## 3 Preliminaries and Definitions
### Agdoa Algorithm
#### 4.2.2 DOA Considering Greedy Strategies
(**a**) The overall welfare results for each algorithm at different wq; (**b**) the variation in SDD for each algorithm at different wq. Figure 6: The result of the experiment under u = 100. (**a**) The overall welfare results for each algorithm at different wq; (**b**) the variation in SDD for each algorithm at different wq. Figure 7: (**a**) The overall welfare results for each algorithm with different Iq in the u = 40 condition; (**b**) the overall welfare results for each algorithm with different Iq in the u = 80 condition. ### Performance of Agdora

#### 6.2.1 Ablation Experiments

The following figure shows a comparison of the energy consumption of DOA, GDOA, ADOA, and AGDOA for the same number of mobile users, number of server base stations, and maximum power. We can see from Figure 8a that a using greedy strategy to optimize the initial value of DOA, the initial energy consumption was significantly reduced, which was conducive to faster convergence. We can see from Figure 8b that after making the parameter na adaptive change, the iteration frequency was perturbed, and the speed of each descent became faster, which helped to prevent the DOA from falling into a local optimum. We can see from Figure 8c that after using the greedy strategy to optimize the initialization process of DOA and making the parameter na change adaptively, the optimized DOA algorithm obtained a better initial value, while descending faster. The overall ablation experiment results in Figure 8d showed that the greedy algorithm and the adaptive strategy improved the DOA significantly, bringing about a lower initial value, speeding up the iteration speed, and preventing from falling into a local optimum. In order to assess the convergence properties of the AGDOA in the ablation experiments, we used the number of iterations required for the algorithm to reach the converged state as the convergence rate for comparison. The number of convergence iterations for the different numbers of mobile users in DOA, GDOA, ADOA, and AGDOA are listed in Table 3. As shown in Table 3, the greedy strategy contributed more to the convergence

\[SSD=\frac{1}{F} \tag{13}\]0 A direct comparison of the energy consumption results of the different algorithms as the number of iterations increased. (**a**) DOA versus GDOA; (**b**) DOA versus ADOA; (**c**) GDOA versus AGDOA; (**d**) DOA, GDOA, ADOA, AGDOA. speed of DOA than parameter adaptation, and AGDOA exhibited the maximum convergence speed in the ablation experiments. In terms of the quantity of iterations required to obtain convergence, AGDOA was at least 11.2% faster than GDOA. This was the result of the joint involvement of the greedy strategy and the adaptive tuning parameter strategy. #### 6.2.2 Energy Consumption vs. Number of Mobile Devices

We set the maximum transmission power Pmax for mobile users uniformly at 5 W. Figure 9 shows a comparison of the energy consumption of the proposed AGDOA compared to GPSO and NCGG for different numbers of mobile users. It is clear that the energy consumption increased as the number of mobile users increased. The energy consumption of AGDOA was always smaller than that of GPSO and NCGG for different numbers of mobile users, and the gap between the energy consumption of AGDOA and the comparison algorithms gradually increased as the number of mobile users increased. The proposed AGDOA increased the degree of improvement in energy consumption from 8.3% to 163.9% compared to the GPSO. This suggests that the AGDOA outperforms GPSO and NCGG in the PA problem and performs better when there are a lot of mobile users. #### 6.2.3 Convergence Properties of AGDOA

To determine the convergence characteristics of AGDOA, we similarly compared the number of iterations required for the algorithms to reach a converged state.