# Joint Optimization of Relay Communication Rates in Clustered Drones under Interference Conditions
## 2 System Model
### Interference Model  
During the transmission of information by the relay drone, the jammer exhibits energy detection and power suppression capabilities, thereby inducing communication interference in the relay drone. The interference detection model based on energy is formulated as follows:  
\[\left\{ \begin{array}{l}C_{1}^{uav}:rs(k)=0\\ C_{2}^{uav}:rs(k)=ts(k)\\ C_{3}^{uav}:rs(k)=ts(k)+j(k)\end{array} \right. \tag{5}\]  
In this context, \(rs(k)\) denotes the currently captured signal, \(ts(k)\) represents the communication signal, and \(j(k)\) signifies the interference signal. After the subband signals pass through the band-pass filter, their signal power, \(\rho^{u}(k)\), is computed. Subsequently, the energy levels for each frequency band are calculated. The corresponding calculation expression is given as follows:  
\[E^{t}=\sum_{i=1}^{v}\left|\rho^{u}(k)\right|^{2} \tag{6}\]  
In this context, \(v\) denotes the number of subbands. By comparing \(E^{t}\) with the respective thresholds, \(\lambda_{C_{1}},\lambda_{C2}\), within the model, the channel state is determined. The relay drone also exhibits spectrum-sensing capabilities, enabling it to intelligently select the operating frequency, \(f_{n}^{Rauv}(1\leq n\leq F)\), from the available frequency set \(F_{f}^{Rauv}=\left[f_{I}^{Rauv},f_{h}^{Rauv}\right]\) through frequency hopping, thereby avoiding the impact of interference on relay transmission. The subfrequency ranges within each frequency point do not overlap, and the available frequency set contains \(F\) frequency points, with subchannel bandwidths of \(B_{n}^{Rauv}\). The limits for the working frequency range of the relay drone, shared with the jammers, are defined by \(f_{I}^{Rauv}\) and \(f_{h}^{Rauv}\). Assuming the maximum transmission power of cluster drone \(i\) is \(P_{i}^{F}(k),\ k\in K\), the transmission power of the relay drone is \(P^{R}(k)\), and the maximum transmission power of the jammer is \(P^{I}\), with the product of the antenna gains between them being \(H_{1}^{*}\). In a relay scenario in which the cluster drones need to transmit detection information back to the ground station, the Signal-to-Interference-plus-Noise Ratio (SINR) expression for a relay drone working at frequency \(f_{n}^{Rauv}\) receiving the signal transmitted by cluster drone \(i\) is as follows:  
\[SINR_{i,R}=\frac{P_{i}^{F}(k)H_{i}^{u}(k)}{P^{I}H_{1}^{*}\Lambda+n_{0}B_{n}^{ Rauv}}\ i\in M,\ \forall k \tag{7}\]  
In this model, \(n_{0}\) represents the noise power spectral density, \(H_{i}^{uv}(k)\) denotes the channel gain between the cluster drone, \(i\), and the relay drone. The magnitude of the \(SINR_{i,R}\) directly reflects the interference condition of the relay drone; the smaller its value, the greater the degree of interference, and conversely, the larger its value, the lesser the degree of interference. Assuming the normal communication threshold is \(D_{n}\), \(SINR_{i;R}\geq D_{n}\) indicates the normal transmission of relay information, while \(SINR_{i;R}<D_{n}\) signifies a failure in the information relay. The interference model proposed in this paper encompasses constant frequency interference, sweep frequency interference, and hybrid frequency interference. The corresponding expressions are as follows:  
\[ \begin{array}{l}I_{fixed}^{interf}(k,f)=A_{fixed}\delta(f-f_{fixed})\\ I_{super}^{inter}(k,f)=A_{super}Sa(\frac{f-f_{super}(k)}{B^{kaw}})\\ I_{mixed}^{interf}(k,f)=I_{fixed}^{interf}(k,f)+I_{sweep}^{interf}(k,f)\end{array}  \tag{8}\]  
In this context, \(I_{fixed}^{interf}(k,f),\ I_{sweep}^{interf}(k,f),\ I_{mixed}^{interf}(k,f)\) represent the interference intensity of constant frequency interference, sweep frequency interference, and hybrid frequency interference, respectively, which are functions of time and frequency.