Barrier coverage in bistatic radar sensor networks: cassini oval sensing and optimal placement

Abstract

By taking advantage of active sensing using radio waves, radar sensors can offer several advantages over passive sensors. Although much recent attention has been given to multistatic and MIMO radar concepts, little has been paid to understanding the performance of radar networks (i.e., multiple individual radars working in concert). In this context, we study the optimal placement of a bistatic radar (BR) sensor network for barrier coverage. The coverage problem in a bistatic radar network (BRN) is challenging because: 1) in contrast to the disk sensing model of a traditional passive sensor, the sensing region of a BR depends on the locations of both the BR transmitter and receiver, and is characterized by a Cassini oval; 2) since a BR transmitter (or receiver) can potentially form multiple BRs with different BR transmitters (or receivers, respectively), the sensing regions of different BRs are coupled, making the coverage of a BRN highly non-trivial. This paper considers the problem of deploying a network of BRs in a region for maximizing the worst-case intrusion detectability, which amounts to minimizing the vulnerability of a barrier. We show that the shortest barrier-based placement is optimal if the shortest barrier is also the shortest line segment connecting the region's two boundaries. Based on this observation, we study the optimal placement of the BRs on a line segment for minimizing its vulnerability, which is a non-convex optimization problem. By exploiting some specific structural properties pertaining to the problem (particularly an important structure of detectability), we find the optimal placement order and the optimal placement spacing of the BR nodes, both of which exhibit elegant balanced structures. Our findings give valuable insight for the placement of BRs for barrier coverage. To our best knowledge, this is the first work to explore the coverage of a network of BRs.