## 4 Performance Evaluation
### Performance of the Proposed DPC for Different Channel Environments in the Absence of Cellular Users  
The proposed DPC scheme is trained with the channel parameters that are set at the beginning of Section 4. In this section, we use the trained DPC scheme to obtain the performance results for different channel environments, i.e., different path loss exponents and Nakagami factors. In addition, the optimal results presented in Figures 9-12 are obtained by the exhaustive search algorithm that maximizes the SE while achieving perfect IF. Figures 9 and 10 show the SE and IF results of the conventional schemes and the proposed scheme with \(\lambda=0.0001\) for \(\alpha=5\) in Rayleigh fading channels, respectively, where the proposed DPC is trained when \(\alpha=3.8\). It is noted that an increase in the path loss exponent \(\alpha\) means that the wireless channel condition becomes severer. In Figure 9, the conventional DPC scheme for SE maximization has worse SE performance than the WMMSE scheme, and the proposed DPC scheme provides the best  
Figure 8: Index of fairness of the proposed DPC scheme with \(\lambda=1\) and 0.0001 in Rayleigh fading channels. Figure 9: Average spectral efficiency of the conventional and proposed schemes for \(\alpha=5\) in Rayleigh fading channels. SE performance when compared to the conventional schemes. In Figure 10, the proposed DPC scheme as well as the WMMSE scheme have the perfect fairness, as shown in the previous results in Figures 5 and 8. However, the conventional DPC scheme provides the worst IF result, which is almost 0.1. Figures 11 and 12 show the SE and IF results of the conventional schemes and the proposed scheme with \(\lambda=0.0001\) for \(\alpha=3.8\) in Nakagami-\(m\) fading channels with \(m=3\), respectively, where the proposed DPC is trained in Rayleigh fading channels when \(\alpha=3.8\). An increase in the Nakagami factor \(m\) implies that the line-of-sight component becomes stronger when compared to the non-line-of-sight component. In Figure 11, when comparing to the results for Rayleigh fading channels, the WMMSE scheme has slightly worse SE results, but both the DPC schemes have better SE results. In addition, in Figure 12, it is shown that the proposed DPC scheme as well as the WMMSE scheme, still achieve the perfect IF, but the conventional DPC scheme has the worst fairness performance. From the simulation results presented in Figures 9-12, it is verified that the proposed DPC scheme, which is trained in a certain channel condition, can work effectively, even in different channel environments. In addition, in Figures 9 and 11, it is observed that there is a non-negligible performance gap between the proposed DPC scheme and the optimal one, and the performance gap is not changed according to the size of area and the channel environment. Thus, the proposed DPC scheme can be further enhanced to achieve the optimal SE result. Performance of the Proposed DPC for Different Channel Environments in the Presence of Cellular Users  
In this section, we evaluate the impact of the interference from the cellular users on the spectral efficiency of the proposed DPC scheme. Figures 13 and 14 show the SE results of the proposed scheme for \(\alpha=5\) in Rayleigh fading channels and \(\alpha=3.8\) in Nakagami-\(m\) fading channels with \(m=3\), respectively, when the cellular users are in the D2D communication area and \(P_{c}=23\) dBm. These figures demonstrate that the SE performance is significantly degraded by the interference from the cellular users, even when a single cellular user exists, and the performance degradation becomes more severe as the size of D2D communication area decreases because the interference power from the cellular user becomes stronger. In addition, when \(U=1,2,5\), the SE results for Nakagami fading channels are worse than those for Rayleigh fading channels, since the interference power from the cellular users is stronger in Nakagami fading channels than Rayleigh fading channels.