###### Abstract
A different overlay relay cooperation was proposed in [22] in which a dedicated NOMA-based relay was used to forward assistant signals to primary users and secondary users. However, the above research do not consider the cooperative coexistence of user cooperation and dedicated relay cooperation, nor do they consider the power adaption. Unlike the overlay mode, the underlay mode of CRNs pays more attention to ensuring the performance of secondary networks under interference constraints. In an underlay CR-NOMA system [23], signals of two secondary users were forwarded using the dedicated NOMA-based relay. In [24], authors investigated the performance of two-hop underlay CR-NOMA networks under interference constraints, but using a single relay could not ensure reliable communication at the user side. Thus, extending the model to multi-relay cooperation is necessary. In [25], authors analyzed the outage performance of CR-NOMA networks with AF relays by using the partial relay selection method, and results indicated that the adoption of adaptive power allocation strategy helps to improve system performance. In [26], authors studied the impact of multiple antennas and cooperative NOMA users on the performance of CR-NOMA, in which the multi-antenna base station selected the user with strong channel gain as a relay to help another user with poor channel gain. Results showed that the cell edge user with poor channel gain can benefit from cooperative NOMA and opportunistic relay transmission [26]. Different from the above research, authors in [27; 28] considered the coexistence of direct link and relay-cooperative links between the far user and base station, in which relays existed to compensate for the reduction of reliability and coverage of cognitive networks due to power constraints. However, user cooperation is not considered in [23; 24; 25; 27; 28]. The scenario developed in [29] considered the link from near user to far user in addition to links from relays to far user, but the transmit power constraints were not fully taken into account. However, cooperative CR-NOMA in underlay spectrum sharing mode still has the following problems: (i) most CR-NOMA systems only consider partial interference links; (ii) partial relay selection strategy based on the first hop may not result in the optimal outage performance; (iii) fixed power allocation coefficient cannot guarantee optimal system performance; (iv) the links between near user and relays, near user and far user should be considered, as this can effectively improve communication efficiency. Inspired by [6; 28], this paper investigates adaptive relay selection and power allocation in cooperative underlay CR-NOMA networks by considering mutual interference and constraints between primary network and secondary network. In order to guarantee the reliable transmission of the primary network, transmit powers of secondary source and the selected relay are restricted. The main contributions are summarized as follows:  
* A novel cooperation scheme is established for underlay CR-NOMA networks, where dedicated relay cooperation and user cooperation are used in secondary network to achieve communication between the base station and the far (and near) user. * A two-stage adaptive relay selection and power allocation strategy is proposed to maximize the achievable data rate of the far user and to obtain the optimal power allocation coefficient on the premise of guaranteeing the QoS of near user. Through the proposed strategy, the challenging issue of whether only the far user needs assistance or both the near and the far users need assistance is addressed. * A novel decoding order for successive interference cancellation (SIC) is introduced to the secondary users. Both secondary users can adaptively adjust their decoding order in the second time slot according to the decoding status of the near user in the first time slot, which is different from the existing works that mostly depend on the channel quality.