# Computational-Intelligence-Based Spectrum-Sharing Scheme for NOMA-Based Cognitive Radio Networks
## 2 System Model and Problem Formulation  
Consider a dual-hop cooperative spectrum-sharing network as shown in Figure 1, consisting of primary and secondary networks. The primary network comprises a primary base station (PBS) and a primary receiver \(Q\), whereas the secondary network consists of a set of \(K\) potential secondary users \(\Gamma=\{SU_{k}\}_{k=1}^{K}\) and a NOMA-based secondary relay SR. All the channels follow Rayleigh block fading. The signals required by \(Q\) and \(SU_{k}\) are denoted by \(x_{0}\) and \(x_{k}\), respectively. The DL between the primary transmit-receive pair is absent due to deep shadowing, as a result of which the PBS receives assistance from the SR to reach its intended receiver \(Q\). In addition, one best SU from the set of potential SUs, i.e., \(SU_{sel}\), is selected to retransmit the primary signal \(x_{0}\) to \(Q\). In this scenario, NOMA being a combination of SIC and SC techniques is the best choice for simultaneously transmitting the primary and secondary signals. In the overlay scenario of CRNs, the NOMA-based secondary relay has the potential to enhance the performance of the primary network in shadowing areas and provide high spectral efficiency. NOMA ensures user fairness through variable power allocation, taking into consideration the distance between the  
\begin{table}
\begin{tabular}{c c} \hline
**Notation** & **Definition** \\ \hline \(SU_{k}\) & \(k^{th}\) secondary user \\ \(SU_{sel}\) & Selected SU for retransmission of \(x_{Q}\) \\ \(\Gamma\) & Set of potential SUs \\ \(K\) & Number of potential SUs \\ \(Q\) & Primary Receiver \\ \(x_{0}\) & Signal required by \(Q\) \\ \(x_{k}\) & Signal required by \(SU_{k}\) \\ \(x_{SR}\) & Signal received by SR \\ \(x_{I}\) & Composite signal transmitted by SR \\ \(g_{0}\) & Link gain between SR and \(Q\) \\ \(g_{k}\) & Link gain between SR and \(SU_{k}\) \\ \(h_{0}\) & Link gain between PBS and SR \\ \(h_{k}\) & Link gain between \(SU_{k}\) and \(Q\) \\ \(h_{sel}\) & Link gain between \(SU_{sel}\) and \(Q\) \\ \(P_{0}\) & Transmit power of PBS allocated to \(Q\) \\ \(P_{S}\) & Transmit power of SR \\ \(P_{k}\) & Power allocated to \(SU_{k}\) \\ \(P_{sel}\) & Transmit power of \(SU_{sel}\) \\ \(\gamma_{0}\) & Rate threshold required by \(Q\) \\ \(\gamma_{k}\) & Rate threshold required by \(SU_{k}\) \\ \(\lambda_{0}\) & Power allocation coefficient of \(Q\) \\ \(\lambda_{k}\) & Power allocation coefficient of \(SU_{k}\) \\ \(R_{p}\) & Achievable rate at SR \\ \(R_{k}\) & Achievable rate at \(SU_{k}\) \\ \(R_{Q}\) & Achievable rate at \(Q\) \\ \(\sigma^{2}\) & Noise variance \\ \(\rho\) & Probability of fitness \\ \hline \end{tabular}
\end{table}
Table 2: Notations.  
transmit-receive pair and the channel conditions. Thus, users at long distances or having poor channel conditions are allocated more power to achieve the desired total throughput.  
Without loss of generality, the following assumptions are made.  
* Each node is equipped with a single antenna and thus operates in a half-duplex mode.
* Distance between SR and \(Q\) is greater than the distance between SR and any \(k^{th}\) SU, hence the channel gains are arranged in the order of \(\left\lvert g_{0}\right\rvert\leq\left\lvert g_{1}\right\rvert\leq\ldots\leq \left\lvert g_{K}\right\rvert\).
* The whole communication process is controlled by NOMA relay SR with necessary control signals.
* Background noise is modeled as Additive White Gaussian Noise (AWGN) with zero mean and variance \(\sigma^{2}\).