# RIS-Assisted Cooperative Time-Division Multiple Access
## 2 RIS-Assisted Cooperative Time-Division Multiple Access  
### System Model  
We consider a multiuser downlink TDMA, which consists of \(K\) UEs, one RIS, and one BS, as shown in Figure 1. Each UE, RIS, and BS has a single antenna, \(N\) passive reflecting elements, and \(M\) transmit antennas, respectively. A frequency flat block fading channel is assumed among them so that each channel is constant within a block. The total number of time slots in a block is \(T\), the total number of UEs in a block is \(K\), and each time slot is allocated to each UE, as shown in Figure 2. Since each UE has a dedicated time slot, the total number of UEs is the same as the total number of time slots, i.e., \(T=K\). In conventional TDMA systems, each UE is served once in the dedicated time slot. However, in the proposed TDMA system, the UE, which does not meet the required SINR, can be served once more, i.e., two UEs can simultaneously be served in a time slot dedicated to the UE that satisfies the required SINR. When serving two UEs in the time slot, the RIS turns on and then assists the data transmission of the UE that d  
Figure 1: System model for RIS-assisted cooperative time-division multiple access. Figure 2: An example of time slot allocation for RIS-assisted cooperative time-division multiple access. SINR. The proposed system's primary goal is that all users' required SINR is guaranteed as much as possible by opportunistic use of the RIS for cooperative transmission. Estimation methods for wireless channels with RISs are being actively studied [15; 16; 17; 18; 19; 20]. However, it is difficult to estimate the channels between BS-RIS and RIS-UE separately. Thus, a randomly given phase shift on the RIS is used in a block, which enables a UE to estimate the effective channel for BS-RIS-UE. Since each UE can estimate the effective channel from BS and feed it back to BS, it can be assumed that BS has perfect CSI for the effective channel from BS to each UE. In the proposed RC-TDMA system shown in Figure 1, the BS schedules UEs in increasing order of channel gain so that the earlier time slots are allocated to the UEs with a weak channel condition. Inversely, the later time slots are allocated to UEs with a strong channel condition. If some UEs allocated to the earlier time slots cannot satisfy the required capacity, they can have an opportunity to receive the remaining data at the later time slots. In other words, their data can be transmitted at the later slot with the strong-channel-conditioned UEs' data. Figure 2 shows an example of time slot allocation for the RC-TDMA. In this example, \(UE_{1}\) and \(UE_{2}\) are the weak-channel-conditioned UEs. Thus, BS allocates them to the front time slot. Since the required capacities of UEs cannot be guaranteed, time slot 1 and time slot 2 are solely dedicated to \(UE_{1}\) and \(UE_{2}\), respectively. Subsequently, in the case of \(UE_{K-1}\) and \(UE_{K}\), if their required capacities can be sufficiently guaranteed, BS performs user pairing between the strong-channel-conditioned UE (i.e., \(UE_{K-1}\) or \(UE_{K}\)) and the weak-channel-conditioned UE (i.e., \(UE_{1}\) or \(UE_{2}\)) and serves two scheduled UEs at the same time for guaranteeing the required capacity of the weak-channel-conditioned UE as much as possible. These slots are called cooperative time slots. The other time slots, except the cooperative time slots, are called non-cooperative time slots. At this time, time slots \(K-1\) and \(K\) are dedicated slots for \(UE_{K-1}\) and \(UE_{K}\), respectively. Thus, the data transmission for \(UE_{1}\) and \(UE_{2}\) must not interfere with \(UE_{K-1}\) and \(UE_{K}\). In the non-cooperative time slots, RIS maintains a turn-off for power efficiency. In the cooperative time slots, the RIS turns on and performs a passive relay to maximize the capacities of two UEs. Hereafter, the indexes of both UE and time slot are omitted for simplicity.