## 5 Conclusions  
This study tackles the challenge of center frequency selection for unmanned aerial vehicles (UAVs) faced with jamming attacks by employing a bimatrix Stackelberg game framework. We model the interaction between the UAV and the jammer as a Stackelberg game, subsequently transforming it into a bimatrix formulation to ascertain the UAV's optimal mixed strategy. Furthermore, we craft a linear programming solution algorithm. We provide a rigorous proof demonstrating that this algorithm is capable of determining the UAV's mixed strategy against each individual strategy employed by the jammer, all within polynomial time complexity. Ultimately, this facilitates the derivation of the UAV's optimal mixed strategy. The efficacy of our approach is corroborated through simulation experiments, which confirm convergence to a Nash equilibrium.  
Our simulation results compellingly demonstrate that the proposed method significantly outperforms existing alternatives, such as Frequency-Hopping Spread Spectrum (FHSS) and Random Selection (RS), in terms of both stability and payoff in A2G communication scenarios. By adeptly selecting the optimal center frequency for the UAV, our approach effectively neutralizes the adverse impact of jamming attacks and optimizes communication efficiency. Utilizing the Stackelberg game framework and achieving convergence to the Nash equilibrium, this research offers valuable insights and practical implications for the judicious selection of UAV center frequencies in jamming-prone environments, thereby enhancing the overall performance and reliability of A2G communications.  
In our study, we focused on a scenario with a singular receiver and jammer. While this provides insights, it might not encapsulate the intricacies of real-world environments where interactions among multiple transmitters and jammers are commonplace. Recog  
Figure 5: The communication payoffs of the UAV in different scenarios.  
Figure 6: The impact of sub-bandwidth on communication payoff of the UAV.  
nizing this constraint, our future endeavors aim to broaden the scope by incorporating multiple jammers and receivers. Such an extension will furnish a holistic assessment of our algorithm's resilience to jamming, especially in multifaceted interference landscapes with numerous transmitters.  
Conceptualization, L.C., D.T. and X.D.; methodology, L.C. and Z.X.; software, L.C., Z.X., and D.T.; validation, D.Z. and L.C.; formal analysis, L.C. and J.Z.; investigation, K.Q.; resources, X.D. and D.Z.; data curation, L.C. and X.D.; writing--original draft preparation, L.C. and Z.X.; writing--review and editing, D.Z.; visualization, L.C., D.T. and K.Q.; supervision, Z.X.; project administration, J.Z.; funding acquisition, D.T. and J.Z. All authors have read and agreed to the published version of the manuscript.  
This research is partly supported by the National Natural Science Foundation of China (Grant No. 52202391, 52302510, and U20A20155) and the Fundamental Research Funds for the Central Universities (Grant No.YWF-23-Q-1066).  
Our data will be available at [[https://github.com/LongboCheng123](https://github.com/LongboCheng123)]([https://github.com/LongboCheng123](https://github.com/LongboCheng123)) /Electronics-2623630-dataset.git.  
The authors declare no conflict of interest.