In recent years, the rapid development of wireless communication networks has greatly promoted the advancement of unmanned aerial vehicles (UAVs) technology. UAVs have been increasingly deployed in various mission scenarios including military reconnaissance, disaster rescue, environmental monitoring, and intelligent agriculture. A single UAV can perform simple tasks, while a swarm of UAVs is often required to accomplish more complex and diverse missions. However, in practical application scenarios, UAV swarms face severe challenges caused by limited spectrum resources, insufficient spectrum utilization, dynamic task variations, and malicious jamming. To address these challenges, I focus on mission-driven spectrum allocation and cooperative methods for UAV swarms in this work. Specifically, I investigate three typical scenarios: homogeneous multi-task execution, heterogeneous multi-task execution, and jamming-affected task execution. For each scenario, I formulate optimization models, propose efficient solution algorithms, and verify their effectiveness through extensive simulations. The main contributions of this work are summarized as follows.
First, aiming at the problem of insufficient spectrum sharing among UAV swarms when they perform homogeneous multi-tasks under limited spectrum resources, I construct a spectrum resource allocation model for UAV groups based on multi-task grouping. The model considers both channel allocation and power allocation for cluster-head UAVs and member UAVs. I propose a joint power and spectrum resource optimization algorithm that simultaneously optimizes the channel assignment and transmit power of each UAV to maximize the minimum group throughput. The simulation results demonstrate that the proposed algorithm improves the group throughput while ensuring transmission fairness among groups. Second, for the scenario where UAV swarms execute heterogeneous multi-tasks with dynamic task changes, I introduce the channel switching cost caused by different task types and construct a dynamic spectrum allocation model for UAV clusters. The objective is to minimize the total task completion time by jointly optimizing channel and power resources. A block-coordinate-descent-based spectrum resource joint optimization method is proposed, and simulation results show that the proposed method significantly reduces the task completion time compared with benchmark algorithms. Third, when UAV swarms are subjected to malicious jamming, I formulate a Stackelberg game model in which the jammer is the leader and the cluster-head UAVs are followers. Different utility functions are designed for the jammer and the cluster-head UAVs, and a hierarchical adversarial game-based spectrum cooperation algorithm is proposed. The existence of a stable Stackelberg equilibrium is proved, and simulation results verify that the proposed algorithm effectively reduces frequency conflicts among cluster-head UAVs and achieves the optimal channel selection strategy against jamming.
1 Introduction
Unmanned aerial vehicles have been widely used in both military and civilian fields due to their small size, low cost, strong concealment, high survivability, and flexible deployment. In military applications, UAV swarms can perform reconnaissance, electronic jamming, saturation attack, and regional blockade. In civilian applications, UAVs are used for express delivery, environmental monitoring, disaster rescue, and intelligent agriculture. With the increasing complexity of tasks, a single UAV cannot meet the requirements of complicated missions because of its limitations in payload, energy, and communication capability. Therefore, multi-UAV cooperation has become a promising paradigm. A UAV swarm can compensate for the shortcomings of a single UAV by cooperative operation, which improves the system cost efficiency, scalability, survivability, and task execution efficiency. However, the large-scale deployment of UAV swarms introduces new challenges such as massive data exchange, frequent network topology changes, unstable links, and low spectrum utilization. In addition, the spectrum resources available to UAV swarms are usually limited and non-renewable. With the rapid growth of wireless devices and services, the demand for spectrum resources has increased dramatically, which aggravates the shortage of spectrum. Therefore, how to allocate and coordinate spectrum resources efficiently in mission-driven UAV swarms has become an important research topic.
Traditional fixed spectrum allocation methods cannot adapt to the dynamic and heterogeneous requirements of UAV swarm missions. Different tasks, such as search and rescue, surveillance, and communication relay, have different requirements for bandwidth, delay, and reliability. If the spectrum allocation is unreasonable, the communication between UAVs will suffer from severe interference, which degrades the cooperative performance and reduces the mission completion rate. On the other hand, the dynamic flight trajectories and varying task areas make the wireless environment time-varying. Thus, a task-driven dynamic spectrum allocation approach is necessary to improve spectrum utilization and support reliable communication in UAV swarms. Furthermore, when UAV swarms are confronted with malicious jamming, the control links may be interrupted, and the UAVs cannot obtain accurate spectrum usage information from others. In such weak-information scenarios, cooperative spectrum allocation becomes even more challenging. To address these problems, I study the spectrum allocation and cooperation methods for UAV swarms from the perspective of mission requirements. The contributions of this thesis are summarized as follows.
