## 3 System Model and Problem Formulation
### System Model  
In this subsection, we present the search and rescue scenario with single UAV equipped with single 5G NR base station, which is shown in Figure 1. This system consists of one UAV that deploys one 5G NR base station with antennas in a Uniform Rectangular Array (URA) and numbers of UEs. The UEs are denoted as \(U=\{ue_{i}\}\), where \(i\) represents the identifier of each UE. We establish the three-dimensional coordinate system with the UAV starting point as the origin \((0,0,0)\). Therefore, the position of the UAV and UEs can be denoted as \(P_{uw}=(x_{uav},y_{uav},z_{uav})\) and \(P_{ue_{i}}=(x_{ue_{i}},y_{ue_{i}},z_{ue_{i}})\), respectively. We assume that all UEs are static and UAV is moving with a trajectory \(T_{juav}=\{(x^{(i)}_{uav},y^{(i)}_{uav},z^{(i)}_{uav})|j=0,1,\ldots,N\}\) where \(j\) represents the UAV coordinate at the \(j\)th refresh time. In this system, the 5G NR base station on UAV deploys phased antenna array that is URA. With beamforming, AoD estimation process consists of two procedures including initial acquisition based on SSB and beam refinement using DL-PRS. **Remark 1**: _The practical equipping of drones with 5G base stations involves meticulous consideration of various issues, including the weight and power requirements of 5G hardware, the stability and durability of UAVs carrying and operating these base stations, as well as the logistics and costs of on-site maintenance and service of UAVs and their 5G infrastructure. These factors will affect the practical application of the technology proposed in this paper. Consequently, it is imperative to  
Figure 1: System model: single UAV for search and rescue. adaptably select diverse workflows and strategies tailored to the specific requirements of varying scenarios, ensuring optimal performance and efficiency._  
During the initial acquisition, beam sweeping takes place at both base station and UEs to select the best beam pair based on the Reference Signal Received Power (RSRP) measurement. Down-link SSBs are a pivotal synchronization mechanism in 5G NR networks, providing a structured and efficient means for time and frequency synchronization, cell search, and channel estimation through periodic transmission of Orthogonal Frequency Division Multiplexing (OFDM) symbols. These SSBs enhance network performance by facilitating rapid cell identification and acquisition, offering robust synchronization even in high-mobility and dense deployment scenarios, and are crucial for achieving the high data rates and low latency that define 5G services. During the beam refinement, beam sweeping happens at the base station where a set of PRS resources are configured and transmitted over different directions by using finer beams. PRS, or DL-PRS, is designed for multi-Base Station (BS) signal reception by UE, similar to its LTE equivalent. A distinctive feature of PRS is its enhanced audibility, achieved through a muting mechanism that coordinates transmissions from multiple BSs, muting less relevant signals to minimize interference. The PRS Resource Elements (REs) exhibit a staggered pattern that enhances correlation properties, which is instrumental for peak detection. By employing a comb-\(N\) pattern with \(N\in\{2,4,6,12\}\), it enables the frequency-multiplexing of \(N\) distinct Transmission Resource Patterns (TRPs) within a single time slot, each distinguished by a unique frequency offset. Customization of each PRS is facilitated by varying its periodicity (\(T_{\text{PRS\,per}}\)), slot offset (\(T_{\text{PRS\,offset}}\)), Resource Block (RB) offset (\(T_{\text{PRS\,offset,RB}}\)), and RE offset (\(T_{\text{PRS\,offset,RE}}\)). This customization caters to diverse service requirements, such as the need for frequent PRS transmissions in latency-sensitive applications, or less frequent transmissions for energy conservation in other devices.