Optimizing the Number and Size of Signature Cells in a Modulated Sensor System

The localization and tracking capabilities of binary sensors can be significantly enhanced by associating sensor nodes with modulators. The addition of modulators segments the detection area into subregions, called signature cells. While much of the related research focuses on modulator design and sensor data processing, there are few studies on the optimum number of cells, especially when considering small area cells with small area variances. This paper studies the optimum number of cells for varying numbers of per-sensor modulators under a placement scenario that produces signature cells with small area variances. We first derive the optimum number of signature cells and find necessary and sufficient conditions under which the maximum is achieved. We then focus on the sensors’ spatial awareness and deduct the conditions under which maximal spatial awareness is achieved. Finally, we study the asymptotic behavior of the individual cells’ areas in terms of the number of modulators. Our study can guide researchers in enhancing the tracking and localization precision of applications and improve the spatial awareness of sensors.