(1) For homogeneous multi-task scenarios, I propose a joint power and spectrum resource optimization algorithm. The UAV swarm is divided into multiple groups, each group contains one cluster-head UAV and several member UAVs. The spectrum sharing mechanism allows member UAVs to reuse the channels occupied by cluster-head UAVs from other groups in an underlay manner. The objective is to maximize the minimum throughput among all groups while considering co-channel interference. The mixed integer nonlinear programming problem is decomposed into channel allocation and power allocation subproblems. An improved genetic algorithm is proposed for channel allocation, and geometric programming is used to transform the non-convex power allocation problem into a convex problem. Simulation results show that the proposed algorithm achieves a higher minimum group throughput than benchmark algorithms.
(2) For heterogeneous multi-task scenarios, I consider multiple types of tasks with different data transmission requirements and dynamic task arrivals. The UAV swarm executes tasks in different groups, and each group may switch among different task types over time. To reduce the negative impact of channel switching, I introduce a channel switching cost into the objective function. The target is to minimize the maximum task completion time among all groups. A block coordinate descent (BCD) framework is designed to alternately optimize channel assignment and transmit power. The channel assignment is optimized by an improved genetic algorithm, and the power allocation is solved via geometric programming and the gradient projection method. Extensive simulations validate that the proposed method outperforms fixed-power, fixed-channel, and random allocation strategies.
(3) For jamming-affected scenarios, I formulate a dynamic spectrum hierarchical game based on the Stackelberg game. The jammer acts as the leader and chooses the jamming channel to maximize its utility, while the cluster-head UAVs act as followers and choose the transmission channels to maximize their utilities. For the leader subproblem, a Q-learning-based channel selection algorithm is employed. For the follower subproblem, a multi-agent proximal policy optimization (MAPPO) algorithm is proposed to achieve cooperative channel selection among multiple UAVs in a distributed manner. The simulation results show that the proposed hierarchical adversarial game algorithm can effectively reduce the frequency conflicts among cluster-head UAVs and improve the sum throughput against malicious jamming.
2 System Models and Problem Formulations
2.1 System Model for Homogeneous Multi-task Scenario
In the homogeneous multi-task scenario, a UAV swarm is deployed in a large target area to perform reconnaissance tasks. The target area is divided into \(G\) disjoint subareas, and each subarea is assigned to one UAV group. The set of UAV groups and cluster-head UAVs is denoted by \(\mathcal{G}=\{1,2,\ldots,G\}\). Each group consists of one cluster-head UAV and \(N\) member UAVs, and the set of member UAVs is denoted by \(\mathcal{N}=\{1,2,\ldots,N\}\). The swarm has \(M\) available channels with bandwidth \(B_0\), and the channel set is \(\mathcal{M}=\{1,2,\ldots,M\}\). Cluster-head UAVs transmit the aggregated reconnaissance information to a ground control station (GCS) using orthogonal channels, so there is no co-channel interference among cluster-head UAVs. Member UAVs send their collected data to the cluster-head UAV in an underlay manner, i.e., they may reuse the channels of cluster-head UAVs from other groups. The channel allocation matrix of cluster-head UAVs is denoted by \(\boldsymbol{\theta}^G=[\theta^G_{g,m}]_{G \times M}\), where \(\theta^G_{g,m}=1\) if channel \(m\) is assigned to cluster-head UAV \(g\), otherwise zero. Similarly, the channel allocation matrix of member UAVs is \(\boldsymbol{\theta}^N=[\theta^{N,g}_{n,m}]_{G \times N \times M}\), where \(\theta^{N,g}_{n,m}=1\) if channel \(m\) is assigned to member UAV \(n\) in group \(g\). The transmit power matrices are expressed as \(\mathbf{P}^G=[P^G_{g,m}]_{G \times M}\) and \(\mathbf{P}^N=[P^{N,g}_{n,m}]_{G \times N \times M}\).
