## 3 Interference Coordination Scheme Analysis
### User Pairing Scheme Combined with ABS
### Dynamic Power Allocation Scheme

While the user pairing is completed, the problem of power allocation between users on the same channel needs to be considered. This paper takes a dynamic power allocation scheme. Since this paper considers maximizing the average throughput of edge users, the difference between the SINR of users in the same pair should be as small as possible in order to improve the throughput performance of edge users. The SINR of users in the same pair transmitted during non-ABS can be expressed as:

\[\gamma_{1}=\frac{{{{\left|{{h_{1}}}\right|}^{2}}\alpha{p_{b}}}}{{{{\left|{{h_{1 }}}\right|}^{2}}(1-\alpha){p_{b}}+\sum\limits_{{ \begin{subarray}{c}{{\boldsymbol{v} }^{\prime}=1,{\boldsymbol{b}}^{\prime}\
eq b\end{subarray} }}}^{{N_{\text{B}}}}{ {{\left|{{h_{1}},{\boldsymbol{b}}^{\prime}}\right|}^{2}}{p_{{\boldsymbol{b}}^{ \prime}}}+\frac{{{\sigma^{2}}B}}{{{N_{\text{SC}}}}}}}, \tag{17}\]

\[\gamma_{2}=\frac{{{{\left|{{h_{2}}}\right|}^{2}}(1-\alpha){p_{b}}}}{{\sum \limits_{{ \begin{subarray}{c}{{\boldsymbol{v}}^{\prime}=1,{\boldsymbol{b}}^{ \prime}\
eq b\end{subarray} }}}^{{N_{\text{B}}}}{{{\left|{{h_{2}},{\boldsymbol{ v}}^{\prime}}\right|}^{2}}{p_{{\boldsymbol{b}}^{\prime}}}+\frac{{{\sigma^{2}}B}}{{{N_{ \text{SC}}}}}}}}, \tag{18}\]

where \(\alpha\) is the power allocation factor of a weak user in the same pair of users, and \(0.5<\alpha<1\). The power optimization problem is expressed as:

\[ \begin{array}{c}\min\limits_{\alpha}{\left|{\frac{{{\left|{{h_{1}}}\right|}^ {2}}\alpha{p_{b}}}{{{\left|{{h_{1}}}\right|}^{2}}(1-\alpha){p_{b}}+\sum\limits _{{\begin{subarray}{c}{{\boldsymbol{v}}^{\prime}=1,{\boldsymbol{b}}^{\prime} \
eq b\end{subarray}}}}^{{N_{\text{B}}}}{{{\left|{{h_{1}},{\boldsymbol{b}}^{ \prime}}\right|}^{2}}{p_{{\boldsymbol{b}}^{\prime}}}+\frac{{{\sigma^{2}}B}}{{{N_ {\text{SC}}}}}}-\frac{{{{\left|{{h_{2}}}\right|}^{2}}(1-\alpha){p_{b}}}}{{\sum \limits_{{\begin{subarray}{c}{{\boldsymbol{v}}^{\prime}=1,{\boldsymbol{b}}^{ \prime}\
eq b\end{subarray}}}}^{{N_{\text{B}}}}{{{\left|{{h_{2}},{\boldsymbol{ v}}^{\prime}}\right|}^{2}}{p_{{\boldsymbol{b}}^{\prime}}}+\frac{{{\sigma^{2}}B}}{{{N_{ \text{SC}}}}}}}}}\right|}},\\ s.t.\gamma_{1}\geq\gamma_{\text{TH}}\\ \gamma_{2}\geq\gamma_{\text{TH}}\\ 0.5<\alpha<1\end{array}  \tag{19}\]

where \(\gamma_{\text{TH}}\) represents the threshold of the SINR of the user. Let \(PA(\alpha)=\gamma_{1}-\gamma_{2}\), and \(d(PA(\alpha))/d(\alpha)>0\). So, \(PA(\alpha)\) is a monotonically increasing function and there is only one minimum point in \(|PA(\alpha)|\). Let \(PA(\alpha)=0\),

\[{{\left|{{h_{1}}}\right|}^{2}}\alpha{P_{b}}\left({\sum\limits_{{ \begin{subarray}{c}{{\boldsymbol{v}}^{\prime}=1,{\boldsymbol{b}}^{\prime} \
eq b\end{subarray} }}}^{{N_{\text{B}}}}{{{\left|{{h_{2}},{\boldsymbol{v}}^{ \prime}}\right|}^{2}}{P_{{\boldsymbol{b}}^{\prime}}}+{\sigma^{2}}B}}\right)={{ {\left|{{h_{2}}}\right|}^{2}}(1-\alpha){P_{b}}}\left({{{\left|{{h_{1}}}\right|} ^{2}}(1-\alpha){P_{b}}+\sum\limits_{{ \begin{subarray}{c}{{\boldsymbol{v}}^{ \prime}=1,{\boldsymbol{b}}^{\prime}\
eq b\end{subarray} }}}^{{N_{\text{B}}}}{{{ \left|{{h_{1}},{\boldsymbol{b}}^{\prime}}\right|}^{2}}{P_{{\boldsymbol{b}}^{ \prime}}}+{\sigma^{2}}B}}\right). \tag{20}\]

Let, \({S_{u}}={{\left|{{h_{u}}}\right|}^{2}}{P_{b}}\), \({IN_{u}}=\sum\limits_{{ \begin{subarray}{c}{{\boldsymbol{v}}^{\prime}=1,{ \boldsymbol{b}}^{\prime}\
eq b\end{subarray} }}}^{{N_{\text{B}}}}{{{\left|{{h_{u }},{\boldsymbol{v}}}\right|}^{2}}{P_{{\boldsymbol{b}}^{\prime}}}+{\sigma^{2}}B}\).