MAPRT Detector-Based Air-Ground ISAC Systems: Joint UAV Placement and Precoding

The existing unmanned aerial vehicle (UAV) enabled integrated sensing and communications (ISAC) systems primarily focus on the sensing capabilities of the UAV itself, overlooking the fact that the existing ground access points (APs) can receive the reflected signals for passive sensing, which can enhance the overall sensing performance. To address this issue, this paper introduces a UAV empowered air-ground ISAC system, where a UAV serves multiple communication users and performs detection for a potential target simultaneously, with the help of several ground APs. Specifically, the UAV works in active mode by transmitting ISAC signals and extracting information from echoes reflected from the target. In contrast, the ground APs function as sensing receivers, receiving and processing the reflected sensing signals from the target. Considering the limited capacity of the wireless backhaul links, we propose a two-step joint detection method, which contains local detection and result fusion steps. By incorporating the knowledge about the distribution of the reflection coefficient, we propose a maximum a-posteriori ratio test (MAPRT) detector, which is a generalization of earlier approaches such as the generalized likelihood ratio test detectors. Subsequently, the asymptotic distribution of test statistics of the MAPRT detector is derived. Furthermore, to improve the target detection performance, we propose an optimization algorithm that jointly optimizes the placement and transmit beamformer of the UAV, aiming at minimizing the probability of fusion error while guaranteeing the quality of service requirements of the users. Finally, numerical results demonstrate the effectiveness of the proposed algorithm.