For cluster-head UAV \(g\) using channel \(m\), the signal-to-interference-plus-noise ratio (SINR) can be written as
$$ \gamma^G_{g,m}=\frac{P^G_{g,m}d_{g,O}^{-\alpha}}{\sum_{j\neq g}\sum_{n=1}^{N}\theta^{N,j}_{n,m}P^N_{n,j}d_{n,O}^{-\alpha}+\delta_0}, $$
where \(d_{g,O}\) is the distance between cluster-head UAV \(g\) and the GCS, \(d_{n,O}\) is the distance between member UAV \(n\) in group \(j\) and the GCS, \(\alpha\) is the path-loss exponent, and \(\delta_0\) is the noise power. The throughput of cluster-head UAV \(g\) on channel \(m\) is
$$ R^G_{g,m}=B_0 \theta^G_{g,m}\log_2\left(1+\gamma^G_{g,m}\right). $$
For member UAV \(n\) in group \(g\) using channel \(m\), the SINR is expressed as
$$ \gamma^{N,g}_{n,m}=\frac{P^{N,g}_{n,m}d_{n,g}^{-\alpha}}{\sum_{j\neq g}P^G_{j,m}d_{j,g}^{-\alpha}+\sum_{i\neq n}\theta^{N,g}_{i,m}P^{N,g}_{i,m}d_{i,g}^{-\alpha}+\delta_0}, $$
where \(d_{n,g}\) is the distance from member UAV \(n\) to its cluster-head UAV in group \(g\), \(d_{j,g}\) and \(d_{i,g}\) are the distances from cluster-head UAV \(j\) and member UAV \(i\) to cluster-head UAV \(g\), respectively. The throughput of member UAV \(n\) on channel \(m\) is
$$ R^{N,g}_{n,m}=B_0 \theta^{N,g}_{n,m}\log_2\left(1+\gamma^{N,g}_{n,m}\right). $$
The group throughput is determined by the smaller value of the cluster-head link throughput and the aggregate member-to-cluster-head throughput. I define \(R_g=\min\left\{\sum_{m=1}^{M}R^G_{g,m}, \sum_{n=1}^{N}\sum_{m=1}^{M}R^{N,g}_{n,m}\right\}\). To ensure fairness among groups, I maximize the minimum group throughput. The optimization problem is formulated as
$$ \begin{aligned} \max_{\boldsymbol{\theta}^G,\boldsymbol{\theta}^N,\mathbf{P}^G,\mathbf{P}^N} \; & \eta \\ \text{s.t.} \quad & C1: \theta^G_{g,m}, \theta^{N,g}_{n,m}\in\{0,1\}, \forall g,m,n, \\ & C2: \theta^G_{g,m}+\theta^{N,g}_{n,m}\le 1, \forall g,m,n, \\ & C3: \sum_{g=1}^{G}\theta^G_{g,m}\le 1, \forall m, \\ & C4: \sum_{m=1}^{M}\theta^G_{g,m}=1, \forall g, \\ & C5: \sum_{m=1}^{M}\theta^{N,g}_{n,m}=1, \forall g,n, \\ & C6: 0\le P^G_{g,m}\le P^G_{\max}, \forall g,m, \\ & C7: 0\le P^{N,g}_{n,m}\le P^N_{\max}, \forall g,n,m, \\ & C8: \sum_{m=1}^{M}R^G_{g,m}\ge \eta, \forall g, \\ & C9: \sum_{n=1}^{N}\sum_{m=1}^{M}R^{N,g}_{n,m}\ge \eta, \forall g, \\ & C10: R_g\ge \eta, \forall g. \end{aligned} $$
This problem is a mixed integer nonlinear programming (MINLP) problem, which is generally NP-hard and difficult to solve directly. Therefore, I decompose it into a channel allocation subproblem and a power allocation subproblem, as described in the next section.
