# Joint Optimization of Relay Communication Rates in Clustered Drones under Interference Conditions
## 3 Problem Description  
This section focuses on a scenario in which swarm drones transmit collected information back to the ground station in real time, exploring the modeling issues of real-time communication between the swarm drones and the ground station with the assistance of a relay drone. Assume that the working frequency of the relay drone is \(f_{n}^{Rauv}\), and this channel comprises \(M/2\) subcarriers for the paired transmission of information from the swarm drones. During this process, the relay drone often faces a certain degree of malicious interference. Considering the high-speed movement of drones and the complex electromagnetic environment, their channel state information (CSI) may become imperfect or outdated. In this context, the traditional assumption of perfect CSI is unrealistic. By referring to current mainstream methods for CSI estimation and prediction, such as deep learning algorithms [19], adaptive algorithms [20], and coding techniques [21], it is possible to dynamically predict and compensate for the quality of the CSI, thereby addressing the issues related to outdated and imperfect CSI. According to the principles of Non-Orthogonal Multiple Access (NOMA), the sender transmits data by allocating different levels of transmission power to different users, and the receiver decodes the signals sequentially by detecting the gain differences of the received signals, thus canceling the links with smaller channel gains [22]. In the designated task scenario, the communication link gains from swarm drone \(i\) and swarm drone \(j\) to the relay drone are \(H_{i}^{w}(k)\) and \(H_{j}^{w}(k)\), respectively. When \(H_{i}^{w}(k)<H_{j}^{w}(k)\), the relay drone decodes the link from swarm drone \(j\) first; otherwise, it decodes the link from swarm drone \(i\) first. The power allocation factor set for the swarm drones is \(\lambda=\{\lambda_{1},\lambda_{2},...,\lambda_{M}\}\), and since the swarm drones select only one channel for data transmission in different time slots, in time slot \(k\), the SINR for the relay drone working on the frequency \(f_{n}^{Raw}\) channel and receiving the transmission signal from swarm drone \(i\) is as follows:  
\[ \begin{split} SINR_{i,R}^{Raw}=\frac{\lambda_{i}(k)P^{F}(k)H_{i}^{ w}(k)}{Y(f,f_{x})(P^{I}H_{1}^{*}\Lambda/S)+\sum\limits_{j\in\Gamma}\lambda_{j}(k)P^{F} (k)H_{j}^{w}(k)+n_{0}B_{n}^{Raw}}i\in M,\ \forall k\\ =\frac{\lambda_{i}(k)P^{F}(k)G_{t}G_{r}(\lambda^{\copyright)}^{2}} {\left(4\pi\|Q(k)-F_{i}(k)\|_{2}\right)^{2}(Y(f,f_{x})(P^{I}H_{1}^{*}\Lambda/S)+ \sum\limits_{j\in\Gamma}\lambda_{j}(k)P^{F}(k)H_{j}^{w}(k)+n_{0}B_{n}^{Raw}}\\ \Gamma=\Big{\{}j\Big{|}H_{j}^{w}(k)<H_{i}^{w}(k),1<j\leq M\Big{\}} \end{split}  \tag{14}\]  
Similarly, in time slot \(k\), the Signal-to-Noise Ratio (SNR) for the ground station receiving the transmission signal from the relay drone is as follows:  
\[SNR_{R,S}^{Raw}=\frac{P^{R}(k)H^{w}(k)}{n_{0}B_{n}^{Raw}}=\frac{P^{R}(k)G_{t}G _{r}(\lambda^{\copyright)}^{2}}{n_{0}B_{n}^{Raw}(4\pi\|Q(k)\|_{2})^{2}}\ \forall k \tag{15}\]  
The relay drone employs an amplify-and-forward method to transmit information. As stated in reference [23], in time slot \(k\), the SNR for the ground station receiving the two-hop link from cluster drone \(i\) is a follows:  
\[ \begin{split} SNR_{i,S}=\frac{\dot{S}NR_{i,R}^{\text{Carr}}SN_{R, S}^{Raw}}{\dot{S}NR_{i,R}^{Raw}+\dot{S}NR_{i,R}^{Raw}+\dot{S}NR_{i,R}^{Raw}+ \dot{S}NR_{i,R}^{Raw}+\dot{S}NR_{i,R}^{Raw}+\dot{S}NR_{i,R}^{Raw}+\dot{S}NR_{i,R }^{Raw}+\dot{S}NR_{i,R}^{Raw}+\dot{S}NR_{i,R}^{Raw}+\dot{S}NR_{i,R}^{Raw}\\ =\frac{\lambda_{i}(k)P^{F}(k)P^{R}(k)\left(G_{t}G_{r}(\lambda^{ \copyright)}^{2})^{2}}{I_{1}^{t}+I_{2}^{t}}\\ I_{2}^{t}=P^{R}(k)G_{t}G_{r}(\lambda^{\copyright)}^{2}(4\pi\|Q(k)-F_ {i}(k)\|_{2})^{2}+n_{0}B_{n}^{Raw}(4\pi\|Q(k)\|_{2})^{2}(4\pi\|Q(k)-F_{i}(k)\|_ {2})^{2}\\ I_{3}^{t}=Y(f,f_{x})(Pf\,H_{1}^{*}\Lambda/S)+\sum\limits_{j\in \Gamma}\lambda_{j}(k)P^{F}(k)H_{j}^{w}(k)+n_{0}B_{n}^{Raw}\end{split}