# Research on Joint Resource Allocation for Multibeam Satellite Based on Metaheuristic Algorithms
## 4 Results  
The simulation scenario was configured as a GEO multibeam satellite with 37 beams. Figure 6 depicts the beam distribution. The majority of the simulation scenario parameters were obtained from [1; 20]. Table 3 details some of the most important parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Degree of Domination** & **UBA** & **NDBC** \\ \hline
0 & 0 & \(\approx M/2\) \\
1 & 2 & 2 \\
2 & \(M-2\) & \(\approx M/2-2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Domination degree of UBA and NDBC. \begin{table}
\begin{tabular}{c c} \hline \hline
**Input:**\(D\)(Demand); \\
**Output:**\(P_{best}\), \(BW_{best}\), \(R_{best}\) \\ \hline
1: /*Initialization*/ \\
2: /*Non-dominated Beam Coding*/ \\
3: **while** iteration < Maximum iterations \\
4: /*Population Evolution*/ \\
5: **for** each operator in Algorithm do \\
6: /*Population Evolution*/ \\
7: **/*Power Constraint Handling*/** \\
8: **end for** \\
9: /*Population Evaluation*/ \\
10: /*Bandwidth Constraint Handling*/ \\
11: /*Dominated Beam Bandwidth Calculation*/ \\
12: /*Beam Data Rate Calculation*/ \\
13: /*Get Optimal Solution*/ \\
14: **end while** \\
15: **Return** the final solution \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The general architecture of the metaheuristic algorithm using the NDBC method. Standard metaheuristic algorithms, such as GA [20], DE [28], PSO [29], and QPSO [30], were utilized in our simulations. For a fair comparison, each algorithm's population size and termination conditions were set to the maximum number of iterations. Table 4 provides the algorithm parameters. A DVB-S2 [31] and DVB-S2X [32] hybrid MODCOD table was used, which was screened such that as the threshold value increased, the spectral efficiency increases uniformly. As depicted in Figure 7, the execution time of the constraint handling session varied across iterations due to the random nature of the algorithm's evolution. NDBC was more stable and required less time to execute each algorithm than UBA. The execution time of constraint handling is proportional to the number of iterations. Quantitatively, NDBC required approximately one-fourth to one-fifth of the time required by UBA, achieving an effective reduction, indicating that the computational complexity of NDBC is lower than that of UBA. This result is consistent with the analysis presented in Section 3.3 regarding computational complexity. Figure 6: Schematic diagram of the distribution of 37 beams. Using the NDBC method, all red and blue beams (17 in total) are selected as non-dominated beams, whereas all green and yellow beams (20 in total) are dominated beams. The total demand for traffic across all beams is 24.16 Gbps, with a standard deviation of 177 Mbps. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Total power & \(B_{tot}\) & 2350 & W \\ Total bandwidth & \(B_{tot}\) & \(375\) (\(\times\)2) & MHz \\ Power maximum & \(Pb_{max}\) & 100 & W \\ Transmit antenna gain & \(G_{t}\) & 52.2 & dB \\ Receive antenna gain & \(G_{r}\) & 41.5 & dB \\ Free-space path losses & \(L_{FS}\) & 209 & dB \\ System temperature & \(T_{sys}\) & 320 & K \\ Roll-off factor & \(\alpha_{r}\) & 0.2 & — \\ Link margin & \(\mu\) & 1.0 & dB \\ Carrier-to-adjacent-beam interference & \(C/ABI\) & 36 & dB \\ Carrier-to-adjacent-satellite interference & \(C/ASI\) & 28 & dB \\ Carrier-to-cross-polarization interference & \(C/XPI\) & 30 & dB \\ Carrier-to-third-order inter-modulation interference & \(C/IMI\) & 21 & dB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters used in the simulation scenario. The optimal results of each algorithm with UBA and NDBC are depicted in Figure 8. According to the model presented in this paper, the USC was 1.967 Gbps when bandwidth and power are distributed uniformly (denoted as average bandwidth and average power allocation, ABAP). Figure 8a illustrates the execution time of each algorithm for varying population sizes.