2.2 System Model for Heterogeneous Multi-task Scenario
In the heterogeneous multi-task scenario, the UAV swarm performs \(H\) different types of tasks in a predefined sequence. Each UAV group independently executes tasks in its assigned subarea. I divide the whole mission horizon into \(T\) time slots, and in each time slot, the task type and spectrum allocation remain unchanged. Let \(D_{g,h}\) denote the amount of data that group \(g\) needs to transmit for task \(h\). The task execution time for group \(g\) and task \(h\) is \(T_{g,h}=D_{g,h}/R_g\), where \(R_g\) is the actual throughput of group \(g\). The spectrum allocation in the current time slot may differ from that in the previous slot, and switching a channel incurs a throughput loss. Let \(\mu\) be the channel switching cost factor. For cluster-head UAV \(g\) switching to channel \(m\) in time slot \(t\), the loss is given by
$$ R^{\mathrm{loss},G}_{g,m}(t)=\frac{\mu}{2}\left(\theta^G_{g,m}(t)-\theta^G_{g,m}(t-1)\right)^2 R^G_{g,m}(t). $$
To avoid the square term, I use the equivalent expression
$$ R^{\mathrm{loss},G}_{g,m}(t)=\frac{\mu}{2}\left(\theta^G_{g,m}(t)(1-\theta^G_{g,m}(t-1))+\theta^G_{g,m}(t-1)(1-\theta^G_{g,m}(t))\right) R^G_{g,m}(t). $$
Similarly, for member UAV \(n\) in group \(g\), the switching loss is
$$ R^{\mathrm{loss},N}_{n,m}(t)=\frac{\mu}{2}\left(\theta^{N,g}_{n,m}(t)-\theta^{N,g}_{n,m}(t-1)\right)^2 R^{N,g}_{n,m}(t). $$
Then, the actual throughput of cluster-head UAV \(g\) and member UAV \(n\) in the time slot \(t\) are, respectively,
$$ \tilde{R}^G_{g}(t)=\sum_{m=1}^{M}\left(R^G_{g,m}(t)-R^{\mathrm{loss},G}_{g,m}(t)\right), $$
$$ \tilde{R}^{N,g}_{n}(t)=\sum_{m=1}^{M}\left(R^{N,g}_{n,m}(t)-R^{\mathrm{loss},N}_{n,m}(t)\right). $$
The actual group throughput is \(\tilde{R}_g(t)=\min\left\{\tilde{R}^G_{g}(t), \sum_{n=1}^{N}\tilde{R}^{N,g}_{n}(t)\right\}\). The objective is to minimize the maximum total task completion time of all groups. Consequently, the optimization problem is formulated as
$$ \begin{aligned} \min_{\boldsymbol{\theta}^G,\boldsymbol{\theta}^N,\mathbf{P}^G,\mathbf{P}^N} \quad & \max_{g\in\mathcal{G}} \sum_{h=1}^{H} \frac{D_{g,h}}{\sum_{t=1}^{T}\tilde{R}_g(t)} \\ \text{s.t.}\quad & C1: \theta^G_{g,m}(t),\theta^{N,g}_{n,m}(t)\in\{0,1\}, \\ & C2: \theta^G_{g,m}(t)+\theta^{N,g}_{n,m}(t)\le 1, \\ & C3: \sum_{g=1}^{G}\theta^G_{g,m}(t)\le 1, \\ & C4: \sum_{m=1}^{M}\theta^G_{g,m}(t)=1,\\ & C5: \sum_{m=1}^{M}\theta^{N,g}_{n,m}(t)=1,\\ & C6: 0\le P^G_{g,m}(t)\le P^G_{\max},\\ & C7: 0\le P^{N,g}_{n,m}(t)\le P^N_{\max},\\ & C8: \frac{D_{g,h}}{\tilde{R}^G_{g}(t)}\le T_g, \quad \forall g,h,t,\\ & C9: \frac{D_{g,h}}{\tilde{R}^{N,g}_{n}(t)}\le T_g, \quad \forall g,h,n,t. \end{aligned} $$
This problem is also a MINLP because of the binary channel assignment variables and continuous power variables. In addition, the coupling between the channel allocation and power allocation makes the problem even more challenging. I will solve it by a block coordinate descent method.
