# A Power Control and Intervention Algorithm for Co-Existing IMT Base Stations and Satellite Services
## 3 Optimisation Algorithm
### Average Power Allocation Algorithm Based on Partitioning Strategy  
When the maximum transmit power of the virtual large IMT-2020 base station in the sub-area is determined, the average power distribution scheme distributes the maximum transmit power of this virtual large base station equally to all IMT-2020 base stations in the area, thus determining the transmit power of the IMT-2020 base station. The following table describes the Algorithm 1. ```
1:Determine the total number of base stations based on the coverage area
2:Obtain the number of base stations within the partition
3:Calculate the aggregate interference of the virtual large base station based on each partition
4:Solve for the maximum transmission power of the base station based on the threshold value
5:Perform average power allocation

Figure 3: Flowchart of power allocation algorithm based on partitioning strategy. ### Power Allocation Algorithm Based on Channel Gain

The core idea of the method is to allocate power according to the channel relationship between the user and the base station, i.e., the better the channel conditions, the higher the transmit power. ### Maximum and Rate-Based Power Allocation

The maximum sum rate based power allocation algorithm can be mathematically represented as:

\[\max\quad\sum_{j=1}^{N_{u}}R_{j}\]

\[\text{s.t.}\hskip 56.905512 pt\sum_{j=1}^{J_{N}}P_{j}\leq P_{\max}^{n}\quad \quad, \tag{14}\]

\[\frac{I_{total}}{N}\leq I_{threshold}\]

In the above equation, \(R_{j}\) denotes the rate of the user \(j\), which can be expressed as:

\[R_{j}=\log_{2}(1+\frac{P_{j}G_{t}G_{r}\abs{\mathbf{h}_{j}}^{2}}{\sigma^{2}}), \tag{15}\]

In addition, \(P_{j}\) denotes the transmit power of the IMT-2020 base station \(j.P_{max}^{n}\) denotes the maximum transmit power of the virtual IMT-2020 large base station in the sub-area \(n\),\(I_{total}\) denotes the aggregate interference to the FSS satellites from all IMT-2020 base stations in the sub-area, and \(I_{t}\)_threshold_ denotes the interference threshold for the aggregate interference to the FSS in the sub-area. Since the objective function in the optimisation problem is non-convex, in order to solve the problem, the non-convex objective function is transformed into a convex function as follows: Introducing the slack variable \(x_{j}\) satisfies: \(x_{i}\leq P_{j}G_{t}G_{r}\abs{h_{j}}^{2}\)

\[e^{x_{i}}\leq P_{j}G_{t}G_{r}\abs{\mathbf{h}_{j}}^{2}, \tag{16}\]

Then the optimisation objective function of the original problem can be written as

\[\log_{2}e(\sum_{j=1}^{N_{u}}x_{j}-\ln(\sigma^{2})), \tag{17}\]

At this point the problem is convex and an optimised solution can be obtained by the solver. ## 4 Simulation Verification

### Simulation Parameters

The simulation parameters are given in this section in Table 5 below. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Number of base stations & 439,860 \\ Satellite maximum antenna gain & 22 dBi \\ Network load factor & 20\% \\ TDD activity factor & 75\% \\ Noise temperature & 630 K \\ Satellite antenna half-beam angle & 15\({}^{\circ}\) \\ Antenna bypass level & \(-\)25 dB \\ Satellite altitude & 35,786 km \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation parameters. ### Performance of Average Power Allocation Algorithm Based on Partitioning Strategy

In Figure 4, it can be seen that the aggregate interference I/N value from the terrestrial network to the satellite without interference control is concentrated in the range of 5.2-6.8 dB, which exceeds the interference threshold by about 13 dB. Therefore, an appropriate interference control scheme is needed to satisfy the I/N threshold requirement needed for network coexistence. In Figure 5, the simulation results of the proposed partition-based interference avoidance method are presented. The ground base stations are divided into 1000 partitions.