## 1 Introduction
### Related Work  
D2D communication shares cellular spectrum resource with cellular users in two modes: underlay and overlay. Based on the underlay cellular spectrum-sharing scheme, the cellular users and the D2D devices simultaneously access the same spectrum band. Hence, the interference mitigation between D2D communication and cellular transmission is inevitable and significant [5; 6; 7; 8], when underlay cellular spectrum-sharing scheme is exploited. Considering the interference generated by the D2D communications, a fair distribution of the cellular resources shared by the D2D transmission pairs was developed with the aid of [PERSON]'s fairness index method [5]. Moreover, in order to minimize the interference caused by multiple D2D transmission pairs which simultaneously share a single cellular link, a power control scheme was proposed for supporting underlay D2D communications [6; 7; 8]. Aiming for minimizing the interference generated by multiple D2D transmission pairs which share the spectrum resource in multiple cells, a spectrum-sharing scheme was proposed in [9]. The works in the above literature [5; 6; 7; 8; 9] focused on the mitigation of the interference between the underlay D2D communication and cellular transmission. Based on the overlay spectrum-sharing scheme, the cellular users and D2D users intend to access different channels. Hence, the interference between the D2D and cellular users were not considered in [10; 11; 12]. Without considering the interference between users, improving spectral efficiency in overlay mode is the main goal [10; 11; 12]. Based on cellular spectrum-sharing scheme, the benefits of the D2D-enabled cellular network may be improved with the aid of cooperative communications, where the relay node (RN) forwards the source's data. More explicitly, the cell edge user (EU) may suffer from the poor link quality due to high path loss and deep path fading. However, the D2D transmitter (DT) may be capable of improving the quality of service (QoS) for the cellular users by providing cooperation assistance [13; 14]. Based on the underlay cellular spectrum-sharing scheme, many meritorious contributions have been made for improving the performance of the D2D-enabled cellular network and simultaneously reducing the interference generated by the underlay D2D communication with the aid of cooperative communications [4; 15; 16; 17; 18]. However, few existing works focus on the performance of the D2D-enabled cellular network supporting overlay cellular spectrum-sharing strategies and cooperative transmission [19; 20; 21]. Based on the overlay spectrum-sharing scheme, the cellular users and D2D users intend to access different channels. Hence, the interference between the D2D and cellular users were not considered in [13; 14; 19; 20; 21]. Aiming for maximizing system capacity, an overlay spectrum-sharing scheme was proposed for supporting millimeter wave transmitting and D2D communication in [19]. The work in [20] jointly considered incremental relay technology and overlay spectrum-sharing scheme to allow the cellular users to share their transmission resources with the D2D users, instead of treating D2D as interference. Based on the overlay spectrum-sharing scheme, a cooperative D2D communication framework was proposed in [21] for the sake of maximizing transmission rate. However, in order to support the combination of the overlay scheme and cooperative communication, the works in [13; 14; 19; 20; 21] performed the D2D transmissions and the cooperative transmissions within different time slots. Compared to the underlay scheme, the spectrum efficiency of the cooperative overlay schemes in [13; 14; 19; 20; 21] may be reduced. Hence, more efforts are required to improve the spectrum efficiency of the cellular network supporting overlay D2D communication and cooperative communication. Aiming for improving spectral efficiency, Non-Orthogonal Multiple Access (NOMA) superposes multiple users in the power domain [22; 23].