## 1 Introduction  
With the commercialization of fifth-generation (SG) wireless technology and the development of beyond-fifth-generation (B5G) and sixth-generation (6G) wireless technology, the introduction of various emerging high-capacity applications and the dramatic rise in the demand for and use of wireless data has put a huge burden on existing wireless networks. Non-orthogonal multiple access (NOMA) has been identified as a critical key technology in the next generations of wireless communications because of its ability to improve spectrum efficiency, reduce latency, and balance system throughput and user fairness [1]. Previously, traditional orthogonal multiple access (OMA) schemes, such as frequency division multiple access (FDMA), time division multiple access (TDMA), code division multiple access (CDMA), and orthogonal frequency division (OFDMA) were used for the air interface. The number of users served by these schemes is limited to the maximum number of available orthogonal resources. However, NOMA can be used to break the orthogonal resource limit and thus serve more users at the cost of increased receiver complexity [2]. NOMA technology introduces two domains, i.e., power-domain NOMA and code-domain NOMA. In a similar way to CDMA, code-domain NOMA is differentiated by assigning each user different codes, except that non-orthogonal time-frequency resources are used for transmission. In power-domain NOMA, different power levels are assigned to different users. Once received, the signal is decoded at the receiver using successive interference cancellation (SIC), which decodes each user's signal in turn according to its power level until the desired signal is obtained [3]. Although code-domain NOMA has better performance compared to power-domain NOMA, it requires more bandwidth and is more complex to implement. Cooperative relay is seen as a promising solution to effectively combat the shadowing effect in order to extend radio coverage while significantly increasing channel capacity. The signal-forwarding methods used by the relay nodes can be divided into amplify-and-forward (AF) and decode-and-forward (DF). Combining the technical advantages of cooperative relay and NOMA, cooperative NOMA (C-NOMA) is proposed to further improve transmission efficiency [4; 5; 6]. In [6], the performance of the NOMA system over Rician fading channels was investigated, and the expression of the average achievable rate was obtained. The operation modes of transceivers can be divided into half-duplex (HD) and full-duplex (FD) modes. Conventional wireless communication systems often rely on HD operation, resulting in reduced resource utilisation. FD mode enables transceivers to simultaneously transmit and receive signals on the same frequency band, which has the potential to double the spectrum efficiency and is considered a promising technology for application in the next generation of wireless communication systems [7; 8; 9]. However, the excessive power difference between the device's own transmitted signal and the low-power received signal arriving from the remote transmit antenna generates loopback interference (LI) between the receiver and the transmitter. The LI causes the capacity of the FD system to be reduced to even less than the capacity of the HD system. Nevertheless, with the continuous development of interference cancellation chain technology consisting of an antenna domain, analogue circuit domain, and digital circuit domain, loopback interference can be suppressed to an acceptable range at the cost of increased receiver complexity [10; 11]. In order to further improve the spectral efficiency of C-NOMA systems and reduce the time slot required for transmission, the use of FD mode has been proposed [12; 13; 14; 15].