## 3 Interference Coordination Scheme Analysis
### User Pairing Scheme Combined with ABS
Then the complexity of Algorithm 2 is \(O\bigl{(}N_{\mathrm{M}}N_{\mathrm{ABS}}T_{\max}N_{\mathrm{M}}^{\mathrm{P}}N_{ \mathrm{CRE}}N_{\mathrm{U}}\bigr{)}\) where the number of feasible solutions of the ABS ratio and CRE bias are denoted by \(N_{\mathrm{ABS}}\) and \(N_{\mathrm{CRE}}\). Compared with the complexity of the traversal method \(O\bigl{(}N_{\mathrm{M}}N_{\mathrm{ABS}}N_{\mathrm{CRE}}N_{\mathrm{M}}^{ \mathrm{P}}N_{\mathrm{U}}\bigr{)}\), this algorithm can effectively reduce the computational complexity, and the larger \(N_{\mathrm{CRE}}\) is, the more obvious the complexity advantage of the algorithm in this paper. ## 4 Simulation Results

The specific simulation parameters are shown in Table 1. In the scenario, users are not evenly distributed. Part of the users near the PBS and the remains are randomly distributed in the macrocell. If not clearly stated, this paper sets 60 users in each macrocell. The path loss model and shadow fading are given in [2]. Moreover, the noise density of \(-174\) dBm/Hz is shown in [8] while the statis power of the MBS and PBS are shown in [31]. The relation between the average throughput of edge users and the fairness index under the proposed user pairing scheme is shown in Figure 2(a). Moreover, the pairing scheme adopts a fixed power allocation scheme and the joint optimization algorithm of adaptive CRE and ABS shown in this paper. As the power allocation factor increases, both the average throughput of edge users and the fairness index grow simultaneously. As the throughput of edge users becomes higher, the resource allocation is more balanced and the network fairness index is higher. Moreover, that can prove that the performance of edge users can reflect the network fairness to a certain extent. The average throughput of edge users and the fairness index under different user pairing schemes are shown in Figure 2(b). The fixed power allocation factor is 0.9 because the proposed scheme achieves the best performance with this power allocation factor in Figure 2(a). The RUP scheme is a random user pairing while the near-far user pairing (NFUP) scheme and uniform channel gain difference (UCGD) pairing scheme are shown in reference [32]. These schemes are selected for comparison because of their similar complexity. Compared with NFUP and UCGD, the average throughput of edge users of MBS in RUP is higher. Because the distribution of base stations in HetNets is complex, the traditional pairing scheme performed by channel gain is not suitable for HetNets. The users with good channel gain in MBS may suffer severe cross-tier interference from PBSs, resulting in poor user performance. The closer the fairness index is to 1, the better the fairness in the network. The fairness of RUP is greater than that of NFUP and UCGD and that means that the allocation of base station resources is unbalanced in NFUP and UCGD and we need a novel user pairing scheme for HetNets. The proposed pairing scheme combined with ABS technology in this paper can greatly improve the throughput performance of edge users and network fairness. This is because we set the condition that the throughput of the user does not drop as the transmission subframe is switched. The users will be dynamically switched from non-ABS to ABS according to the ABS ratio before pairing. Moreover, the users are paired by SINR instead of channel gain so that the resources of BS can be assigned preferably.