# Dynamic Repositioning of Aerial Base Stations for Enhanced User Experience in 5G and Beyond
## 5 Solution Modeling
The inequality constraint matrices A for SIR maximization is constructed as shown in Algorithm 5. ```
Input: Number of users, \(N_{s}\) and Number of candidate positions, \(N_{l}\) Output: Matrix A
```

**Algorithm 5**Construction of matrix A for SIR maximization

B is a (\(2N_{s}N_{l}+N_{l}\))-by-1 column vector and is initialized to all zero entries. The matrix F is then constructed as given in Algorithm 6. Figure 2 shows the flowchart of the designed solutions. The flowchart first checks whether the received power or the SIR needs to be maximized. Once this choice is made, the matrices and vectors needed for the bintprog as input are constructed in a series of steps. As described above, this construction ensures that all constraints, as specified in the problem formulation, are satisfied. As evident from the discussion above and from the flowchart, the construction processes for each problem is different from the other and involves using matrices and vectors of certain dimensions and then filling out certain

entries in those matrices and vectors, thereby incorporating the problem constraints and ensuring, for each problem, that the bintprog properly evaluates the objective function. Figure 2: Flowchart indicating the steps the proposed solutions involve. ## 6 Results and Discussion

In this section, we discuss the MATLAB simulation results obtained while studying the effect of various parameters on performance improvement due to the optimal placement of the Aerial BSs. The deployment area was kept at 1000 \(\times\) 1000 m\({}^{2}\). The heights of candidate positions (and hence those of the ABSs) were maintained between 50 and 100 m. The transmit power of the ABSs was kept at 30 dBm. User positions were generated using the Poisson point process and Poisson cluster process. A Poisson cluster process is a mathematical model used to describe the spatial distribution of points in a given region. In this process, points are grouped into clusters, where each cluster is generated independently according to a Poisson distribution. The superposition of these clusters allows for individual points to be random and have the tendency to cluster together in certain regions. Candidate positions for ABSs were generated using evenly spaced grid points. A suburban environment was considered with the parameters given in Table 1.

### Results

Figure 3 demonstrates how the dynamic repositioning of BSs enhances performance. In particular, the figure shows how the optimal placement of the ABSs becomes suboptimal due to the mobility of users. With the passage of time, the suboptimality increases and, hence, the normalized total received power decreases. After a time of 100 epochs, the optimal positions for the ABSs are recomputed, and the ABSs are repositioned, which results again in the maximum achievable total received power. Note that the vertical scale has been normalized between 0 and 1 by subtracting the minimum value from the data and then dividing it by the maximum value. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline a & 4.88 \\ b & 0.49 \\ \(\eta LoS\) & 0.1 dB \\ \(\eta NLoS\) & 21 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for the suburban environment. Figure 3: Degradation in total received power due to mobility of users. Figure 4 shows the effect of the number of ABSs on the improvement in the total received power that is achieved with the optimal placement of the ABSs compared to a uniform distributed placement. The user positions were created using two different deployment processes: the Poisson cluster process and the Poisson process. In the Poisson cluster process, users tend to concentrate around certain hot spots. The candidate positions of the ABSs were created using squared grids of 5-by-5, 6-by-6, and 7-by-6. From Figure 4, it is evident that greater improvement in the total received power is achieved with the optimal placement of the ABSs compared to the Poisson cluster process.