# Resource Allocation for Reconfigurable Intelligent Surface Assisted Dual Connectivity
## 5 Numerical Results
This is due to the fact that the throughput in (37) for \(\alpha=1\) is the geometric mean rate. The geometric mean rate is better when all the users' rates are better. Therefore, in order to observe the gain of RISDC system when compared to the other systems, the throughput for only _users in coverage (non-zero rate users)_ are computed and shown in Figure 4. The users with \(SINR\geq-6.5\) dB are only in coverage and have non-zero rate according to [21]. The significant gain of the RISDC system when compared to other benchmarks (12%), DC(6%), and RIS (2.4%) for systems considering only non zero rate users is observed in Figure 4. \begin{table}
\begin{tabular}{c c} \hline \hline \(f_{c}\) & 28 GHz \\ \hline Penetration loss (\(v_{sc}\)) & 20 dB for NLOS path \\ \hline Loss due to shadowing (\(\rho\)) & Standard deviation of 4 dB \\ \hline P\({}_{j}\) & 30 dBm \\ \hline PL(d) & Urban micro [23] \\ \hline \(C\) & 99 \\ \hline Subchannel Bandwidth & 720 KHz \\ \hline SC\({}_{OFDM}\) & 12 \\ \hline SY\({}_{OFDM}\) & 14 \\ \hline T\({}_{Subframe}\) & 0.25 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters. Figure 2: Simulation settings. The coverage of the system with varying number of RISs and the user density of \(\rho_{user}=60\) for different number of BSs are shown in Figure 5. We evaluated for two mmWave based BSs (2 BS) and four mmWave based BSs (4 BS) deployed in the same area. The coverage in Figure 5 is computed over \(10^{4}\) iterations. Each time, the number of users in coverage are computed and averaged over \(10^{4}\) realizations. The coverage with more number of BSs is less than the coverage with less number of BSs. This is because, as the number of BSs in the system increases, the interference also increases which substantially reduces the SINR of the users. In this, the coverage with RIS and RISDC is also less because we consider interference from other BSs for RIS and RISDC users. Further, the throughput performance with varying user densities for different number of BSs in the systems are shown in Figures 6 and 7. Since all the users in the system are considered for computing  
Figure 4: Variation of throughput of non-zero rate users (users only in coverage) with respect to number of RISs when \(\rho_{bs}=2\), \(\rho_{user}=60\), and \(\mu_{b}=10\). Figure 3: Variation of throughput with respect to number of RISs when \(\rho_{bs}=2\), \(\rho_{user}=60\), and \(\mu_{b}=10\). throughput, the gain that we observe from Figures 6 and 7 is minimal. If we consider throughput of the users in coverage, then a significant gain is achieved with the RISDC system. However, the throughput with 4 BSs in Figure 7 is less than the 2 BS case as in Figure 6 because it becomes interference limited system when the number of BSs increases. The users' rates are arranged in increasing order. We consider evaluating the throughput for \(\alpha=1\) in (37) for every 10% of users. This is defined as the lowest \(m^{th}\) percentile of users. This \(m\) is varied as every 10% as shown in Figure 8. The same interference limited scenario for increasing number of BSs is observed while computing this worst case users' throughput also. There is a small gain achieved by RISDC system but the performance is similar when compared to RIS system. Those increase in comparable throughput is maintained even with varying the blockage density in the system as shown in Figure 9. As the average number of blockages (\(\mu_{b}\)) in the system increases, the gain direct LOS decreases significantly, which in turn reduces the throughput of the system. However, the gain of the proposed RISDC system with respect to the RIS system is 0.56%, 0.94%, 5.19%, and 11.8% for blockage densities of 10, 20, 30, and 40, respectively. The proposed RISDC system is for a \(\alpha\)-fair utility function. While the \(\alpha\) increases, the fairness to the worst case users' rate increase at the cost of best case user's rate.