Target detection in bistatic radar networks: Node placement and repeated security game

We consider a bistatic radar network that consists of multiple separated radar transmitters and receivers, which are deployed to detect potential attacks at some points of interest (PoIs). To better defend these PoIs, the design of the bistatic radar network is investigated in two stages. First, we study the problem of optimally placing a number of radar transmitters and receivers in the sense of minimizing the maximum distance product between a PoI and its closest transmitter-receiver pair. For this problem, we propose a randomized Voronoi algorithm. Next, given the radars' locations, assuming that the transmitters use fixed and orthogonal frequencies to illuminate signals for interference avoidance, we study the problem of frequency selection for the receivers. Since an intelligent attacker can adaptively change the PoI to attack, the receivers should dynamically adapt their frequencies to cover different subsets of the PoIs. Accordingly, we model the dynamic interactions between the bistatic radar network and the attacker as a repeated security game. Based on their respective information, we propose two learning algorithms for each of them, respectively. We show that if both players follow the modified-regret-matching procedures, the empirical distributions of their actions converge to the set of correlated equilibria.