# RIS-Assisted Cooperative Time-Division Multiple Access
## 3 Simulation Results  
In this section, simulation and numerical results are provided to validate the performance of the proposed algorithm compared with the conventional TDMA system. The proposed scheme can be used with the other schemes or used alone in the TDMA system. Therefore, in this simulation section, we measure the feasibility of whether the proposed scheme can be combined with the TDMA systems from the perspective of various performance metrics. It is assumed that the channel from BS to RIS, \(\mathbf{H}\), is the Rician fading channel, and the channels from the RIS to UE and from BS to UE, i.e., \(\mathbf{h}\) and \(\mathbf{g}\), are Rayleigh fading channels. The main simulation parameters are given in Table 2. For the performance comparison, we adopt the conventional TDMA system, in which each UE is served using MRT beamforming in each dedicated time slot without a RIS. Figure 3 shows the capacity for each UE and time slot under an instantaneous channel when the transmit SNR is 5 dB, i.e., \(\rho=5\) dB. The dotted line in Figure 3a is the required capacity, \(\mathbf{C}_{req}\), and time slots are sequentially allocated to UEs that are sorted in increasing order of channel gain, \(\|\mathbf{h}\|^{2}\). For example, time slot 1 is allocated to the weakest-channel-conditioned UE, and time slot 10 is allocated to the strongest-channel-conditioned UE in both TDMA systems. As shown in Figure 3a, in the conventional TDMA, three UEs, i.e., the indexes of UE, 1, 2, and 3, are unsatisfied with the required capacity. In the proposed RC-TDMA, these UEs' capacities are significantly improved and are satisfied with the required capacity. This is because the weak-channel-conditioned UEs are additionally served in cooperative time slots with the strong-channel-conditioned UEs. As shown in Figure 3b,  
the capacities of time slots 5, 8, and 10 in the RC-TDMA are significantly higher than the others because these slots are cooperative time slots. In other words, a pair of UEs, i.e., the weak- and strong-channel-conditioned UEs, are served simultaneously in the cooperative time slots. On the contrary, in the conventional TDMA, the capacity of each UE is the same as the capacity of each time slot because there is no additional cooperative transmission. Figure 4 shows the remaining required capacities, i.e., \(\mathbf{C}_{short,RIS}\) and \(\mathbf{C}_{short,BS}\), according to the transmit SNR. As mentioned in Section 2.3, the number of cooperative time slots is determined as a minimum value of either the number of weak-channel-conditioned UEs or the number of strong-channel-conditioned UEs. In the low SNR region, i.e., between \(-4\) dB and \(0\) dB, both TDMA systems show a similar remaining required capacity because most UEs are weak-channel-conditioned. Conversely, In the high SNR region, i.e., between \(10\) dB and \(16\) dB, both TDMA systems show a similar remaining required capacity because most UEs are strong-channel-conditioned. In both cases, there are few opportunities to set the cooperative slots in the RC-TDMA. In the moderate SNR region, i.e., the range between \(0\) dB and \(10\) dB, the RC-TDMA shows lower remaining required capacity compared with the conventional TDMA due to the opportunities to perform RIS-assisted transmission in the cooperative time slots. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of transmit antennas at BS, \(M\) & 4 \\ \hline Total number of UEs, \(K\) & 10 \\ \hline Total number of time slots, \(T\) & 10 \\ \hline Number of passive reflecting elements, \(N\) & 64 \\ \hline Distance between BS and RIS & 500 m \\ \hline Frequency band & 800 MHz \\ \hline Rician factor & 3 dB \\ \hline Power consumption at BS, \(P_{c}\tau\), \(0\leq\tau\leq 1\) \\ \hline Required SINR, \(\gamma_{req}\) & 10 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 3: Capacity comparison: (**a**) capacity per UE (**b**) capacity per time slot.