# Multi-User Scheduling for 6G V2X Ultra-Massive MIMO System
## 2 System Model  
### G V2X Ultra-Massive MIMO System Model Based on Multi-User Scheduling  
In this section, we consider a typical 6G V2X communication scenario, as shown in Figure 1, and the ultra-massive MIMO downlink system in the 6G V2X autonomous scenario shown in Figure 2. The system consists of a base station (BS), a roadside unit (RSU), and vehicles connected to the base station (BS). BS and RSU are connected by optical fiber. The RSU (transmitting end) is equipped with \(N_{t}\) antennas and the set of vehicles is \(\mathrm{N}=\{1,\ 2,\ \ldots,\ k\}\), where each vehicle user is equipped with \(N_{t}\) receiving antennas and multiple sensors. The system can schedule \(\mathrm{R}=\{1,\ 2,\ \ldots,\ R\},\mathrm{R}\subset\mathrm{N}\) vehicles each time. In the downlink of the system with the assumption that the channel state information (CSI) is available, the maximum number of transmission data streams that each user can support is \(N_{s}\), the total number of data streams sent by the base station is \(RN_{s}\). This paper assumes that the user channel information is known at the transmitter and receiver. In the time division duplex mode, the base station can obtain the user's channel information through uplink channel estimation. In the frequency division duplex mode, at the beginning of each communication time slot, the user uses the feedback link to obtain the user's channel information. The channel information is fed back to the transmitting end, and the transmitting end selects and designs the corresponding precoding matrix for users based on the channel feedback information and then communicates with the selected users. Figure 1: 6G V2X classic communication scenario. It can be seen from Figure 2 that the original signal is transmitted through the precoder at the antenna end and received by the receiving antenna of the receiving end through the channel. The received signal passes through the combiner to eliminate the interference between the user sub-channels, and finally undergoes signal processing to obtain the transmitted signal vector. At the BS side, the transmitted data information is given as  
\[\mathbf{s}=\sum_{k=1}^{R}\mathbf{F}_{k}\mathbf{s}_{k} \tag{1}\]  
where \(\mathbf{s}\in\mathbb{C}^{(R\times N_{s})\times 1}\) denotes the original transmission symbol vector and is such that \(E\big{\{}\mathbf{s}\mathbf{s}^{H}\big{\}}=\mathbf{I}_{\mathbf{R}N_{s}}\), \(\mathbf{s}_{k}\in\mathbb{C}^{N_{s}\times 1}\) is the original signal vector sent by the RSU to user \(k\) with \(E\big{\{}\mathbf{s}_{k}\mathbf{s}_{k}^{H}\big{\}}=\mathbf{I}_{N_{s}}\), and \(\mathbf{F}_{k}\in\mathbb{C}^{N_{t}\times N_{t}}\) is the precoding matrix of user \(k\) with \(\left\|\mathbf{F}_{k}\right\|^{2}=1\), which is the unitary matrix. If the vehicle has perfect time and frequency synchronization for each time slot \(t\), the received signal of user \(k\) after passing through the channel is expressed as  
\[\mathbf{y}_{k}(t)=\mathbf{H}_{k}(t)\mathbf{F}_{k}\mathbf{s}_{k}+\sum_{i=1,j \
eq k}^{R}\mathbf{H}_{k}(t)\mathbf{F}_{i}\mathbf{s}_{i}+\mathbf{n}_{k}(t),k =1,2,\ldots R \tag{2}\]  
where the first item denotes useful data for user \(k\), \(\mathbf{H}_{k}(t)\in\mathbb{C}^{N_{t}\times N_{t}}\) is the channel matrix between the RSU and user \(k\) in the \(t^{th}\) time slot, and each element of the matrix obeys a Gaussian distribution with zero mean and unit variance. The second item denotes interference from other user data to the user data. The third item \(\mathbf{n}_{k}(t)\in\mathbb{C}^{N_{t}\times 1}\) is additive white Gaussian noise of \(\mathcal{CN}\big{(}0,\sigma_{k}^{2}\mathbf{I}\big{)}\). The received signal obtained after the combiner is given as  
\[\widetilde{\mathbf{y}}_{k}(t)=\mathbf{W}_{k}^{\ H}\mathbf{H}_{k}(t)\mathbf{F }_{k}\mathbf{s}_{k}+\sum_{i=1,j\
eq k}^{R}\mathbf{W}_{k}^{\ H}\mathbf{H}_{k}(t )\mathbf{F}_{i}\mathbf{s}_{i}+\mathbf{W}_{k}^{\ H}\mathbf{n}_{k}(t),k=1,\ 2,\ \ldots R \tag{3}\]  
where \(\mathbf{W}_{k}\) is combiner of user \(k\). Figure 2: Multi-user scheduling for ultra-massive MIMO systems.