# An Integrated Access and Backhaul Approach to Sustainable Dense Small Cell Network Planning
## 4 Simulation Result
### Multi-Hop Simulation Result  
We formulated the multi-hop problem of IAB network planning for random sparse distributions of donors. In our pursuit to establish the effectiveness of the proposed algorithm, we initially embarked on a one-hop greedy simulation. The results obtained from the simulation were compared to the outcome of the earlier mixed-integer linear programming (MILP) optimization problem. As shown in Figure 9, we found that as the number of donors swells, the one-hop greedy algorithm becomes more proficient, gradually approximating the globally optimal solution provided by MILP. For example, when the donor count escalates to 20, this difference dwindles to approximately 0.5 nodes. This performance of the single-hop greedy algorithm, in particular the gradual agreement with the MILP results (less than one node difference) as the number of donors increases, is concrete proof of the effectiveness of the algorithm. In the given multi-hop scenario, where the coverage radius and backhaul radius for each donor/node are stipulated at 200 and 300, respectively, a deployment comprising six donors resulted in the utilization of 16 nodes in one successful deployment, as shown in  
Figure 8: Average deployed nodes for one-hop optimal in 100 simulations with 200 m coverage radius and 300 m backhaul radius. Figure 9: Comparison of average nodes deployed using one-hop optimal and one-hop greedy strategies as a function of the number of donors, with boxplots indicating variability around the means. Figure 10. One noteworthy observation from the results is that, while a node possesses the capability to connect with multiple donors, it does not necessarily imply simultaneous connections with all of them. Instead, this potential for multi-hop connections can be attributed to the donor providing sufficient data transfer rates to satisfy the node's requirements. This suggests that following a multi-hop formulation can effectively limit the hop length by the data rate constraint. Next, we conducted a comparative analysis of the greedy multi-hop method and the one-hop optimal strategy. For each specified donor, we conducted 100 simulations and documented the results. There are significant differences between the one-hop optimal and the multi-hop greedy approach, as shown in Figure 11. Starting with only five donors, the one-hop yields two feasible models out of 100 simulations, compared to the multi-hop strategy's 12, which means that the multiple hops increase the likelihood of successful deployment. As donor nodes increase, the successful number for the multi-hop method grows more slowly than its optimal one-hop counterpart. At 11 donors, the one-hop method achieves 45 successful deployments, compared to the multi-hop's 62. And with the increment in donor nodes, the successful rates of both methods approach convergence, which means the advantage of the multi-hop strategy diminishes. Figure 12 investigates the influence of multi-hop on the average number of nodes deployed. The data reveal a trend of decrement in the average number of nodes concomitant with increment in the multi-hop. The values oscillate from an initial 16.916 with five donor nodes, attenuating to 7.914 when the donor nodes ascend to 20. Figure 10: Deployment result of greedy multi-hop in a 1000 m \(*\) 1000 m area with coverage radius 200 m and backhaul radius 300 m. The line shows that the remaining data rate of the current hop can provide enough backhaul service for the next hop. To examine the effect of the potential node location density on network coverage, we simulated various potential node distances ranging from 10 m to 50 m, with the results displayed in Figure 13. A critical observation from the early stages of network deployment emerged, particularly with fewer donors, such as five. The data suggest that as the gap between potential positions widens, the average number of nodes deployed incrementally increases. This implies that in environments with limited donors, larger separations might require deployment of more nodes for full coverage.