The Maximum Number of Cells With Modulated Binary Sensors

Due to the low cost and good privacy protection of binary sensors, there are many applications of binary sensors. To enhance the spatial awareness of binary sensors, researchers utilize modulators to modulate views of sensors into visible and invisible regions so that the monitoring space is segmented into small cells identified by signatures. When a warm object moves in these cells, its location or moving trajectory can be acquired more accurately with modulators than without modulators. Accordingly, the maximum number of cells (MNC) in a deployment determines partially the maximal spatial awareness of the binary sensor system. In this paper, we provide a theoretical study of the MNC, given the number of sensors and the number of modulators. We also find the sufficient and necessary conditions to achieve the MNC so that we provide the reasons why deployment cannot obtain the MNC. These conditions can guide researchers to design the MNC deployments. Furthermore, we provide a method to calculate the number of cells when a deployment sometime cannot obtain the MNC. Our experiments provide deep insights into the influences of those conditions on the MNC and the MNC on the spatial awareness of binary sensor systems.