# Coverage and Rate Analysis for Location-Aware Cross-Tier Cooperation in Two-Tier HetNets
## 4 Numerical Results
### Performance Comparison with Other User Association Schemes  
Figure 5 on the next page illustrates the coverage probability and average rate for the typical user with an increasing of the radius of the inner region \(D\) for the proposed LA-CTC scheme, for the MRP and for the CRE. From the perspective of MIUs, as the prescribed distance \(D\) increases, all schemes degrade the performance of the macro inner region while maintaining the same performance. This is caused by the fact that more users belong to the macro inner region; hence, the interference from the macro tier increases. In terms of the coverage and rate of the edge users and the overall system, the proposed LA-CTC scheme outperforms the MRP and the CRE. Compared to the MRP, the CRE degrades the performance of the macro edge region and the overall system. This is because the offloaded users usually do not experience the strongest received power, which deteriorates the SINR of the users. Note that all these results are obtained from the assumption that each BS has full buffer traffic downlink transmission for its connected user. On the other hand, compared to the CRE, the proposed LA-CTC scheme significantly improves the overall performance. This improvement is due to the offloaded users (i.e., CoMP users) being served by both the BSs, which improves the SINR of these users. The SINR degradation of offloaded users resulting from the CRE can be compensated  
Figure 4: Effect of the radius of inner region on the overall coverage probability and average rate for different cooperation thresholds. (**a**) Overall coverage probability; (**b**) Overall average probability.  
for by CoMP transmission. Meanwhile, compared to the MRP, the overall performance gain from the proposed LA-CTC scheme results by means of jointly achieving load balancing for all the tiers and by interference mitigation for the offloaded users. The outperformance of the proposed LA-CTC scheme is guaranteed by the backhaul links between the BSs for exchanging the users' data and the control information.  
Figure 6 on the next page presents the overall coverage probability and the average rate versus the radius of the inner region \(D\) for the proposed LA-CTC scheme and for the LA-CTCT scheme [23]. The LA-CTCT scheme in [23] proposes cross-tier CoMP transmission for offloaded users when the small cells are uniformly deployed over the entire plane, without considering the poor offloading  
Figure 5: The coverage probability and average rate for the proposed location-aware cross-tier cooperation (LA-CTC) scheme, the maximum-received-power (MRP) and the cell range expansion (CRE) when the cooperation threshold (bias factor) \(\beta=5\) dB. (**a**) Coverage probability; (**b**) Average rate.  
effect of small cells in the vicinity of the MBS. Therefore, by increasing the prescribed distance \(D\), it can be seen in Figure 6 that the overall coverage probability and average rate of the LA-CTCT scheme remains invariant. However, the overall performance of the proposed LA-CTC scheme initially increases as the prescribed distance \(D\) increases, but decreases beyond a certain prescribed distance value. Compared to the LA-CTCT scheme, it is apparent that a higher overall coverage probability and average rate can be achieved by the proposed LA-CTC scheme, given an appropriate value of \(D\). This improvement is due to the spatial separation between the MBSs and FBSs by means of deactivating the FBSs within the inner region of the MBSs. The excessive interference from the MBS to the FBS transmissions can be mitigated by this spatial separation.