# A Semi-Random Elliptical Movement Model for Relay Nodes in Flying Ad Hoc Networks
## 3 SREM Model  
### Design of SREM  
As discussed in Section 2, existing mobility models are not well-suited for relay-based network experiments. To address this gap, we propose the the SRCM model. WhileSREM retains SRCM's core strength--balancing structured repetition with random mobility--it is modified to better suit relay-centric FANET scenarios. The structural design of SRCM proves effective for scanning-oriented applications. However, due to its constraint of circular trajectories, SRCM is limited in its ability to naturally align nodes along linear paths, such as those between a source and destination. SREM replaces the circular trajectory with an elliptical one, allowing the spatial distribution of nodes to naturally align along the relay axis. This design modification makes SREM well-suited for relay-centric FANET experiments. As illustrated in Figure 2, the SREM model defines the major axis of the ellipse along the straight line connecting the source and destination nodes, positioning the center of the ellipse at the midpoint of this communication path. In the context of this study, we refer to this straight-line path as the relay axis, which serves as the primary geometric reference for UAV movement and packet forwarding. Within the SREM framework, multiple nodes are assumed to rotate counterclockwise around the center \(O\) of a two-dimensional elliptical space \(\Omega\), which has a major axis length of \(2a\) and a minor axis length of \(2b\). The values of \(a\) and \(b\) can be configured depending on the simulation objectives. By aligning the elliptical trajectory with the relay axis, the model promotes a natural spatial distribution of UAV nodes along the intended communication route, thereby enhancing connectivity and facilitating efficient relay operations in FANET scenarios. All nodes are assumed to fly at a fixed altitude, and takeoff and landing phases are excluded from the simulation. Each node \(n_{i}\) is initially positioned at \(P_{i}^{(0)}=(x_{i}^{(0)},y_{i}^{(0)})\), and its location can be expressed in Cartesian coordinates according to the equation of an ellipse, as follows:  
\[x_{i}^{(0)}=a\cdot\cos(\theta_{i}^{(0)}),\quad y_{i}^{(0)}=b\cdot\sin(\theta_{ i}^{(0)}) \tag{1}\]  
Here, \(\theta_{i}^{(0)}\) denotes the initial angle. Each node selects its next destination \(P_{i}^{(1)}\) randomly within a defined angular range along its initial elliptical trajectory \(E_{i}^{(0)}\) and moves in a straight line toward that point with velocity \(v_{i}\). After completing one full revolution along the elliptical path, the node selects a new elliptical trajectory \(E_{i}^{(1)}\), defined by a different pair of semi-major and semi-minor axes while keeping the center \(O\) fixed, and repeats the same movement process. During this transition, the node adjusts its radial position toward the center before entering the new trajectory. Figure 2: Structural principle of SREM using elliptical paths. The conventional SRCM model assumes that UAVs move continuously along a circular path with a constant angular velocity \(\omega\). However, in the case of elliptical movement, the curvature varies depending on the location along the ellipse. Under constant angular velocity, the distance traveled per unit time is not uniform--nodes travel farther per angular increment along the major axis and shorter along the minor axis. This leads to longer residence times in the minor-axis regions, resulting in an imbalanced spatial distribution that does not reflect realistic UAV navigation dynamics. In practice, UAV platforms generally operate based on linear speed, covering a fixed distance over a given time. This distance-based speed control is also standard in widely used simulation frameworks such as NS-3, PX4, and ArduPilot [35; 36]. Accordingly, the SREM model in this study adopts a constant linear speed assumption, rather than constant angular velocity.