# Low-Altitude Sensing Model: Analysis Leveraging ISAC in Real-World Environments
## 2 The Model of Single Base Station 3D Sensing
### Model and Key Parameters Design  
As illustrated in Figure 1, in low-altitude 3D ISAC networks, sensing range is constrained by the vertical FOV of the antenna, limiting the scanning range to a specific angular extent. This limitation results in coverage blind spots in the tower-top area of the base station. The coverage capability of base stations varies at different altitudes. As the altitude increases, the horizontal coverage range decreases. The area of the coverage blind spots at the tower top expands, as shown in Figure 2. O represents the antenna coordinate point, A represents the farthest sensing boundary point in the direction at the same height as the antenna, and OA denotes the radial distance between point O and point A. The key to achieving continuous 3D coverage at low altitudes lies in ensuring seamless primary lobe coverage at the maximum altitude, which imposes specific requirements on the vertical FOV \(\alpha\) of the base station antenna. Figure 1: Vertical FOV of an antenna. We constructed a hexagonal cellular-like network topology to achieve effective coverage in the low-altitude area. In low-altitude sensing scenarios, ensuring continuous primary lobe coverage at the maximum altitude is crucial, which requires maximizing the coverage range of the main lobe of the local base station while minimizing the coverage of the main lobe of neighboring stations over the blind spots at the tower top of the local base station. By precisely balancing the coverage ratio between the main lobe of the local station and those of neighboring stations, we could achieve continuous coverage across different altitudes. In the low-altitude network topology at the highest defined altitude, as shown in Figure 2(a), it is clear that the main lobes of neighboring stations cover the tower-top area of the local base station. However, when focusing on lower altitudes, the situation changes. As the coverage range of the base station increases at lower altitudes, overlapping coverage becomes evident, particularly at the horizontal height of the antenna, as intuitively depicted in Figure 2(b). Based on the above analysis, we further proposed an integrated low-altitude sensing model, as illustrated in Figure 4. The definitions of O and A remain consistent with those in Figure 1. Point C is the intersection point between the direction of the maximum vertical FOV extension of the antenna and the maximum flight altitude. OC is the radial distance between point O and point C. Point B is the maximum flight altitude point of A, extending vertically upwards. Point X is the intersection of the vertical line from C downward with the OA, and the radial distance from point O to point X is denoted as \(s\). Using B and C as the longest diagonals, we constructed a horizontal regular hexagon CDEBGF. At the maximum flight altitude, the main lobe coverage area of one sector of the BS0 base station  
Figure 3: Low-altitude neighboring cell coverage over the tower top. Figure 2: Low-altitude network coverage at different altitudes. is the area enclosed by CDEBGF. Q and N are the vertical projections from points E and G to the plane at the antenna height, while OM and OP are parallel and equal in length to AQ and AN, respectively. Thus, on the antenna height plane, a hexagon OPQANM is formed, representing the main lobe coverage area of one sector of BS0 at the base station height level. Additionally, H is the vertical projection from point O to the maximum flight altitude, \(h_{1}\) represents the distance OH, and \(d\) represents the distance OA, which is the station spacing. The angle between OP and OA is the horizontal FOV \(\gamma\) of the antenna. Under typical three-sector cellular networking conditions, \(\gamma\) is usually set to 60\({}^{\circ}\). To construct an accurate mathematical model for analyzing the coverage characteristics of base stations in low-altitude sensing networks, we defined the location of the base station antenna as the coordinate origin \(O\)(0,0,0).