# Rapid Deployment Method for Multi-Scene UAV Base Stations for Disaster Emergency Communications
## 3 UAVs Deployment Methods for Disaster Scenarios of Different Scales
### Small Area UAVs Deployment Improved-Broyden-Fletcher-Goldfarb-Shanno  
The quasi-Newton method is one of the most efficient approaches for solving nonlinear optimization problems, initially proposed by American physicist [PERSON] in the 1950s. Presently, the prevalent variants of the quasi-Newton method are the well-established Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Additionally, the steepest descent methods (SD) are frequently employed to tackle nonlinear optimization problems [19].  
The conventional BFGS quasi-Newton method, due to its excessive computational demands, is not suitable for application in disaster emergency communications UAV deployment tasks. Therefore, this paper proposes the low-complexity and low-storage-demand SAIBFGS method. The SAIBFGS algorithm process is defined in Algorithm 1.  
The standard iterative form of the BFGS algorithm is as follows:  
\[x_{k+1}=x_{k}+a_{k}d_{k}=x_{k}-a_{k}b_{k}g_{k} \tag{12}\]  
From the above equation, it can be observed that the computational burden of the standard BFGS algorithm primarily lies in the search direction \(d_{k}\) and iteration step \(a_{k}\). In order to cater to the exigent communication scenarios during disaster emergencies, improvements need to be made in these two aspects.  
Firstly, we consider the iteration step size \(a_{k}\). In the quasi-Newton method, in order to ensure the convergence of the function, it is required that the line search be monotonic. Considering the requirement of conserving computational resources in disaster emergency communication, we made the following improvements.  
Exact search step size:  
\[a_{k}=\frac{(d_{k})^{T}(g_{k})}{(d_{k})^{T}B(d_{k})} \tag{13}\]  
Simplify the direction of the search:  
\[d_{k+1}=-g_{k+1}+\frac{(a_{k}d_{k})(a_{k}Bd_{k})^{T}}{(a_{k}d_{k})^{T}(a_{k}Bd _{k})}g_{k+1} \tag{14}\]In the equation, \(B\) is a positive definite matrix.  
Compared to the standard BFGS algorithm, the SAIBFGS algorithm obviates the need for direct calculation of the inverse Hessian matrix \(b_{k}\), thereby effectively reducing computational complexity. The computational complexity of the standard BFGS algorithm is \(L(6k^{2}+6k)\), while that of the SAIBFGS algorithm is \(L(2k^{2}+7k)\).  
```
Input: The starting coordinates of the UAV and the coordinates of the ground users awaiting rescue. Output: The final coordinates for the deployment of the unmanned aerial vehicle. Step1: Initialize the two-dimensional coordinate points for the unmanned aerial vehicle, initialize the step size, and store the data of the nearest m iterations. Step2: While it is less than the iteration number and greater than the error, do the following. Step3: Calculate the iterative step size: \(a_{k}\). Step4: Modify and refine key points: \(x_{k+1}=x_{k}+a_{k}d_{k}\) Step5: Compute the correction operator: \(p_{k}=a_{k}d_{k},q_{k}=a_{k}Bd_{k}\). Step6: Calculate the updated gradient value: \(g_{k+1}=g_{k}+q_{k}\). Step7: Compute a novel trajectory for the search: \(d_{k+1}\). Step8: Update: \(k=k+1\) Step9: End
```  
**Algorithm 1** Small-Area UAV Deployment Improved-Broyden-Fletcher-Goldfarb-Shanno (SAIBFGS)  
The accuracy of SAIBFGS is high, but as the number of UAVs increases and the deployment range expands, it is prone to getting trapped in local optima. Additionally, SAIBFGS further reduces computational complexity, making it suitable for small-scale UAV deployment.