## 4 Numerical Results  
In this section, we provide several simulation results to evaluate the performance of our proposed resource allocation scheme. The simulated network is contained in a single cell with a radius of 500 m where CUs and D2D multicast groups are uniformly and randomly distributed. We follow the clustered distribution model in [25], where D2D multicast groups of radius r are randomly locatedin a cell and the D2D users in each group are randomly distributed in the corresponding cluster. Simulation parameters such as path loss models, maximum transmission power, etc. are the same as those proposed in [26], and the main simulation parameters are listed in Table 1.  
We evaluate the performance of the proposed scheme by comparing it with four benchmarks: (1) power minimization (\"MinP\"); (2) capacity maximization (\"MaxC\"); (3) multi-objective optimization with each D2D group reusing one single sub-channel (\"Single\"); and (4) sum rate Maximization scheme in [12]. The first three can be regarded as the special cases of the proposed scheme by setting (\(\eta=1\)), (\(\eta=0\)) and (\(|\mathcal{S}_{m}|=1\)) for \"MinP\", \"MaxC\" and \"Single\". The fourth one is a pure throughput optimization scheme, which assumes each D2D group can reuse the sub-channel of at most one CU. Figure 2 presents the power consumption and system capacity performance with the varying of the weighted factor \(\eta\), where \(K=20\), \(M=10\), \(|\mathcal{D}_{m}|=10\), \(R=500\)m, \(r=50\)m, \(\Gamma_{k}^{C}=5\) dB and \(\Gamma_{m}^{D}=35\) dB. For the proposed scheme, the power consumption preference is enhanced with larger \(\eta\), while, from Figure 2b, the system capacity preference requires smaller \(\eta\) with upper bound identical to the performance of the benchmark \"MaxC\". Hence, using the proposed scheme, the operator can flexibly configure the network with different preferences to satisfy specific system or user requirements simply by varying the weighted factors. Furthermore, it can be seen from Figure 2 that for the proposed scheme, increasing \(\eta\) decreases its power consumption value from 150 to 82, and its number of admitted D2D links from 87.3 to 76.4; while the power consumption and the number of admitted D2D links for \"MaxR\" are about 461.8 and 43.5, respectively. This implies that compared to the \"MaxR\" scheme, the proposed scheme seems to achieve more admitted D2D links in the network by consuming less power. This is because adopting the single sub-channel reusing for the \"MaxR\" scheme makes the power on the sub-channel fixed while the proposed scheme enables one D2D group to reuse multiple sub-channels and fully explore the spatial gain among different sub-channels, and be able to adjust power level on each sub-channel so as to perform power consumption minimization as well as admitting the maximum number of D2D links into the system. Moreover, we observe that the performance of the \"Single\" scheme is close to \"MaxR\" when weighted factor \(\eta\leq 0.2\), while the consumed power in the \"Single\" scheme is less than in \"MaxR\" at the cost of removing more D2D links from the system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Cellular layout & one isolated cellular cell \\ Cell radius, \(R\) & 300 m\(\sim\)700 m \\ Uplink bandwidth & 180 kHz \\ Noise spectral density & \(-174\) dBm/Hz \\ Path loss for cellular links & 128.1 + 37.6 log10 (d (km)) \\ Path loss for D2D links & 148 + 40 log10 (d (km)) \\ Shadowing standard deviation & 10 dB for cellular links \\  & 12 dB for D2D links \\ Noise spectral density & \(-174\) dBm/Hz \\ Maximum transmission power of CU & 20 dBm \\ Maximum transmission power of D2D & 20 dBm \\ SINR threshold of CU & 0 dB\(\sim\)10 dB \\ SINR threshold of CU link & 10 dB\(\sim\)35 dB \\ Number of CUs, \(K\) & 20 \\ Number of D2D groups, \(M\) & 3\(\sim\)10 \\ Number of D2D receivers in each group & 10 \\ D2D group size, \(r\) & 20 m\(\sim\)60 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main Simulation Parameters.