## 3 Bimatrix Stackelberg Game
### Algorithm Design and Analysis  
As delineated in Algorithm 1, the proposed computational framework commences each time slot by quantitatively assessing the Euclidean distances between the UAV, the designated receiver RSU, and the adversarial jammer. These computed spatial metrics serve as the foundational parameters upon which the algorithm constructs the respective payoff matrices, denoted as \(\mathbf{A}\) and \(\mathbf{B}\). Specifically, \(\mathbf{A}\) is constructed as a matrix with column vectors \([\mathbf{\alpha}_{1},\dots,\mathbf{\alpha}_{M}]\), while \(\mathbf{B}\) is formulated as \([\beta_{1},\dots,\beta_{M}]\). For example, in vector \(\mathbf{\alpha}_{m}\), each element quantifies the utility the UAV gains upon selecting various center frequencies, given that the jammer adopts the \(m\)-th center frequency. Subsequently, for each identified pure strategy \(\pi_{I}\) available to the jammer, the algorithm rigorously determines the UAV's corresponding optimal mixed strategy by solving a well-posed linear programming problem. To effectively tackle the linear programming complexities outlined in Algorithm 1, we introduce Algorithm 2. The developed method serves as a robust and computationally proficient framework specifically tailored to address the linear programming challenges presented in Algorithm 1. After performing a series of mathematical manipulations, including the inversion of the original objective function and the introduction of slack variables, Problem (16) is meticulously transformed into its standard form, indicated as  
\[\min\mathbf{\alpha}_{m}^{\text{s}}\text{$\,\mathrm{T}$}\mathbf{x}, \tag{17}\] \[\text{s.t. }\left\{ \begin{array}{l}\mathbf{C}\mathbf{x}=0,\\ \sum\limits_{m=1}^{2M-1}\mathbf{x}_{m}=1,\\ \mathbf{x}=\left[\begin{matrix}\pi_{U}\\ \mathbf{s}\end{matrix}\right],\mathbf{x}\in\mathbb{R}^{2M-1},\\ \mathbf{x}\geq 0,\\ \mathbf{\alpha}_{m}^{\text{s}}=\left[\begin{matrix}\mathbf{\alpha}_{m}\\ 0\\ \vdots\\ 0\end{matrix}\right],\mathbf{\alpha}_{m}^{\text{s}}\in\mathbb{R}^{2M-1},\end{array} \right.\]  
where \(\mathbf{s}\) as a set of slack variables, given the inequality constraints inherent in the original problem (16). These variables are seamlessly integrated into the decision variable \(\pi_{U}\) from the original problem, leading to the composite formation of \(\mathbf{x}\). Within this context, \(\mathbf{\alpha}_{m}^{s}\) denotes the coefficient in the objective function following the inclusion of the slack variable, ensuring that all coefficients corresponding to these slack variables remain consistently zero. The coefficient matrix \(\mathbf{C}\) is displayed as follows:\[\mathbf{C}= \begin{bmatrix}\beta_{m}-\beta_{1}&-1&\cdots&0&0&0&\cdots&0\\ \vdots&&&&&&&&&&\\ \beta_{m}-\beta_{m-1}&0&\cdots&-1&0&0&\cdots&0\\ \beta_{m}-\beta_{m+1}&0&\cdots&0&0&-1&\cdots&0\\ \vdots&&&&&&&\\ \beta_{m}-\beta_{M}&0&\cdots&0&0&0&\cdots&-1\end{bmatrix} ,\mathbf{C}\in\mathbb{R} ^{(M-1)\times(2M-1)}, \tag{18}\]  
where the matrix \(\mathbf{C}\) is the standardized coefficient matrix. This matrix elucidates that, when the jammer adopts any strategy other than the \(m\)-strategy, the resultant payoff will invariably not exceed that achieved by adopting the \(m\)-strategy. This solidifies the hypothesis that selecting the \(m\)-strategy emerges as the jammer's optimal response. Through projective transformation, the optimization problem in (17) is converted into a sphere domain where minimization occurs. After finding the optimal solution in the sphere domain, an inverse transformation maps this solution back to the original decision space, thus approximating the solution of the initial problem. This iterative process eventually results in an optimal \(p_{f_{ll}}\) that converges in polynomial time. Subsequently, the transformation process of Problem (17) is analyzed in detail.