that cluster OK algorithms outperform conventional OK algorithms of corresponding domains on time complexity. A comparative study on RMSE, correlation coefficient (CC), and relative recovery error (RRE) show that cluster OK improves the accuracy. Cluster 2D and 3D OK-based detected TVGS volume is 13450 m3, 5.634% of the whole building volume.