# Resource Allocation for Reconfigurable Intelligent Surface Assisted Dual Connectivity
## 5 Numerical Results  
We consider an area of 200 m \(\times\) 200 m. We consider deterministic BSs and RIS locations. This is acceptable because the RIS is determined to be deployed based on the BS locations and its associated high blockage loss places. The users and blockers are deployed uniformly randomly in the considered area. The results of throughput are averaged over \(10^{4}\) independent location realizations. For each location realization, fading is averaged over 100 realizations. The number of elements of RIS considered in this simulation is 40. The simulation parameters are listed in Table 2. The channel between BS and user is considered to be NLOS and its associated pathloss is computed from [23]. We evaluate the performance of the mmWave based cellular system. However, given the channel, the derived results are applicable for any system with any number of RIS elements in general. We consider evaluating the coverage and throughput performance of four systems, namely benchmark (Ben) as in [21], DC as in [20], RIS, and RIS-assisted DC (RISDC). The benchmark system is the conventional mmWave based cellular system without DC and RIS technologies. In DC, an eligible user is able to utilize radio resources from two different BSs directly. Since mmWave based cellular systems are prone to high blockage and attenuation, a controllable path with RIS has been considered. The eligible RIS users are served via RIS by the associated BSs. To further improve the per users' rate, the proposed RISDC system leverage the advantage of DC in a RIS based system. In this RISDC system, the users eligible to be served as RISDC are identified and then RIS based users are also selected based on the predetermined SINR threshold. The RISDC system consists of both RISDC and RIS users. Bbased on the formulation and user selection, the RISDC users are the subset of RIS users, i.e., The user will be RISDC only if its two associated RIS links' SINR are greater than a certain predetermined threshold, \(\tau\). The coverage, RIS user selection, and RISDC user selection threshold are set to be \(-6.5\) dB [21] throughout the simulation. However, these values can be varied based on the scenario and derived results remains the same for all the scenarios. The throughput corresponding to the (14) is given as follows. \[T_{\alpha}=\left\{ \begin{array}{ll}\left(\dfrac{1}{\text{U}}\sum\limits_{u \in\mathbf{U}}\lambda_{u}^{1-\alpha}\right)^{\frac{1}{1-\alpha}}&,\alpha>0,\ \alpha\
eq 1,\\ \left(\prod\limits_{u\in\mathbf{U}}\lambda_{u}\right)^{\frac{1}{\mathbf{U}}}&,\alpha= 1,\end{array} \right. \tag{37}\]  
where, \(\alpha\) is the fairness parameter, \(\lambda_{u}\) is as defined in (15), and \(\mathbf{U}\) is the set of users in the system. To study the impact of distributed RIS, the number of RIS-associated to BS are varied. The impact on throughput and coverage by varying user and BS densities. Further, the user density is varied from 20 to 120 users in the considered area (0.04 /km\({}^{2}\)) to see the performance of RIS-assisted DC with different user densities. The simulation parameters are specified in Table 2 and a snapshot of simulation settings is shown in Figure 2.  
We follow a snapshot-based approach, where the users and blockages are distributed uniformly randomly in the considered area. The simulation is carried out using MATLAB R2020b. We consider throughput for all the users in the system and throughput for non zero rate users in the system. The non zero rate users are defined as the users under coverage by the BSs (its \(SINR\geq-6.5\) dB). The variation of throughput with respect to number of RIS in the system is shown in Figure 3. The proposed RISDC system performs better than the benchmark and DC system in Figure 3 with a gain of approximately 52% and 48%, respectively. However, the RISDC performs similarly to the RIS with a gain of 0.56% when we consider throughput of all users. However, if we consider only the users in coverage, the gain due to RISDC is comparably higher than the RIS system which is approximately 2.5%.