# Hybrid Cooperative Spectrum Sharing Protocols Based on OMA and NOMA in Cognitive Radio Networks
## 2 System Model and Protocol Descriptions
### Hybrid Cooperative Cognitive Radio Networks Based on Pure OMA  
In the hybrid cooperative cognitive radio network of pure OMA, the transmission is also divided into three modes: non-cognitive transmission mode, underlay NOMA mode, and overlay OMA cooperative mode. In the overlay OMA corporative mode, ST only acts as a relay to assist the transmission of PUs, but does not transmit its own packets. The other two modes are the same as the hybrid cooperative cognitive radio network based on OMA/NOMA, so the operation process of overlay OMA mode is only explained here. The flow chart of the hybrid cooperative cognitive radio network based on pure OMA is shown in Figure 2.  
If a NACK is received from PR in the non-CR mode, the transmission is divided into two cases: (1) if ST correctly decodes the PU's packet, transmission switches to overlay OMA mode; and (2) if ST fails to decode the PU's packet, PT will retransmit the PU's packet that failed previously while SUs keeps silent. (1) If ST correctly decodes the PU's packet, transmission mode switches to overlay OMA mode. In the overlay OMA, the ST acts as a cooperative relay and retransmits the PU's packets to PR. The received packet at PR is given by:  
\[y_{PR}=\sqrt{P_{S}}h_{SP}x_{P}+n_{PR}, \tag{12}\]  
(2) If ST fails to decode the PU's packet, PT will retransmit that the PU's packet failed previously while SUs keeps silent. Then, the received packet at PR is the same as the one in non-CR mode. Based on the above description, the operation of the proposed spectrum sharing protocol is specified by four states, as illustrated in Table 2. Specifically, State S\({}_{3}\): in this situation it is redefined as ST transmits PU's packet to PR in the overlay OMA cooperative mode. The next state moves to S\({}_{1}\) irrespective of whether the PR feedback is ACK or a NACK. Other states are defined similar to the situation of OMA/NOMA. The Markov model is the same as the hybrid cooperative cognitive wireless network based on OMA/NOMA, except that the transition probability of state S\({}_{3}\) to S\({}_{1}\) in the model is different. The transition probability of state S\({}_{3}\) to S\({}_{1}\) is defined as \(P_{5}^{\prime}\). Throughput Analysis of Primary and Secondary Users in Hybrid Cooperative Cognitive Radio Network Based on OMA and NOMA  
In non-CR transmission mode, the achieved rates of the channels \(\text{PT}\rightarrow\text{PR}\), \(\text{PT}\rightarrow\text{ST}\) and \(\text{PT}\rightarrow\text{SR}\) are given as:  
\[R_{PT\to PR,x_{p}}^{\text{non-CR}}=log_{2}\Bigg{(}1+\frac{|h_{PP}|^{2}P_{p}}{ \sigma^{2}}\Bigg{)}, \tag{13}\]  
\[R_{PT\to ST,x_{p}}^{\text{non-CR}}=log_{2}\Bigg{(}1+\frac{|h_{PS}|^{2}P_{p}}{ \sigma^{2}}\Bigg{)}, \tag{14}\]  
\[R_{PT\to SR,x_{p}}^{\text{non-CR}}=log_{2}\Bigg{(}1+\frac{|h_{PR}|^{2}P_{p}}{ \sigma^{2}}\Bigg{)}. \tag{15}\]  
In underlay OMA mode, the achieved rates of the channels \(\text{PT}\rightarrow\text{PR}\) and \(\text{ST}\rightarrow\text{SR}\) with interference are given as:  
\[R_{PT\to PR,x_{p}}^{\text{underlay}}=log_{2}\Bigg{(}1+\frac{|h_{PP}|^{2}P_{p }}{|h_{SP}|^{2}P_{S}+\sigma^{2}}\Bigg{)}, \tag{16}\]  
\[R_{ST\to SR,x_{s}}^{\text{underlay}}=log_{2}\Bigg{(}1+\frac{|h_{SS}|^{2}P_{S }}{|h_{PR}|^{2}P_{p}+\sigma^{2}}\Bigg{)}. \tag{17}\]  
In the non-CR mode, if NACK feedback from PR, the transmission is divided into two cases:  
1. If ST can decode the PU's packet, transmission switches to overlay NOMA mode. The achieved rate of the channels \(\text{ST}\rightarrow\text{PR}\) and \(\text{ST}\rightarrow\text{SR}\) are given as: \[R_{ST\to PR,x_{p}}^{\text{overlay,NOMA}}=log_{2}\Bigg{(}1+\frac{|h_{SP}|^{2} \alpha_{P}P_{S}}{|h_{SP}|^{2}\alpha_{S}P_{S}+\sigma^{2}}\Bigg{)},\] (18)  
\[R_{ST\to SR,x_{p}}^{\text{overlay,NOMA}}=log_{2}\Bigg{(}1+\frac{|h_{SS}|^{2} \alpha_{P}P_{S}}{|h_{SS}|^{2}\alpha_{S}P_{S}+\sigma^{2}}\Bigg{)}. \tag{19}\]  
When \(R_{ST\to SR}\geq R_{P}\), SR can correctly decode PU's packet and move it.