# OTFS-Based Handover Triggering in UAV Networks
## 7 Numerical Analysis
### Against N and M Values  
In this part of the numerical analysis, we study the effect of the critical parameters \(M\) and \(N\) on the handover performances of the compared schemes. In these simulations, six UAVs, an HST speed of 500 Km/Hr, \(P_{th}=0\), \(n^{\prime}=12\), and perfect channel estimation are considered. Figures 15-17 show the handover overhead, the average throughput, and the ping-pong ratio of the compared schemes against increasing the values of \(M\) and \(N\). Figure 15 illustrates the handover overhead associated with the evaluated schemes as a function of the parameters \(M\) and \(N\). As observed in the figure, when \(M\) and \(N\) are doubled, the handover overhead in the RSS scheme also doubles. This phenomenon arises due to the increased number of handovers resulting from the extended OTFS symbol duration, as given in (54). For OTFS, although the number of handovers remains unchanged as we increase \(M\) and \(N\), the single handover duration increases proportionally with them. Consequently, this leads to a marginal increase in its overall handover overhead compared to RSS, as depicted in Figure 15. Similarly, in OFDM, the single handover  
Figure 14: Ping-pong ratio against HST speed. Figure 13: Average throughput against HST speed. duration is increased when increasing the value of \(M\), resulting in slightly increasing its overall handover overhead. However, its rate of increase is lower than OTFS, indicating a lower number of handovers as we increase the value of \(M\) and \(N\). As a quantitative example, when \(M\) and \(N\) increase from 32 to 256, the handover overhead in the RSS scheme exhibits a 7.8-fold increase. In contrast, the corresponding increases for OFDM and OTFS are 2.42-fold and 8.23-fold, respectively. Notably, the rate of increase in handover overhead for OFDM is the lowest among the evaluated schemes, demonstrating that it does not scale linearly with \(M\) and \(N\). This can be attributed to the improved averaging process inherent in OFDM symbols, which effectively mitigates handover frequency, reducing the number of handovers, and enhances its handover performance. Nevertheless, OTFS exhibits the most superior performance overall. Figure 16: Average throughput against the values of \(M\) and \(N\)..  
Figure 15: Handover overhead against the values of \(M\) and \(N\). Figure 16 presents the average throughput of the evaluated schemes as a function of \(M\) and \(N\). All schemes exhibit performance gains with increasing \(M\) and \(N\), primarily due to the corresponding rise in achievable data rate (\(M\Delta f\psi_{\mathcal{H}}\)), resulting from the expanded allocated bandwidth (\(M\Delta f\)), as described in (55). Owing to the dominant impact of (\(M\Delta f\)) over the ratio \(\left(\frac{\text{OTFS symbols duration}}{\text{OTFS symbols duration}+\text{Handover Overhead}}\right)\), \(\Psi\) of OTFS nearly doubles when \(M\) and \(N\) are doubled due to its marginal increase in handover overhead as given in Figure 15. In contrast, the OFDM scheme exhibits an increase in \(\Psi\) that exceeds a factor of two when doubling the values of \(M\) and \(N\), a behavior attributed to its enhanced handover strategy arising from the averaging process over large \(M\) and \(N\) values. Meanwhile, the RSS scheme does not attain an exact doubling of \(\Psi\), owing to its increased handover overhead, as illustrated in Figure 15. As a numerical example, when \(M\) and \(N\) increase from 32 to 256, the average throughput in the RSS scheme improves by a factor of 7. By comparison, OFDM and OTFS attain improvements of 15.1-fold and 7.98-fold, respectively. These findings confirm both the superior performance of the proposed OTFS scheme and the significant enhancements in OFDM performance with increasing \(M\) and \(N\). Figure 17 depicts the ping-pong ratio of the evaluated schemes as \(M\) and \(N\) increase. Due to the higher number of handovers, the RSS scheme exhibits an elevated ping-pong ratio, which approaches nearly 100% when \(M\) and \(N\) are both set to 256.