## 4 Numerical Results
Figure 3 shows the power consumption and system capacity with different D2D group size, where \(K=20\), \(M=10\), \(|\mathcal{D}_{m}|=10\), \(R=500\) m, \(\Gamma_{k}^{C}=5\) dB, \(\Gamma_{m}^{D}=35\) dB and \(\eta=0.5\). As shown in Figure 3b, the number of admitted D2D links decreases with increasing of the D2D group size. Especially, the \"MaxR\" and \"Single\" schemes fall faster than the proposed scheme. Since the channel gain of D2D link decreases when the multicast radius increases, more D2D links are likely to be removed to benefit the QoS maintenance of the remaining system, with bigger influence on the single sub-channel reusing scheme (\"MaxR\" and \"Single\"). However, the change in power consumption is not monotonic and depends on the following two factors: (i) more transmission power is required for the D2D groups to satisfy the SINR threshold constraint; and (ii) the worst channel condition of D2D multicast becomes relatively better along with the removed D2D links, thus the required transmission power decreases. It is seen from Figure 3a that the power consumption of \"MaxR\" shows a trend of earlier increase and later decrease. The decrement of proposed scheme in the number of admitted D2D links is much less than that of the \"MaxR\" scheme, thus power consumption of the proposed scheme keeps growing. Figure 3: Power consumption and number of D2D links versus D2D group size: (**a**) Impact of D2D group size on power consumption; (**b**) Impact of D2D group size on system capacity. Figure 2: Power consumption and number of D2D links versus weighted factor: (**a**) Impact of weighted factor on power consumption; (**b**) Impact of weighted factor on system capacity. The power consumption and system capacity with different cell radius is depicted in Figure 4, where \(K=20\), \(M=10\), \(|\mathcal{D}_{m}|=10\), \(r=50\) m, \(\Gamma_{k}^{\mathrm{C}}=5\) dB, \(\Gamma_{m}^{\mathrm{D}}=35\) dB and \(\eta=0.5\). Intuitively, the larger the cell radius, the greater the distance between the CUs and D2D receivers in groups, hence the smaller the interference from CUs to the D2D receivers. Thus the number of admitted D2D links increases with the cell radius as shown in Figure 4b. Similarly, the change in power consumption depends on the following two factors: (i) transmission power decreases along with the lower interference between CUs and the D2D receivers; and (ii) the worst channel condition of D2D multicast becomes relatively worse with the increment of the number of admitted D2D links, thus the required transmission power increases. From Figure 4a, compared to the scheme of reusing single sub-channel (\"MaxR\" and \"Single\"), the proposed scheme further utilizes the gain that is brought by the decrement of interference between CUs and the D2D receivers on multiple sub-channels. In Figures 5 and 6, the power consumption and system capacity performance with different SINR thresholds of CUs and D2D links are illustrated, where \(K=20\), \(M=10\), \(|\mathcal{D}_{m}|=10\), \(R=500\) m, \(r=50\) m and \(\eta=0.5\). It is seen that increasing the SINR threshold leads to decreasing the number of admitted D2D links since it tightens the SINR threshold constraints of both CUs and D2D links and limits the chances for a D2D group to find a CU partner. From Figure 5a, the increase in the SINR threshold of CUs, which has a greater impact on reusing single sub-channel scheme (\"MaxR\" and \"Single\"), is helpful to reduce D2D transmission power. As shown in Figure 6a, as the SINR threshold of D2D links increases, the power consumption rises gradually. Furthermore, the power consumption in \"MaxR\" and \"Single\" scheme begins a downward trend when the SINR threshold 30 dB. This due to the fact that the dramatic reduction in the number of admitted D2D links reduces the power consumption efficiently. In Figure 7, the fairness of the proposed scheme is compared with the \"MaxR\" scheme. The [PERSON]'s fairness index is used to evaluate the fairness of the algorithms.