## 2 System Model
The SU set of \(MG_{i}\) is denoted by \(\mathcal{S}_{i}=\{SU_{i,k_{i}}|1\leq k_{i}\leq s_{i}\}\), where \(SU_{i,k_{i}}\) denotes the \(k_{i}\)-th SU from \(MG_{i}\), and \(s_{1}+s_{2}=C_{1}(M_{1}+M_{2})\). The corresponding channel gain set is \(\mathcal{H}_{\mathcal{S}_{i}}=\{H_{i,k_{i}}|1\leq k_{i}\leq s_{i}\}\), where \(H_{i,k_{i}}=\left|h_{i,k_{i}}\right|^{2}\gamma_{i,k_{i}}^{-\beta}\). Elements in \(\mathcal{H}_{\mathcal{S}_{i}}\) are ranged in descending order. \(h_{i,k_{i}}\) represents small scale channel fading. \(\gamma_{i,k_{i}}^{-\beta}\) is path loss. \(\gamma_{i,k_{i}}\) is the distance from BS to \(SU_{i,k_{i}}\). \(\beta\) is path loss parameter. The smallest channel gain of \(\mathcal{H}_{\mathcal{S}_{i}}\) is \(H_{i,s_{i}}\). Without loss of generality, \(H_{1,s_{1}}>H_{2,s_{2}}\) is assumed. \(\mathcal{H}_{\mathcal{S}_{2}}^{w}=\{H_{2,k_{2}}|H_{2,s_{2}}\leq H_{2,k_{2}}<H_ {1,s_{1}}\}\) represents the worst channel gain subset of \(\mathcal{H}_{\mathcal{S}_{2}}\). The corresponding user set is denoted by \(\mathcal{S}_{2}^{w}\). Therefore, \(\mathcal{H}_{\mathcal{S}_{2}}^{w}<\mathcal{H}_{\mathcal{S}_{1}}\). \(\mathcal{S}_{1}\) and \(\mathcal{S}_{2}^{w}\) constitute a subgroup pair. The required signals of two subgroups are superimposed and transmitted on the system frequency band by NOMA technology. The transmission signal of BS in the first sub-slot is  
\[X_{T_{1}}=\sqrt{\alpha_{1}P}x_{1}+\sqrt{\alpha_{2}P}x_{2}, \tag{1}\]  
where \(P\) is the transmission power of BS. \(x_{i}\) is the required signal of \(MG_{i}\). \(\alpha_{1}\) and \(\alpha_{2}\) are the power allocation factors (PAFs) of the paired subgroups, \(\alpha_{1}+\alpha_{2}=1\). Because \(\mathcal{H}_{\mathcal{S}_{2}}^{w}<\mathcal{H}_{\mathcal{S}_{1}}\), \(0<\alpha_{1}<\alpha_{2}<1\). In OMS, in order to guarantee successful reception, for two required signals, the modulation and coding schemes (MCSs) of BS are both selected according to the least channel gain of subgroup pair, i.e., \(H_{2,s_{2}}\). In the receiving end, after the signal allocated with large PAF is decoded successfully, the required signal can be achieved directly (corresponding to \(x_{2}\)) or after successive interference  
Figure 1: System model of cooperative multicast (COM)-based non-orthogonal multiple access (NOMA). One circle represents a multicast group user. The right side area represents the required signal. When the required signal is \(x_{1}\) or \(x_{2}\), this user belongs to \(MG_{1}\) or \(MG_{2}\) separately. The left side area represents user’s reception signal. When the left side area is filled with NOMA signaling, this user is a successful user (SU). Otherwise, the user is an unsuccessful user (USU). From the perspective of received NOMA signaling, two MGs are regarded one quasi-multicast group (MG). cancellation (SIC) (corresponding to \(x_{1}\)). Therefore, the signal-and-interference-plus-noise ratio (SINR) threshold is  
\[SINR_{\mathcal{S}_{2}}=\frac{\alpha_{2}P\big{|}h_{2,s_{2}}\big{|}^{2}\gamma_{2,s _{2}}^{-\beta}}{\alpha_{1}P\big{|}h_{2,s_{2}}\big{|}^{2}\gamma_{2,s_{2}}^{-\beta }+2N_{0}}, \tag{2}\]  
where \(N_{0}\) is the power of additive white Gaussian noise (AWGN) with variance \(\delta_{n}^{2}\), and \(N_{0}=B\delta_{n}^{2}\). \(B\) is the bandwidth originally allocated to each MG in OFDMA. Because COM-NOMA occupies the bandwidth allocated to two MGs, the power of AWGN is \(2N_{0}\). Since users in \(\mathcal{S}_{2}\setminus\mathcal{S}_{2}^{w}\) own better channel conditions than those in \(\mathcal{S}_{2}^{w}\), they can decode \(x_{2}\), too. Simultaneously, it is assumed that the reception signal is abandoned by the remaining users (i.e., USUs), if only it is failed to be received. To sum up, after the first stage of COM-NOMA, each user in \(\mathcal{S}_{i}\) obtains the NOMA signalling. In the second stage, SU as candidate UR is selected by USU. UR conveys the NOMA signalling to USU.