# 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 OMA and NOMA  
In the non-CR transmission mode, PT transmits a packet while the SU stays silent and eavesdrop on PU transmission. The received packet at PR, ST and SR are given, respectively, by:  
\[y_{PR}^{\text{non-CR}} =\sqrt{P_{P}}h_{PP}x_{P}+n_{PR}, \tag{1}\] \[y_{ST}^{\text{non-CR}} =\sqrt{P_{P}}h_{PS}x_{P}+n_{ST},\] (2) \[y_{SR}^{\text{non-CR}} =\sqrt{P_{P}}h_{PR}x_{P}+n_{SR}, \tag{3}\]  
where \(x_{P}\) is PU's packet, \(P_{P}\) is PT's transmit power, \(h_{PP}\sim(0,\lambda_{PP})\), \(h_{PS}\sim(0,\lambda_{PS})\) and \(h_{PR}\sim(0,\lambda_{PR})\) are the channel coefficients of interference links \(\text{PT}\rightarrow\text{PR},\text{ PT}\rightarrow\text{ST}\) and \(\text{PT}\rightarrow\text{SR}\), respectively, and \(n_{PR}\sim(0,\sigma^{2})\), \(n_{ST}\sim\left(0,\sigma^{2}\right)\) and \(n_{SR}\sim(0,\sigma^{2})\) are AWGN at the receivers PR, ST and SR, respectively. Figure 1: System model. If PR sends an ACK, as a reword, the transmission is switched to underlay OMA mode. In this case, PT transmits a new packet while the SUs transmits their own packet. In underlay CRN, the interference power at PR is not allowed to exceed the maximum interference threshold, \(I_{th}\). Assuming that the maximum allowable transmit power of ST is \(P_{max}\), the transmit power of ST is constrained as [13; 19; 20]:  
\[P_{S}=min\Bigg{\{}\frac{I_{th}}{\left|\mu_{SP}\right|^{2}},P_{max}\Bigg{\}} \tag{4}\]  
where \(h_{SP}\sim(0,\lambda_{SP})\) is the channel coefficient of interference link \(\mathrm{ST}\rightarrow\mathrm{PR}\). In the underlay OMA mode, PT transmits a new packet under the SU's interference while ST transmits its own packet. The received packet at PR and SR are given by:  
\[y_{PR}^{\mathrm{underlay}} =\sqrt{P_{p}}h_{pp}x_{P}+\sqrt{P_{S}}h_{SP}x_{S}+n_{PR}, \tag{5}\] \[y_{SR}^{\mathrm{underlay}} =\sqrt{P_{p}}h_{pp}x_{P}+\sqrt{P_{S}}h_{SS}x_{S}+n_{SR}, \tag{6}\]  
where \(x_{S}\) is SU's packet, \(h_{SS}\sim(0,\lambda_{SS})\) is the channel coefficients of interference links \(\mathrm{ST}\rightarrow\mathrm{SR}\). In the underlay OMA mode, if PR sends a NACK, PT will retransmit the PU's packet failed previously while SUs remain silent. If the PU's packet is failed after retransmission, the packet will be lost. Otherwise, if PR replies by a NACK, the transmission is divided into two cases: (1) if ST correctly decodes the PU's packet, transmission switches to overlay NOMA mode; otherwise, (2) if ST fails to decode the PU's packet, PT retransmits that the PU's packet failed previously while SU stays silent. (1) If ST correctly decodes the PU's packet, transmission switches to overlay NOMA mode. In this case, conditioned on ST succeeding in decoding \(x_{P}\), ST combines \(x_{P}\) with its own signal \(x_{S}\) by using NOMA principle. Then, ST transmits the superimposed signal \(\sqrt{\alpha_{P}P_{S}}x_{P}+\sqrt{\alpha_{S}P_{S}}x_{S}\) to PR and SR simultaneously. The received packet at PR and SR are given by:  
\[y_{PR}^{\mathrm{overlay,NOMA}}=\sqrt{\alpha_{P}P_{S}}h_{SP}x_{P}+\sqrt{\alpha_ {S}P_{S}}h_{SP}x_{S}+n_{PR}, \tag{7}\]  
Figure 2: The flow chart of cooperative cognitive radio network based on OMA/NOMA. \[y^{\text{overlay,NOMA}}_{SR}=\sqrt{\alpha_{P}P_{S}}h_{SS}x_{P}+\sqrt{\alpha_{S}P_{S} }h_{SS}x_{S}+n_{SR}, \tag{8}\]  
(2) If ST fails to decode the PU's packet, PT retransmits that the PU's packet failed previously while SU remains silent. The received packet at PR is similar for non-CR transmission mode. Based on the above description, the operation of the proposed spectrum sharing protocol is specified by four states, as illustrated in \[y_{ST}^{\text{non-CR}} =\sqrt{P_{P}}h_{PS}x_{P}+n_{ST},\]0 These states are described as follows:  
State S1: The PU transmits a packet while SU stays silent and eavesdrops on PU's transmission. The next state is S2 if an ACK is received from PR, otherwise PR sends a NACK and the next state moves to S3 or S4 depending on whether ST decodes the PU's packet correctly.