# High Throughput Data Relay in UAV Wireless Networks
## 5 Numerical Results

Table 1: Comparison of optimal max-min average achievable data rate (bits/s/Hz). Figure 3: Comparison of optimal max-min average data rate UAV trajectories for \(T=60\) s.  
DS method first, then victim 3 and victim 4 are supported by the DS method. However, in the non-DS bandwidth contention scheme, from victim 1 to victim 4, each of them occupies the bandwidth sequentially. The bandwidth schedule configurations are delivered to the victims by the UAV via control signals. Figure 5(a) shows the optimal trajectories for the non-DS bandwidth contention scheme for different \(T\) values. As the period \(T\) decreases, the maximum distance that the UAV can traverse between the initial and final positions decreases, thus the UAV flight trajectory eventually becomes unable to reach every victim. However, the UAV tries to approach each victim as close as possible. Meanwhile, the channel gain worsens as the distance between the UAV and victim is increasing, hence resulting in a decrease of the optimal max-min average data rate. Figure 5(b) shows the optimal trajectories for the non-DS fair bandwidth allocation scheme for different \(T\) values. The optimal average data rate for the non-DS fair bandwidth allocation scheme decreases slightly as the period \(T\) decreases. This is because that in the non-DS fair bandwidth allocation scheme, the UAV flies along a trajectory where the distances from each victim to the UAV do not vary much. The length of the resulting trajectory is covered by the maximum UAV traverse distance under different \(T\). Therefore the change of \(T\) slightly changes the optimal UAV flight trajectory. Figure 4: Dual Sampling (DS) method bandwidth schedule for \(T=60\) s.  
Figure 5: Non-DS method bandwidth contention schedule for \(T=60\) s.  
Figure 6: Non-DS schemes optimal UAV trajectory comparison. Figure 7 shows the optimal trajectories for the DS method for different \(T\) values. The change of the period \(T\) only changes the optimal average data rate slightly. In the DS method, the UAV is likely to fly at the positions that are the same distance to both of the DS supported paired victims, as discussed in the theoretical analysis. The maximum UAV traverse distance under different \(T\) values can cope with this kind of trajectory. Hence the change of \(T\) only slightly affects the UAV flying trajectory. Next, we compare the propulsion energy consumed by the UAV for different schemes. As derived in Reference [27], the propulsion power consumption for a rotary-wing UAV in a time slot can be modelled as  
\[ \begin{split} P[k]=& P_{0}(1+\frac{3v[k]^{2}}{U_{ \mathrm{tip}}^{2}})+P_{i}(\sqrt{1+\frac{v[k]^{4}}{4v_{0}^{4}}}-\frac{v[k]^{2}}{2 v_{0}^{2}})^{1/2}\\ &+\frac{1}{2}d_{0}\rho sAv[k]^{3},\end{split}  \tag{13}\]  
where \(v[k]\) is the constant flight speed of the UAV in a time slot. \(P_{0}\) and \(P_{i}\) represent the blade profile power and induced power in hovering status, respectively. \(U_{\mathrm{tip}}\) denotes the tip speed of the rotor blade, \(v_{0}\) is known as the mean rotor induced velocity in hover, and \(d_{0}\) and \(s\) are the fuselage drag ratio and rotor solidity, respectively. \(\rho\) and \(A\) denote the air density and rotor disc area, respectively. Therefore, the propulsion energy in a time slot is \(P[k]\delta_{t}\). Furthermore, the overall propulsion energy of the UAV is  
\[E=\sum_{k=1}^{K}P[k]\delta_{t}. \tag{14}\]  
We assume that \(P_{0}=577.3\) W, \(P_{i}=793.0\) W, \(U_{\mathrm{tip}}=200\) m/s, \(v_{0}=7.21\) m/s, \(d_{0}=0.3\), \(\rho=1.225\) kg/m\({}^{3}\), \(s=0.05\), and \(A=0.79\) m\({}^{2}\)[28]. Based on the optimal UAV trajectory derived for different schemes, the overall propulsion energy consumed by the UAV is listed in Table 2. On observing the results, for shorter time periods, that is when \(T=40\) s, \(30\) s, and \(20\) s, the DS method consumes most propulsion energy, while the non-DS fair bandwidth allocation scheme consumes least propulsion energy.