# OTFS-Based Handover Triggering in UAV Networks
## 5 Proposed UAV-Ground Handover Triggering Based on DD Channel Estimation
### Proposed DD-Channel-Based Handover Triggering
That is, if \(n^{\prime}=1\), then \(\Bigg{|}\frac{\sin\Big{(}n^{\prime}\frac{\pi}{N}\big{(}k-T\beta_{i_{q}}N\big{)} \Big{)}}{\sin\big{(}\frac{\pi}{N}\big{(}k-T\beta_{i_{q}}N\big{)}\big{)}}\Bigg{|} ^{2}=1\), and the DD channel gain will be constant and equals to the first term, i.e., \(\frac{1}{N^{2}}\sum_{q=1}^{Q}\sum_{i_{q}=1}^{P_{q}}\Big{|}\hat{h}_{i_{q}}\Big{|} ^{2}\text{ for }l=\Big{[}\Delta fa_{i_{q}}M\Big{]}_{M}\) and \(\forall k\). On the other hand, when \(n^{\prime}=N\), there will be only one coherence period equal to the whole OTFS symbol duration, and then the DD channel gain will be constant and equal to \(\sum_{i=1}^{p}\left|h_{i}\right|^{2}\) for \(l=\left[\Delta f\alpha_{i_{q}}M\right]_{M}\) and \(k=\left[T\beta_{i_{q}}N\right]_{N}\), and 0 otherwise. For a general \(n^{\prime}\) value, the term \(\left|\frac{\sin\left(n^{\prime}\frac{n}{k}\left(k-T\beta_{i_{q}}N\right) \right)}{\sin\left(\frac{n}{k}\left(k-T\beta_{i_{q}}N\right)\right)}\right|^{2}\) will depend on \(k\), but the \(k^{\prime}s\) channel gain is less than that comes from the first term. Thus, the summation of the DD channel gains over the whole OTFS symbol is constant for a given \(n^{\prime}\) value. In the case of off-grid \(\beta_{i_{q}}\) and \(\alpha_{i_{q}}\) values, i.e., when \(k\
eq\left[T\beta_{i_{q}}N\right]_{N^{\prime}}\) and \(l\
eq\left[\Delta f\alpha_{i_{q}}M\right]_{M^{\prime}}\) both \(\left|\mathcal{A}\left(i_{q},\beta_{i_{q}},k\right)\right|\) and \(\left|\mathcal{B}\left(i_{q},\beta_{i_{q}},l\right)\right|\) will have non-zero values for many \(k^{\prime}s\) and \(l^{\prime}s\) locating at the neighbors of \(\left[T\beta_{i_{q}}N\right]_{N}\) and \(\left[\Delta f\alpha_{i_{q}}M\right]_{M^{\prime}}\), respectively. Although the off-grid case increases the sparsity of the DD channel, the sum of the DD channel gains is still constant over the whole OTFS symbol, and its value varies based on the number of coherence periods and their duration. Figure 2 gives the baseband block diagram of the proposed handover-triggering scheme. In this figure, the mobile entity, e.g., a UAV, estimates the DD CIR of both target and serving cells, i.e., \(h_{DD}^{Tur}[l,k]\) and \(h_{DD}^{scr}[l,k]\), using DD channel estimators like LS [27] or MMSE [28]. This can be accomplished by transmitting pilot symbols from the serving and the target cells. Then, the estimated CIRs are sent to a comparator circuit to evaluate the condition given in (33) using the specified threshold \(P_{th}\), and then the mobile entity decides even to switch to the target cell or continue connecting with the serving one. The values of \(P_{th}\), \(TTT\), and \(NSym_{th}\) given in (24), (29), and (33) affect the number of handovers as follows: (1) Increasing \(P_{th}\) will reduce the number of handovers, as the HST will be linked with a certain UAV for a long time period and vice versa. (2) Similarly, increasing \(TTT\) and \(NSym_{th}\) will reduce the number of handovers, as the HST will be linked to a certain UAV for a long time period and vice versa. Typically, the OTFS symbol duration is longer than the OFDM symbol duration, while both are longer than the RSS symbol duration. Thus, it is expected that \(|z|\) in (24) is shorter than \(NSym_{OFDM}\) in (29), and both are shorter than \(NSym_{OTFS}\) in (33). Consequently, it is expected that the number of handovers in the RSS scheme will be higher than that belonging to the OFDM scheme, and both are higher than that which belongs to the OTFS scheme. Increasing the number of OFDM symbols for handover decisions can improve the stability of FT-based handover mechanisms to some extent. However, this primarily relies on temporal averaging, which may not fully capture the mobility dynamics in high-speed scenarios. In the DD domain, each signal component is localized in both delay and Doppler, making it more resistant to frequency dispersion compared to FT-based representations.