## 3 Interference Coordination Scheme Analysis
### User Pairing Scheme Combined with ABS  
Aiming at the problem of different channel quality requirements in NOMA networks, user pairing is a necessary method in NOMA HetNets. Due to the difference in transmit power and coverage of base stations in heterogeneous networks, the traditional user pairing is not suitable for the network and this paper proposes a novel NOMA user pairing algorithm combined with ABS technology. Firstly, the users are classified by different types of transmission subframes. Secondly, under the condition that the throughput of the user does not drop as the transmission subframe is switched, the transmission subframe of users who transmit during non-ABS can be dynamically switched from non-ABS to ABS according to the ABS ratio. Finally, user pairing is performed in different types of transmission subframes based on the SINR of users and the user of the lowest SINR is paired with the user of the highest SINR in order to maximize the improvement of the throughput of the weak user in the pair. Due to different ABS ratios, users have different throughput in different types of transmission subframes. The essence of dynamically pairing users according to ABS ratio is to make some users with poor transmission performance during non-ABS transmit during ABS while the ABS resources are sufficient. Moreover, the throughput of each user can be balanced. Since the users who transmit during non-ABS are seriously interfered with by the MBS, the case of assigning these users to non-ABS for transmission is not considered. In addition, since the users with poor transmission performance during non-ABS are generally weak users, it is possible for the users to be strong users or weak users if they are assigned to transmit during ABS. For convenience, the throughput expression of weak users is taken to constitute the condition that the throughput of the user does not drop as the transmission subframe switches, it can be expressed as:  
\[ \begin{split}\frac{(1-\zeta)^{B}}{N_{\rm{SC\_nonABSbefore}}^{\rm{ NB}}}\log_{2}\left(1+\frac{\left|h_{u,u}\right|^{2}ap}{\left|h_{u,u}\right|^{2}(1-a)p+ \frac{N_{\rm{P}}^{\rm{sta}}}{\sum\limits_{p^{\prime}=1,p^{\prime}\
eq b}^{ \rm{NB}}\left|h_{u,p^{\prime}}\right|^{2}p_{p^{\prime}}+\frac{e^{2B}}{N_{\rm{ SC\_nonABSbefore}}}}\right)}\\ <\frac{\zeta B}{N_{\rm{SC\_ABSafter}}^{\rm{SB}}}\log_{2}\left(1+ \frac{\left|h_{u,u}\right|^{2}a^{\prime}p^{\prime}}{\left|h_{u,u}\right|^{2}(1-a ^{\prime})p^{\prime}+\frac{N_{\rm{P}}^{\rm{sta}}}{\sum\limits_{p^{\prime}=2,p ^{\prime}\
eq b}^{\rm{NB}}\left|h_{u,u^{\prime}}\right|^{2}p_{p^{\prime}}+ \frac{e^{2B}}{N_{\rm{SC\_ABSafter}}^{\rm{SB}}}}}\right),\end{split}  \tag{14}\]  
where \(\zeta\) represents the ABS ratio and the power allocation factor of the user which before and after the transmission subframe switching are denoted by \(\alpha\) and \(\alpha^{\prime}\). The power allocated for the channel of the user and the number of channels before and after switching are denoted by \(p\), \(N_{\rm{SC\_nonABSbefore}}^{b}\), \(p^{\prime}\) and \(N_{\rm{SC\_ABSafter}}^{b}\). Since the subchannels are assigned the same power in this paper, the product of the subchannel power and the number of subchannels is the total transmit power of the base station. Let, \(P_{b}\) represent the transmit power of the BS \(b\). Since the left-side and right-side of the inequality (13) are monotonically increasing functions of the power allocation factor and the increment of the right-side is larger than that of the left-side as the power allocation factor increases, we assume that power allocation factors before and after switching take the minimum value to achieve a relatively reasonable result, i.e., \(\alpha=\alpha^{\prime}=0.5\).