# I/Q Imbalance and Imperfect SIC on Two-Way Relay NOMA Systems
## 1 Introduction  
The demand for new services and data rate has exploded for wireless communication, due to the growth of data traffic in the mobile Internet. To this end, a higher data rate and massive mobile terminal access are required for the 5 th Generation (5G) systems [1; 2; 3]. Many new technologies such as massive multiple-input multiple-output (MIMO), non-orthogonal multiple access (NOMA), millimetre wave and device-to-device communication have been proposed to meet these demands [4]. Among these techniques, NOMA can significantly improve the spectral efficiency and reduce the system latency. Different from the conventional orthogonal multiple access (OMA), NOMA provides services for multiple users on the same resource by using superposition coding at the transmitter and successive interference cancellation (SIC) at the receiver [5; 6]. Take an example of downlink: signals from the base station (BS) are superimposed and sent to NOMA users. Users with stronger channel gains decodesignals of other users with lower channel gains before decoding their own signals based on the SIC technique [7]. Hence, NOMA can support multiple users with limited resources and improve spectral efficiency, which has attracted considerable attention from academia and industry. For instance, in [8; 9], the authors discussed power allocation under various criteria for a downlink NOMA system. In order to improve the system throughput, a network NOMA technique was proposed and analysed for the uplink coordinated multi-point transmission (CoMP) in [10]. Cooperative communications is another solution to mitigate the fading effects of wireless environments [11]. NOMA in cooperative communication systems is commonly referred to as cooperative-NOMA (C-NOMA), which is able to enhance the system reliability [12]. The authors analysed the effect of the power allocation coefficient on the error performance under a one-way relay C-NOMA system in [13]. The authors in [14] presented a new system detection scheme for a one-way relay C-NOMA system, which used the maximal ratio combining (MRC) and SIC to decode signals. [PERSON] et al. in [15] proposed an adaptive transmission scheme based on a one-way relay C-NOMA network with a dedicated relay, which could temporarily store the received information. Recently, two-way relaying (TWR) has attracted a great deal of research attention because of its ability to achieve higher spectral efficiency in comparison to one-way relaying. It has advantages in the utilization of wireless networks' resources, improving spectral efficiency and enhancing network quality with regards to network throughput and error rate performance [16]. In [17], the authors proposed a scheme of jointly optimizing power and time allocations to minimize outage probability for a TWR C-NOMA network. To increase the system throughput and to ensure secure communications, the authors in [18] derived closed-form expressions of the ergodic secrecy rates under both non-colluding and colluding eavesdroppers in a TWR C-NOMA network. In order to achieve a balance between spectral efficiency and energy conservation, power allocation was discussed for a TWR C-NOMA system in [19]. According to the principle of NOMA, downlink users with stronger channel gains need to decode signals of other users with lower channel gains before decoding their own signals based on the SIC technique [20]. The NOMA systems with perfect SIC (pSIC) conditions were investigated in most of the above works, which is too idealistic. More in particular, the interference signals (IS) cannot be completely cancelled by SIC in practical applications [21]. In order to study the network with more practical scenarios, the imperfect SIC (ipSIC) condition was assumed for the NOMA system in many literature works. For instance, in [22], the outage probability was derived for NOMA systems with ipSIC in the underlay cognitive radio network.