## 6 Conclusions  
In this paper, we analyzed the outage performance of cooperative underlay CR-NOMA networks with a novel cooperation involving dedicated relay cooperation and user cooperation. At the end of the first time slot, four possible decoding results were derived at the near user. Accordingly, a two-stage adaptive relay selection and power allocation strategy in the secondary time slot was presented. By discussing the decoding results, four relay selection criteria and the corresponding power allocation coefficients were obtained. Finally, we derived the closed-form expressions of the outage probability for the two secondary users, and revealed the impacts of essential parameters on outage performance of the secondary network, such as transmit power, number of relays, interference threshold, and target data rate. The Monte Carlo simulations verified the correctness of the theoretical analysis. Compared to the existing cooperative scheme without the link U\({}_{1}\)\(\rightarrow\)U\({}_{2}\), the proposed cooperation with a two-stage adaptive relay selection and power allocation strategy can significantly improve the system outage performance when the number of relays is small. Moreover, the proposed strategy improves the rate fairness of users and achieves the optimal value of outage performance for all users by allocating less power to the far user. Furthermore, we also verify that a low target data rate at the receiver side is more conducive to achieving a lower outage probability, which is consistent with the results for the NOMA system presented in [34]. [PERSON] researched the literatures, conceived the study concepts, designed the algorithm, and took charge of the original draft preparation; [PERSON] improved the mathematical models, provided the systematic research and analysis methodology, and edited the manuscript, and supervised the completion of the refinement of the paper; [PERSON] gave valuable suggestions for revision;[PERSON] and [PERSON] completed some numerical simulations, and checked formula deducing and English grammar. All authors have read and agreed to the published version of the manuscript. This research was funded in part by the National Natural Science Foundation of China under Grant 61663024, in part by the Hongliu First Class Discipline Development Project of Lanzhou University of Technology, and in part by the Excellent Postgraduate \"Innovation Star\" Project of Gansu Province under Grant 2021 CXZX-537. The data supporting this article are from previously reported studies and datasets, which have been cited. The authors declare no conflict of interest. The outage probability of cooperative networks with DF relays is defined as the probability that the achievable data rates of relays or users are less than the target data rates [10]. This means that the outage event occurs at U\({}_{2}\) when all relays in the system do not help U\({}_{2}\) achieve its target data rate. From the Law of Total Probability, the outage probability for U\({}_{2}\) can be written as [6; 10]  
\[P_{2}=\sum_{\Theta\in\{11,10,01,00\}}P^{\Theta}_{out,2} \tag{1}\]  
where \(P^{\Theta}\) denotes the probability of the event that a signaling sent by U\({}_{1}\) is \(\Theta\), and \(P^{\Theta}_{out,2}\) represents the outage probability for U\({}_{2}\) in the case of \(\Theta\). Now let us focus on the derivation of \(P^{\Theta}\). Based on Equation (4), the probability of the event that \(\Theta=\)\(11^{\prime}\) is given by  
\[