# OTFS-Based Handover Triggering in UAV Networks
## 5 Proposed UAV-Ground Handover Triggering Based on DD Channel Estimation
### Proposed DD-Channel-Based Handover Triggering  
In this section, we propose an UAV-to-ground handover triggering based on the estimated DD channel, \(\hat{h}_{DD}[l,k]\), using OTFS transmission. This is motivated by the fact that the sum of the DD channel gains is almost constant over the whole OTFS symbol duration, and its value depends on the number of coherence periods and their duration irrespective of the UAV's speed, as will be deduced shortly. Thus, in the proposed scheme, the UAV always monitors the estimated DD channel from the serving and target cells. If the power achieved through the serving cell's channel in dB is less than that of the target cell by a certain value for several OTFS symbols, i.e., \(NSym_{OTFS}\geq NSym_{th}\), then a handover decision will take place. This can be expressed as follows:  
\[ \begin{split}\text{HO}(Ser\to Tar)=\bigg{\{}1,P_{\text{Tx}} \Big{(}\sum_{l=0}^{M-1}\sum_{k=0}^{N-1}\Big{|}\hat{h}_{DD}^{Tar}[l,k]\Big{|}^{ 2}-\sum_{l=0}^{M-1}\sum_{k=0}^{N-1}\Big{|}\hat{h}_{DD}^{Seg}[l,k]\Big{|}^{2} \Big{)}>P_{th}\bigg{\}},\\ \text{For }NSym_{OTFS}\geq NSym_{th},\end{split}  \tag{33}\]  
The \"\(1\)\" in (33) indicates that the handover should be executed if the condition \(\bigg{(}P_{\text{Tx}}\Big{(}\sum_{l=0}^{M-1}\sum_{k=0}^{N-1}\Big{|}\hat{h}_{ DD}^{Tar}[l,k]\Big{|}^{2}-\sum_{l=0}^{M-1}\sum_{k=0}^{N-1}\Big{|}\hat{h}_{DD}^{ Seg}[l,k]\Big{|}^{2}\bigg{)}>P_{th}\bigg{)}\)For \(NSym_{OTFS}\geq NSym_{th}\) is satisfied. From (2)  
\[\Big{|}\hat{h}_{DD}(l,k)\Big{|}^{2}=\frac{1}{(MN)^{2}}\sum_{q=1}^{Q}\sum_{i_{q} =1}^{P_{q}}\Big{|}\hat{h}_{i_{q}}\Big{|}\hat{h}_{i_{q}}\Big{|}\hat{h}_{i_{q}} \Big{|}\Big{|}\hat{h}_{i_{q}}\Big{|}\Big{|}\Big{|}\Big{|}\Big{|}\Big{|}\Big{|} \Big{(}\hat{h}_{i_{q}},\hat{h}_{i_{q}},k\Big{)}\Big{|}\Big{|}^{2}, \tag{34}\]  
\[=\frac{1}{(MN)^{2}}\sum_{q=1}^{Q}\sum_{i_{q}=1}^{P_{q}}\Big{|}\hat{h}_{i_{q}} \Big{|}^{2}\Big{|}\Big{|}\Big{A}\Big{(}q,\beta_{i_{q}},k\Big{)}\Big{|}^{2}\Big{|} \Big{|}\Big{|}\Big{B}\Big{(}i_{q},\alpha_{i_{q}},I\Big{)}\Big{|}^{2}, \tag{35}\]  
From (3), for on-grid Doppler shifts, i.e., when \(k=\Big{[}T\beta_{i_{q}}N\Big{]}_{N^{\prime}}\)\(\big{|}\mathcal{A}\Big{(}i_{q},\beta_{i_{q}},k\Big{)}\Big{|}=n^{\prime}\), and \(\Big{|}\mathcal{A}\Big{(}i_{q},\beta_{i_{q}},k\Big{)}\Big{|}=\Bigg{|}\frac{ \sin\Big{(}n^{\prime}\frac{\pi}{N}\big{(}k-T\beta_{i_{q}}N\big{)}\Big{)}}{\sin \Big{(}\frac{\pi}{N}\big{(}k-T\beta_{i_{q}}N\big{)}\Big{)}}\Bigg{|}\) otherwise. Also, from (4), for on-grid delay times, i.e., when \(l=\Big{[}\Delta fa_{i_{q}}M\Big{]}_{M^{\prime}}\)\(\big{|}\mathcal{B}\Big{(}i_{q},\alpha_{i_{q}},I\Big{)}\Big{|}=M\), and \(\Big{|}\mathcal{B}\Big{(}i_{q},\alpha_{i_{q}},I\Big{)}\Big{|}=\)0 otherwise. Thus, for on-grid delay and Doppler values:  
\[\Big{|}\hat{h}_{DD}(l,k)\Big{|}^{2}= \begin{cases}\Big{(}\frac{\varphi^{\prime}}{N} \Big{)}^{2}\sum_{q=1}^{Q}\sum_{i_{q}=1}^{P_{q}}\Big{|}\hat{h}_{i_{q}}\Big{|}^{2 }\text{ for }l=\Big{[}\Delta fa_{i_{q}}M\Big{]}_{M^{\prime}},k=\Big{[}T\beta_{i_{q}}N \Big{]}_{N}\\ \frac{1}{N^{\prime}}\sum_{q=1}^{Q}\sum_{i_{q}=1}^{P_{q}}\Big{|}\hat{h}_{i_{q}} \Big{|}^{2}\Big{|}\frac{\sin\Big{(}n^{\prime}\frac{\pi}{N}\big{(}k-T\beta_{i_{ q}}N\big{)}\Big{)}}{\sin\big{(}\frac{\pi}{N}\big{(}k-T\beta_{i_{q}}N\big{)}\big{)}} \Big{|}^{2}\text{ for }l=\Big{[}\Delta fa_{i_{q}}M\Big{]}_{M^{\prime}}k\
eq\Big{[}T\beta_{i_{q}}N \Big{]}_{N},\\ 0\text{ for }l\
eq\Big{[}\Delta fa_{i_{q}}M\Big{]}_{M^{\prime}}\forall k\end{cases}  \tag{36}\]  
The first term in (36) is the summation of all DD channel gains from all coherence periods, which is a constant value for a specified \(n^{\prime}\) value. The second term is the summation of DD channel gains depending on the coherence period \(n^{\prime}\).