# OTFS-Based Handover Triggering in UAV Networks
## 7 Numerical Analysis
### Studying the Effects of \(n^{\prime}\) and \(P_{th}\)
#### 7.1.1 Effect of \(n^{\prime}\)  
Figures 3-5 give the handover performance metrices against the value of \(n^{\prime}\) ranging from 1 to 31 while considering the worst scenario of \(P_{th}=0\) dB. In this regard, \(n^{\prime}=1\) means a highly time-varying DD CIR, while \(n^{\prime}=31\) means the DD CIR is almost constant over the whole OTFS symbol duration.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(f\) & 5.06 GHz [8] \\ \(\Delta f\) & 15 KHz [8] \\ \(M\) & 32 [31] \\ \(N\) & 32 [31] \\ \(\alpha_{\text{max}}\) & 5.47 \(\times\) 10\({}^{-3}\) [8] \\ \(P_{q}\) & 17 [8] \\ \(\sigma_{g}^{2}\) & \(-\)114 dBm \\ \(v\) & 500 Km/Hr \\ \(n^{\prime}\) & 12 [8] \\ \(P_{\text{Tx}}\) & 10 Watts [8] \\ \(P_{th}\) & 0 \\ \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
For the RSS strategy, the handover overhead is marginally decreased when increasing \(n^{\prime}\). This is because RSS fluctuates at every chip duration due to the accumulated effect of multi-path and Doppler shift. Thus, changing the channel every \(T\) s, i.e., when \(n^{\prime}=1\), or changing it every \(NT\) s, i.e., when \(n^{\prime}=31\), will have almost the same impact on the RSS handover performance due to the highly fluctuating RSS in both cases. This is the reason why the handover metrics of the RSS schemes marginally changed when increasing \(n^{\prime}\).  
For OTFS, the handover overhead, the ping-pong ratio, and the average throughput are constant irrespective of the value of \(n^{\prime}\). This comes from the constant \(\left|\hat{h}_{DD}(l,k)\right|^{2}\) value for a given \(n^{\prime}\) value as we proved in detail. The only difference between the low \(n^{\prime}\) values and the high \(n^{\prime}\) values reside in the DD channel sparsity. That is, the DD channel sparsity increases when decreasing \(n^{\prime}\), and vice versa, but the DD channel gain \(\left|\hat{h}_{DD}(l,k)\right|^{2}\)  
Figure 4: Average throughput against \(n^{\prime}\).  
Figure 5: Ping-pong ratio against \(n^{\prime}\).  
Figure 3: Handover overhead against \(n^{\prime}\).  
is constant over the whole OTFS symbol for both cases. Thanks to this phenomenon, the proposed handover strategy has the lowest handover overhead and ping-pong ratio, while it has the highest average throughput in consequence.  
Different from RSS and OTFS, the FT channel using OFDM is highly influenced by the value of \(n^{\prime}\). When \(n^{\prime}=1\), the DD channel changes at every OFDM symbol, and it will be too sparse, which highly increases ISI and ICI of the FT channel. This results in highly fluctuating the FT channel gain making the handover overhead, the average throughput, and the ping-pong ratio almost equal to that which belongs to the RSS strategy. Although both OFDM and RSS have the same handover overhead when \(n^{\prime}=1\), they have different numbers of handovers, and they have different single-handover durations.  
However, when \(n^{\prime}=31\), the DD CIR is almost constant over the whole OTFS symbol and is less sparse, which decreases the ISI and ICI of the corresponding FT channel. This results in highly enhancing the handover metrics of the OFDM strategy, as shown in Figures 3-5. From these figures, when \(n^{\prime}=1\), the handover overhead and the ping-pong ratio of the OTFS-based handover are equal to 0.0643 (0.643) and 0.014 (9.1277 \(\times\) 10\({}^{-4}\)) of that which belongs to OFDM (RSS), respectively. Also, its average throughput is higher than that which belongs to OFDM (RSS) by 9.93 (10.9) times.