## 2 System Model  
The system model is shown in Figure 1, which depicts an FD C-NOMA relaying network consisting of one base station (S), one FD relay (R), and \(N\) pieces of user equipment (UEs). In this network, both the base station and each UE are equipped with a single antenna, while the relay is equipped with one isolate transmit and one isolated receive antenna. Each UE uses a low-resolution ADC for analog-to-digital conversion. We assume that all channels are Rayleigh fading and consider the existence of channel estimation errors. There are no direct links between the BS and UEs due to the obstruction of obstacles. Figure 1: System model of FD C-NOMA relaying system without direct link. Based on the NOMA protocol, we rearrange the \(N\) users according to the estimate of channel gains in the second phase. We denote \((\hat{h}_{1},\cdots,\hat{h}_{N})\) as the order statistic of \((\hat{f}_{\text{RU}_{1}},\cdots,\hat{f}_{\text{RU}_{N}})\) in modulus. \(|\hat{h}_{n}|\) is the \(n\)th-smallest value in \(\{|\hat{f}_{\text{RU}_{1}}|,\cdots,|\hat{f}_{\text{RU}_{N}}|\}\). Then, we have \(|\hat{h}_{1}|\leq\cdots\leq|\hat{h}_{N}|\). Here and in what follows, we shall denote the user corresponding to \(\hat{h}_{n}\) as the \(n\)th user or user \(n\) (\(n\in N\)). According to the channel estimation model of block fading in [20], we assume that all channels are quasi-static Rayleigh-fading channels. All the channels are assumed to be Rayleigh block-fading channels because the channel coefficients are constant on a block and they only change between each block. Each channel coefficient \(h\) is a sum of its estimate and the estimation error, which can be written as  
\[h=\hat{h}+\epsilon_{h}, \tag{1}\]  
where \(\hat{h}\sim\mathcal{CN}(0,\sigma_{h}^{2})\) is the estimate of the channel coefficient \(h\) and \(\epsilon_{h}\sim\mathcal{CN}(0,\sigma_{\epsilon_{h}}^{2})\) is the corresponding estimation error, assuming the channel estimate and estimation error are uncorrelated. Let \(h_{\text{SR}}\sim\mathcal{CN}(0,\tilde{\beta}_{\text{SR}})\) denotes the channel coefficient from S to R. \(h_{\text{RU}_{n}}\overset{\text{i.i.d}}{\sim}\mathcal{CN}(0,\tilde{\beta}_{ \text{RU}})\) denotes the independently identical distribution channel coefficients between R and \(N\) users. Then, we have  
\[h_{\text{SR}} =\hat{h}_{\text{SR}}+\epsilon_{\text{SR}} \tag{2}\] \[h_{\text{RU}_{n}} =\hat{h}_{\text{RU}_{n}}+\epsilon_{\text{RU}_{n}}\]  
where the channel estimation error term \(\epsilon_{\text{SR}}\sim\mathcal{CN}(0,\sigma_{\text{SR}}^{2})\) and \(\epsilon_{\text{RU}_{n}}\overset{\text{i.i.d}}{\sim}\mathcal{CN}(0,\sigma_{ \text{RU}}^{2})\). Then, the channel coefficients can be expressed as \(\hat{h}_{\text{SR}}\sim\mathcal{CN}(0,\beta_{\text{SR}})\), where \(\beta_{\text{SR}}=\tilde{\beta}_{\text{SR}}-\sigma_{\text{SR}}^{2}\) and \(\hat{f}_{\text{RU}_{n}}\overset{\text{i.i.d}}{\sim}\mathcal{CN}(0,\beta_{ \text{RU}})\), where \(\beta_{\text{RU}}=\tilde{\beta}_{\text{RU}}-\sigma_{\text{RU}}^{2}\). Here, we assume that the variables above in the first and second phases are mutually uncorrelated. In the first phase, the base station transmits the superimposed signal to the relay. The transmit signal is denoted as  
\[s_{\text{S}}=\sqrt{P_{\text{S}}}\sum_{n=1}^{N}\sqrt{a_{n}}x_{n} \tag{3}\]  
where \(P_{\text{S}}\) is the transmission power at the base station S, \(a_{n}\) is the power allocation coefficient for user \(n\), and \(x_{n}\) is the information signal transmitted to user \(n\) with unit energy, i.e., \(\mathbb{E}|x_{n}|^{2}=1\), \(n\in N\). The power coefficients are subjected to \(\sum_{n=1}^{N}a_{n}=1\) and \(a_{1}\geq\cdots\geq a_{N}\).