## 3 Analysis of Channel
### Large-Scale Path Loss Model  
Large-scale fading is represented by path loss and shadow fading. Path loss increases with the increase of communication distance. Shadow fading varies along the path loss. In the emergency management of the complex urban environment, there are some obstacles that cause shadow fading, such as buildings, trees, and others. When the receiving end moves to the shaded area, the received signal strength decreases. And the obstructions with different distribution densities and positions are distributed on different transmission paths. Even if the communication distance is the same, the received signal strength is different.  
The free space propagation model is the simplest path loss model, which is used to predict the power of received signal in wireless communication environment. The received signal power can be expressed by the Friis equation as Equation (8):  
\[P_{r}=P_{t}G_{t}G_{r}\left(\frac{\lambda}{4\pi d}\right)^{2} \tag{8}\]  
where \(P_{r}\) is the received signal power, \(P_{t}\) is the transmit signal power, \(G_{t}\) is the transmit antenna gain, \(G_{r}\) is the receive antenna gain, \(\lambda\) is the wavelength and meets \(\lambda=c/f\), \(d\) is the distance of radio wave transmission.  
When there are no obstacles in propagation path, it is approximated as free space propagation. Path loss is expressed as:  
\[PL=10\lg\frac{P_{t}}{P_{r}}=20\lg\left(\frac{4\pi fd}{c}\right) \tag{9}\]  
where \(f\) is the signal transmission frequency.  
The logarithmic distance path loss model is established by introducing the path loss index \(\alpha\) that related to the environment. The logarithmic distance path loss model is expressed as:  
\[PL=PL_{ref}+10\alpha\lg\left(\frac{d}{d_{ref}}\right) \tag{10}\]  
where \(d_{ref}\) is the reference distance, \(\alpha\) is the path loss index. Different path loss indexes correspond to different environments.  
Figure 3: A comparison of measured and calculated values of the signal of Loo model. (**a**) The light shadowing environment; (**b**) The heavy shadowing environment.  
In general, \(PL_{ref}\) represents the path loss gain in free space at distance \(d_{ref}\). When \(G_{t}=G_{r}=1\), the transceiver antenna is unity gain, and the average received signal power is expressed as:  
\[\overline{S}=P_{t}\left(\frac{\lambda}{4\pi d_{ref}}\right)^{2}\left(\frac{d_{ ref}}{d}\right)^{\alpha} \tag{11}\]  
As the UAV keeps moving during the communication process, there are a large number of different obstructions on different transmission paths. Even if the communication distance between the sender and receiver is same, the signals propagating along different paths will have different path losses. The lognormal shadow model is introduced in consideration of the above practical problems. The lognormal shadow model is expressed as:  
\[PL=PL_{ref}+10\alpha\lg\left(\frac{d}{d_{ref}}\right)+X \tag{12}\]  
where \(X\) is a random variable with Zero-mean Gaussian distribution. The variance of \(X\) is \(\sigma_{X}^{2}\), that is, \(X\sim N(0,\sigma_{X}^{2})\). The shadow variance can be estimated in real time based on empirical measurements [16]. When the communication distance is the same, the model can describe the actual shadow effect, and can reduce the error between the actual value and the estimated value of the path loss.