# Utility-Based Wireless Routing Algorithm for Massive MIMO Heterogeneous Networks
## 5 Numerical Results  
### Simulation Environment Settings  
In this section, we evaluate PSR's performance by simulation. As shown in Figure 4, a \(6\times 6\) km square area was generated. MBS (\(BS_{1}\)) was placed in the center and other BSs were randomly distributed in the area. In order to avoid unrealistic approximation between BSs, the minimal distance between any two BSs was set as 0.3 km. To observe the performance in difference distances, the overall simulation area was divided into three ranges: a circle with a diameter of 1 km (blue circle) was regarded as Area 1, nodes between the blue circle and the red circle (a circle with a diameter of 2 km) were regarded as Area 2, and the residual area was regarded as Area 3.  
The number of UE in each BS is set to 60. All other parameters are shown in Table 1. These parameters are very common and have been used in many other works with a similar environment [23]. In order to eliminate the possible adverse results caused by random factors, each setting was repeated 100 times, and the average value was acquired. The simulation software we used was MATLAB R2018a. Under the operating system Windows 10 and system setting of CPU AMD Ryzen5 2600U, 8G RAM, \(I=60\) and \(N_{i}=1200\), it took the PSR 12.6 s to execute the task 100 times. In other words, each single calculation was about 0.1-0.2 s, making PSR feasible for real-time and repeated execution to reflect the time-changing requirement caused by the mobility of UE. Table 1 summarizes the simulation parameters.  
Figure 3: Example of PSR: (**a**) Initialization, (**b**) select parent node of \(BS_{4}\), (**c**) select parent node of \(BS_{5}\), (**d**) complete the entire topology.  
Because there are no existing methods that dynamically combine antenna allocation and routing to provide an integrated solution, PSR was compared with two existing common routing schemes that we have discussed in the related work section: shortest path tree (SPT) and closest forward connection (CFC). SPT forms a shortest-path tree starting from the MBS, while each BS in CFC selects the shortest BS among the BSs that is more closer to the parent until it connects to the MBS. However, as these two schemes only establish topology and do not allocate antennas to form a complete solution, an antenna-allocation scheme Hierarchical Distributed Adjustment (HDA) [25] was used based on the topology they had generated. As shown in the analysis section as well as the simulation in [25], HDA is very efficient and provides a suboptimal solution that is very close to the optimum. Therefore, the comparison is fair and can show the significance of the joint consideration of topology and antenna allocation. Each BS's antennas were adjusted from 400 to 2000. As shown in [27], when the massive MIMO system uses regularized zero-forcing (RZF), point-to-point communication between two BSs with 400 antennas each can reach up to 82% of the system capacity limit. Although this may satisfy a point-to-point transmission, in the UWB problem, where each BS has to connect to multiple BSs to form a tree topology, more antennas is necessary. Therefore, 400 antennas per BS was considered to be the lower bound in the simulation that our simulation started with.