# Low-Altitude Sensing Model: Analysis Leveraging ISAC in Real-World Environments
## 2 The Model of Single Base Station 3D Sensing
### Analysis of Single Base Station Sensing Capabilities  
Single base station sensing is fundamental to achieving seamless 3D networked sensing in a low-altitude ISAC network. At a certain altitude, the coverage area of single base station sensing resembles a sector. Hardware capabilities of a single ISAC base station are mainly constrained by factors such as the horizontal and vertical FOVs of the base station antenna, as well as the coverage height and tilt angle of the active antenna unit (AAU). The farthest sensing boundary is determined jointly by signal propagation characteristics, system gain and loss, and environmental factors. Based on these factors, we can determine the sensing boundaries in various directions by calculating the sensing signal-to-noise ratio (SNR) and ensuring it is not below the minimum sensing threshold. This can ultimately meet the requirements for 3D continuous coverage networking of station spacing. The key parameters in the radar equation include signal transmission power, transmission and reception antenna gains, carrier wavelength, the radar cross-section (RCS) of the target, and the distance between the target and the radar, among others [27]. A mathematical model for the sensing SNR based on the radar equation has been established to quantify the performance of single base station sensing coverage. The SNR of the sensing target can be expressed as follows:  
\[\text{SNR}= \frac{\sigma P_{\text{t}}G_{\text{r}}G_{\text{t}}\lambda^{2}n \tau}{(4\pi)^{3}R^{4}LN_{0}}, \tag{1}\]  
where \(\sigma\) represents the RCS of the target, \(P_{\text{t}}\) denotes the transmission power, \(G_{\text{r}}\) and \(G_{\text{t}}\) are the reception and transmission antenna gains, respectively, \(\lambda\) is the carrier wavelength, \(n\) and \(\tau\) are the total cumulative number of signals and transmission duration (related to the sensing frame structure design), \(R\) is the distance between the target and the base station, \(L\) is the RV processing loss, and \(N_{0}\) represents the noise, including interference. The antenna gains \(G_{\text{r}}\) and \(G_{\text{t}}\) are closely related to the angle of the sensing target relative to the base station antenna and can be expressed as follows:  
\[G(\theta)=G_{\text{max}}\cdot\cos^{n}\left(\theta\right), \tag{2}\]  
where \(G_{\text{max}}\) is the maximum antenna gain, \(n\) is the antenna gain attenuation coefficient, and \(\theta\) is the angle between the target and the antenna's normal direction. The greater the deviation from the central angle, the lower the antenna gain. Therefore, the coverage performance at the edge of the sensing area is usually lower than that in the central area. The introduction of sensing functionality brings interference issues among sensing operations, as well as between sensing and communication. Moreover, the sensing signals transmitted into the air inevitably cause remote interference. Therefore, under the networking conditions, for \(N_{0}\), it is necessary to take into account the adjacent station's sensing in terference \(P_{\text{neighbor-sensing}}\), the uplink communication user interference \(P_{\text{uplink-communication}}\), and the remote interference \(P_{\text{remote-interference}}\) on the basis of the background noise \(P_{\text{noise}}\).