A Coverage Theory of Bistatic Radar Networks: Worst-Case Intrusion Path and Optimal Deployment

Continuing advances in radar technology are driven both by new application regimes and technological innovations. A family of applications of increasing importance is detection of a mobile target intruding into a protected area, and one type of radar system architecture potentially well suited to this type of application entails a network of cooperating radars. In this paper, we study optimal radar deployment for intrusion detection, with focus on network coverage. In contrast to the disk-based sensing model in a traditional sensor network, the detection range of a bistatic radar depends on the locations of both the radar transmitter and radar receiver, and is characterized by Cassini ovals. Furthermore , in a network with multiple radar transmitters and receivers , since any pair of transmitter and receiver can potentially form a bistatic radar, the detection ranges of different bistatic radars are coupled and the corresponding network coverage is intimately related to the locations of all transmitters and receivers, making the optimal deployment design highly non-trivial. Clearly, the detectabil-ity of an intruder depends on the highest SNR received by all possible bistatic radars. We focus on the worst-case intrusion detectability, i.e., the minimum possible detectabil-ity along all possible intrusion paths. Although it is plausible to deploy radars on a shortest line segment across the field, it is not always optimal in general, which we illustrate via counterexamples. We then present a sufficient condition on the field geometry for the optimality of shortest line deployment to hold. Further, we quantify the local structure of detectability corresponding to a given deployment order and spacings of radar transmitters and receivers, building on which we characterize the optimal deployment to maximize the worst-case intrusion detectability. Our results show that the optimal deployment locations exhibit a balanced structure. We also develop a polynomial-time approximation algorithm for characterizing the worse-case intrusion path for any given locations of radars under random deployment.