## 3 Interference Coordination Scheme Analysis
### User Pairing Scheme Combined with ABS
Since each subchannel can accommodate at most two NOMA users, it is assumed that there are as many NOMA user pairs as possible in the network and then \(N_{\text{SC\_nonABS,before}}^{b}=\left[N_{\text{U\_nonABS,before}}^{b}/2\right]\), \(N_{\text{SC\_ABS,after}}^{b}=\left[\left(N_{\text{U\_ABS,before}}^{b}+1\right)/2\right]\), where \(\left[\cdot\right]\) represents the ceiling operation.\(N_{\text{U\_nonABS,before}}^{b}\) and \(N_{\text{U\_ABS,before}}^{b}\) represents the number of users that transmit during non-ABS and ABS before switching to the current user. Then the inequality can be rewritten as  
\[\frac{\left[\left(N_{\text{U\_ABS,before}}^{b}+1\right)/2\right]}{\left[N_{ \text{U\_nonABS,before}}^{b}/2\right]}<\frac{\xi\log_{2}\!\left(1+\frac{\frac{1}{ 2}\big{\|}h_{\text{u},\big{\|}}{2}^{2}p_{\text{b}}}{\frac{1}{2}\big{\|}h_{ \text{u},\big{\|}}{2}^{2}p_{\text{b}}+\sum\limits_{\
u=2,\
u^{\prime}\
eq b}^ {\text{N}_{\text{B}}}\big{\|}h_{\text{u},\
u^{\prime}}\big{\|}^{2}p_{\text{b}^ {\prime}}+\sigma^{2}B}\right)}{\left(1-\xi\right)\log_{2}\!\left(1+\frac{\frac{1 }{2}\big{\|}h_{\text{u},\big{\|}}{2}^{2}p_{\text{b}}}{\frac{1}{\big{\|}h_{ \text{u},\big{\|}}{2}^{2}p_{\text{b}}+\sum\limits_{\
u=2,\
u^{\prime}\
eq b}^ {\text{N}_{\text{B}}}\big{\|}h_{\text{u},\
u^{\prime}}\big{\|}^{2}p_{\text{b}^ {\prime}}+\sigma^{2}B}}\right)}. \tag{15}\]  
The right-side of the inequality is:  
\[SW(u,b,\xi)=\frac{\xi\log_{2}\!\left(1+\frac{\frac{1}{2}\big{\|}h_{\text{u}, \big{\|}}{2}^{2}p_{\text{b}}}{\frac{1}{2}\big{\|}h_{\text{u},\big{\|}}{2}^{2} p_{\text{b}}+\sum\limits_{\
u^{\prime}\
eq b}^{\text{N}_{\text{B}}}\big{\|}h_{ \text{u},\
u^{\prime}}\big{\|}^{2}p_{\text{b}^{\prime}}+\sigma^{2}B}\right)}{ \left(1-\xi\right)\log_{2}\!\left(1+\frac{\frac{1}{2}\big{\|}h_{\text{u}, \big{\|}}{2}^{2}p_{\text{b}}}{\frac{1}{\big{\|}h_{\text{u},\big{\|}}{2}^{2}p_ {\text{b}}+\sum\limits_{\
u^{\prime}\
eq b}^{\text{N}_{\text{B}}}\big{\|}h_{ \text{u},\
u^{\prime}}\big{\|}^{2}p_{\text{b}^{\prime}}+\sigma^{2}B}}\right)}. \tag{16}\]  
Therefore, \(SW(u,b,\xi)>\left[\left(N_{\text{U\_ABS,before}}^{b}+1\right)/2\right]/\left[ N_{\text{U\_nonABS,before}}^{b}/2\right]\) can be used as the condition that the throughput of the user does not drop as the transmission subframe switches. On the other hand, \(SW(u,b,\xi)\) also represents the priority of the user switching. It can be seen from the expression that the user with severe cross-tier interference has higher priority when the co-tier interference is constant. While the user switching is finished, user pairing is performed in different types of transmission subframes based on the SINR of users rather than channel gain. The SINR of users is calculated by the maximum transmit power and then the user of the lowest SINR is paired with the user of the highest SINR. The user pairing algorithm is shown in Algorithm 1. ```
1:Initialize: the ABS ratio of macrocell where BS \(b(b\
eq 1)\) is located is \(\xi\), user pairing table \(\mathbf{U}_{\text{pair}}=\left[\,\right]\). According to the user access situation of the BS \(b\), users are divided into \(\mathbf{U}_{\text{nonABS}}\)
2:whose user transmit during non-ABS and \(\mathbf{U}_{\text{ABS}}\) whose user transmit during ABS and the number of two sets are \(N_{\text{U\_nonABS,before}}^{b}\) and \(N_{\text{U\_ABS,before}}^{b}\). 3:For each user in \(\mathbf{U}_{\text{nonABS}}\), calculate formula (15) to obtain the matrix \(\mathbf{SW}\) of user switching condition and sort in descending order. Traverse the users of \(\mathbf{SW}\) from the beginning, if the formula (14) is satisfied, the user will be assigned to \(\mathbf{U}_{\text{ABS}}\) and update \(N_{\text{U\_nonABS,before}}^{b}\) and \(N_{\text{U\_ABS,before}}^{b}\), otherwise jump out of the traversal. 4:The SINR of users in \(\mathbf{U}_{\text{nonABS}}\) and \(\mathbf{U}_{\text{ABS}}\) are separately calculated and the user pairing is performed in each set.