On the Deployment of Heterogeneous Sensor Networks for Detection of Mobile Targets

Detecting targets moving inside a field of interest is one of the fundamental services of Wireless Sensor Networks. The network performance with respect to target detection, is directly related to the placement of the sensors within the field of interest. In this paper, we address the problem of wireless sensor deployment, for the purpose of detecting mobile targets. We map the target detection problem to a line-set intersection problem and derive analytic expressions for the probability of detecting mobile targets. Compared to previous works, our mapping allows us to consider sensors with heterogeneous sensing capabilities, thus analyzing sensor networks that employ multiple sensing modalities. We show that the complexity of evaluating the target detection probability grows exponentially with the network size and, hence, derive appropriate lower and upper bounds. We also show that maximizing the lower bound is analogous to the problem of minimizing the average symbol error probability in 2-dimensional digital modulation schemes over additive white Gaussian noise, that is, in turn, addressed using the circle packing problem. Using this analogy, we derive sensor constellations from well known signal constellations with low average symbol error probability.