Homology Theory-Based Coverage Hole Localization and Area Estimation for Visible Light Communication Networks

Visible light communication (VLC) is a novel technology for indoor communication and provides illumination at the same time. Due to the limitation of signal-to-noise ratio (SNR) and illumination, coverage holes usually spread in indoor scenarios. Accordingly, the performance of the VLC system will largely deteriorate. To solve this problem, it is indispensable to localize the overage holes and evaluate their areas to improve system performance. The homology theory provides a new solution for coverage holes detection, which includes the Čech complex and Rips complex. Rips complex does not require any knowledge of node location but usually ignores the “triangular hole,” which affects the accuracy of detection. Čech complex provides accurate position information about coverage holes and requires the relative locations of nodes. Fortunately, the number of LEDs is extremely limited in a general VLC scenario, so the acquisition of node location information is not complicated. In this article, we propose a homology theory-based coverage hole localization algorithm. Specifically, the Čech complex of all nodes is constructed first. Subsequently, the Čech complex of LED nodes is simplified, and the minimal hole cycles are searched by constructing a minimal spanning tree from the simplified nodes. Finally, the positions of all coverage holes are achieved. Moreover, we propose an area estimation algorithm for the coverage holes utilizing simple geometric segmentation. The proposed algorithm can simplify the topology of the VLC network, localize the coverage holes, and calculate their accurate areas. The simulation results well verify the efficiency and accuracy of our algorithm.