## 3 Interference Coordination Scheme Analysis
### User Pairing Scheme Combined with ABS
Then the Formula (19) can be rewritten as:

\[{{\alpha^{2}}-\left(2+\frac{{{IN_{1}}}}{{{S_{1}}}}+\frac{{{IN_{2}}}}{{{S_{2}}} }\right)\alpha+1+\frac{{{IN_{1}}}}{{{S_{1}}}}=0}, \tag{21}\]

\[\alpha_{0}=\frac{{{\left(2+\frac{{{IN_{1}}}}{{{S_{1}}}}+\frac{{{IN_{2}}}}{{{S_{2 }}}}\right)-\sqrt{{{\left(2+\frac{{{IN_{1}}}}{{{S_{1}}}}+\frac{{{IN_{2}}}}{{{S_{2 }}}}\right)}^{2}}-4{\left(1+\frac{{{IN_{1}}}}{{{S_{1}}}}\right)}}}}}{2}. \tag{22}\]

Similarly, the power allocation factor of a user which transmits during ABS can also be obtained as Formula (21) where \({IN_{u}}=\sum\limits_{{ \begin{subarray}{c}{{\boldsymbol{v}}^{\prime}=2,{ \boldsymbol{b}}^{\prime}\
eq b\end{subarray} }}}^{{N_{\text{B}}}}{{{\left|{{h_{u }},{\boldsymbol{v}}^{\prime}}\right|}^{2}}{P_{{\boldsymbol{b}}^{\prime}}}+{ \sigma^{2}}B}\). Due to the constraints in Formula (18),

\[\frac{{{\gamma_{\text{TH}}}{{S_{1}}}+{{\gamma_{\text{TH}}}}{{IN_{1}}}}}{{{S_{1}}}+{ {\gamma_{\text{TH}}}}{{S_{1}}}}}\leq\alpha\leq\frac{{{S_{2}}-{{\gamma_{\text{TH}}} }{{IN_{2}}}}}{{{S_{2}}}}. \tag{23}\]Since the signals are recovered at the receivers through SIC technology, the power allocation factor should not be too large or too small. Therefore, the power allocation factor is limited to the interval \([0.6,0.9]\) in this paper and the optimal power allocation factor is expressed as:

\[\alpha^{*}=\min\biggl{(}\max\biggl{(}\frac{\gamma_{\mathrm{TH}}S_{1}+\gamma_{ \mathrm{TH}}IN_{1}}{S_{1}+\gamma_{\mathrm{TH}}S_{1}},\alpha_{0},0.6\biggr{)}, \frac{S_{2}-\gamma_{\mathrm{TH}}IN_{2}}{S_{2}},0.9\biggr{)}. \tag{24}\]

### Joint Optimization Scheme of Adaptive CRE and ABS

For the macrocell \(m\), the traversal method to find the optimal solution of CRE and ABS will use the \(N_{m}^{\mathrm{PBS}}\)-circulation to traverse all feasible solutions where \(N_{m}^{\mathrm{PBS}}\) is the number of PBSs in the macrocell \(m\). The complexity of the traversal method is extremely high. This paper uses the idea of game theory to change the \(N_{m}^{\mathrm{PBS}}\)-circulation into \(N_{m}^{\mathrm{PBS}}\) mutual independent circulation processes and finds the optimal solution by an iterative method. Firstly, we initialize the ABS ratio allocated by the MBS in the macrocell \(m\) and then we assume that each PBS in the macrocell \(m\) is selfish and will take the best CRE bias value while calculating the CRE bias of PBS. The CRE biases of PBSs are calculated in order and will tend to be stable after a certain number of iterations. Then we will achieve the optimal CRE bias matrix under the current ABS ratio. By traversing all feasible solutions of the ABS ratio, the result will be obtained. The joint optimization algorithm of adaptive CRE and ABS is shown in Algorithm 2. ```
Initialize: the macrocell id \(m=1\), the number of macrocells \(N_{\mathrm{M}}\), the ABS ratio value \(\xi=[\xi_{1},\xi_{2},\ldots,\xi_{N_{\mathrm{M}}}]\), the CRE bias value \(\eta=[\eta_{1},\eta_{2},\ldots,\eta_{N_{\mathrm{M}}}]\), \(\eta_{m}=\left[\eta_{1},\eta_{2},\ldots,\eta_{N_{\mathrm{M}}}^{\mathrm{P}}\right]\),  where \(N_{\mathrm{M}}^{\mathrm{P}}\) represents the same number of PBSs in each macrocell, current iteration step \(t=1\), the maximum iteration step \(T_{\max}\), the PBS id \(p=1\). while\(m\leq N_{\mathrm{M}}\)do \(\xi_{m}=1/8\). while\(\xi_{m}<1\)do \(t=1\). while\(t\leq T_{\max}\)do \(p=1\). while\(p\leq N_{m}^{\mathrm{P}}\)do  Traverse the feasible solutions of the CRE bias of the PBS \(p\) and calculate the objective function expressed in Formula (8). Update the solution \(\xi_{m}^{*}\), \(\eta_{m}^{*}\) that maximizes the objective function. \(p=p+1\). endwhile \(t=t+1\). endwhile \(\xi_{m}=\xi_{m}+1/8\). endwhile \(m=m+1\). endwhile STEP3: Return optimal solution \(\xi^{*}\), \(\eta^{*}\). ```

**Algorithm 2** Joint Optimization Algorithm of Adaptive CRE and ABS

It is assumed that the complexity of calculating Formula (8) is \(O(N_{\mathrm{U}})\) and \(N_{\mathrm{U}}\) represents the number of users of the networks.