# Two-Way Transmission for Low-Latency and High-Reliability 5G Cellular V2X Communications
## 2 System Model of V2X Communications  
We consider a two-way relay-assisted NOMA system as depicted in Figure 1. A pair of vehicles, \(\mathrm{D}_{1}\) and \(\mathrm{D}_{2}\), participate in two-way communications via the RSU following the principle of NOMA. Let \(P_{s}\) denote the transmit power of vehicles \(\mathrm{D}_{1}\) and \(\mathrm{D}_{2}\), while \(P_{r}\) denotes the transmit power of RSU. We suppose \(P_{s}\) and \(P_{r}\) are equal for a simple analysis, i.e., \(P_{s}=P_{r}=P\). Let \(x_{1}\) and \(x_{2}\) denote the transmit signals with unit power of vehicles \(\mathrm{D}_{1}\) and \(\mathrm{D}_{2}\), respectively. The RSU plays the role of relay, which transfers the signal from \(\mathrm{D}_{1}\) to \(\mathrm{D}_{2}\) and vice versa within its coverage. The RSU operates in the decode-and-forward half-duplex relaying mode. Note that the proposed transmission scheme can be adopted in the communication from vehicle to vehicle via infrastructure node (relay node). We suppose that the RSU is able to share the same frequency resource with the BS. We also assume that the direct link between two vehicles is weak and ignored due to a large path loss. Vehicles are equipped with multiple antennas, where \(\mathrm{D}_{1}\) and \(\mathrm{D}_{2}\) have \(N\) antennas and \(K\) antennas, respectively. Channel gains between the \(n\)-th antenna of \(\mathrm{D}_{1}\) and RSU for uplink and downlink are denoted by \(h_{n,1}\) and \(g_{1,n}\), respectively, \(n=1,2,...,N\). In the same manner, we denote \(h_{k,2}\) and \(g_{2,k}\), \(k=1,2,...,K\)as channel gains between the \(k\)-th antenna of \(\mathrm{D}_{2}\) and RSU for uplink and downlink, respectively. We let \(h_{n,1}\), \(n=1,\cdots,N\), and assume that they are independent and identically distributed (i.i.d.) Nakagami-m random variables with a fading parameter \(m_{h_{1}}\). In the same manner, \(h_{k,2}\), \(g_{1,n}\), and \(g_{2,k}\) are i.i.d. Nakagami-m distributed with fading parameters \(m_{h_{2}}\), \(m_{g_{1}}\), and \(m_{g_{2}}\), respectively, for all \(k\) and \(n\). We also let \(\lambda_{h_{1}}=\mathbb{E}\left\{\left|h_{n,1}\right|^{2}\right\}\), \(\lambda_{h_{2}}=\mathbb{E}\left\{\left|h_{k,2}\right|^{2}\right\}\), \(\lambda_{g_{1}}=\mathbb{E}\left\{\left|g_{1,n}\right|^{2}\right\}\), and \(\lambda_{g_{2}}=\mathbb{E}\left\{\left|g_{2,k}\right|^{2}\right\}\) for all \(n\) and \(k\). The residual interference signal (IS) caused by ipSIC is also modeled as a Nakagami-m random variable [29]. Let \(f_{1}\) and \(f_{2}\) denote the IS channel coefficients at the RSU and \(\mathrm{D}_{1}\), respectively, where \(\lambda_{f_{1}}=\mathbb{E}\left\{\left|f_{1}\right|^{2}\right\}\) and \(\lambda_{f_{2}}=\mathbb{E}\left\{\left|f_{2}\right|^{2}\right\}\). Then, we define \(\mu_{q}=\frac{m_{q}}{\lambda_{q}}\), where \(q=h_{1},h_{2},g_{1},g_{2},f_{1},f_{2}\). The entire transmission process of NOMA-V2X is divided into two phases. In the first phase, vehicles \(\mathrm{D}_{1}\) and \(\mathrm{D}_{2}\) transmit signals \(x_{1}\) and \(x_{2}\), respectively, with the power of \(P_{s}\) to the RSU. The RSU detects \(x_{1}\) and \(x_{2}\) through a SIC technique, where pSIC or ipSIC are considered. After detecting \(x_{1}\), the RSU subtracts \(x_{1}\) from the received signal and perform the next transmission hop. In the second phase, the RSU transmits the superimposed NOMA signal, combining two signals \(x_{1}\) and \(x_{2}\) to vehicles \(\mathrm{D}_{1}\) and \(\mathrm{D}_{2}\), where \(P_{r}\) is divided by the ratio of \(a_{1}:a_{2}\) to be used for transmitting NOMA signal to \(\mathrm{D}_{2}\) and \(\mathrm{D}_{1}\), respectively. In other words, the RSU uses \(\frac{a_{1}}{a_{1}+a_{2}}P_{r}\) and \(\frac{a_{2}}{a_{1}+a_{2}}P_{r}\) to transmit signals \(x_{1}\) and \(x_{2}\), respectively. We suppose \(\mathrm{D}_{2}\) is farther away from the RSU than \(\mathrm{D}_{1}\), by which the link between \(\mathrm{D}_{1}\) and RSU is stronger than that between \(\mathrm{D}_{2}\) and RSU.