2.3 System Model for Jamming-Affected Multi-task Scenario
In the jamming-affected scenario, the UAV swarm executes reconnaissance missions in \(G\) subareas. Each group has one cluster-head UAV and several member UAVs. There is a malicious jammer \(J\) that can select one channel in each time slot to transmit jamming signals. The cluster-head UAVs communicate with the GCS in a frequency-division multiple access manner. I denote by \(\theta^G_{g,m}(t)\in\{0,1\}\) the channel indicator of cluster-head UAV \(g\) using channel \(m\) in time slot \(t\), and by \(\theta^J_{J,m}(t)\in\{0,1\}\) the jammer’s channel indicator on channel \(m\) in time slot \(t\). The wireless channel between a cluster-head UAV and the GCS is a probabilistic line-of-sight (LoS)/non-line-of-sight (NLoS) channel. The average path loss of cluster-head UAV \(g\) is
$$ h_g(t)=P^{\mathrm{LoS}}_g(t)h^{\mathrm{LoS}}_g(t)+P^{\mathrm{NLoS}}_g(t)h^{\mathrm{NLoS}}_g(t), $$
where
$$ h^{\mathrm{LoS}}_g(t)=20\log_{10}\left(\frac{4\pi f_c d_g^t}{c}\right), $$
$$ h^{\mathrm{NLoS}}_g(t)=20\log_{10}\left(\frac{4\pi f_c d_g^t}{c}\right)+\psi_{\mathrm{NLoS}}, $$
$$ P^{\mathrm{LoS}}_g(t)=\frac{1}{1+b_1\exp\left(-b_2(\delta_g^t-b_1)\right)}, $$
$$ P^{\mathrm{NLoS}}_g(t)=1-P^{\mathrm{LoS}}_g(t), $$
$$ \delta_g^t=\frac{180}{\pi}\arcsin\left(\frac{H}{d_g^t}\right). $$
Here, \(f_c\) is the carrier frequency, \(d_g^t\) is the distance from cluster-head UAV \(g\) to the GCS at time slot \(t\), \(c\) is the speed of light, \(\psi_{\mathrm{NLoS}}\) is the extra loss due to NLoS, \(b_1\) and \(b_2\) are environment-dependent constants, \(H\) is the UAV flight altitude, and \(\delta_g^t\) is the elevation angle. The SINR of cluster-head UAV \(g\) on channel \(m\) in time slot \(t\) is given by
$$ \gamma_{g,m}(t)=\frac{P^G h_g(t)^{-1}}{\sum_{i\neq g}\theta^G_{i,m}(t)P^G h_i(t)^{-1}+\theta^J_{J,m}(t)P^J h_J(t)^{-1}+\delta_0}, $$
where \(P^G\) is the transmit power of a cluster-head UAV, \(P^J\) is the jamming power, \(h_J(t)\) is the path loss from the jammer to the GCS, and \(\delta_0\) is the noise power. The achievable rate of cluster-head UAV \(g\) on channel \(m\) in time slot \(t\) is
$$ R_{g,m}(t)=B_0\log_2\left(1+\gamma_{g,m}(t)\right). $$
Considering the channel switching cost, the actual rate of cluster-head UAV \(g\) on channel \(m\) is
$$ R^{\mathrm{act}}_{g,m}(t)=R_{g,m}(t)-\frac{\mu}{2}\left(\theta^G_{g,m}(t)-\theta^G_{g,m}(t-1)\right)^2R_{g,m}(t). $$
The utility function of the cluster-head UAVs is the total actual throughput:
$$ U_G=\sum_{g=1}^{G}\sum_{t=1}^{T}\sum_{m=1}^{M}R^{\mathrm{act}}_{g,m}(t). $$
The objective of the UAVs is to maximize this utility by optimizing the channel assignment \(\boldsymbol{\theta}^G\). On the contrary, the jammer aims to minimize the UAV’s total throughput, so its utility is
$$ U_J=-U_G. $$
I model the interactions between the jammer and the UAVs as a Stackelberg game. The jammer is the leader and first chooses its jamming channel selection strategy \(\varepsilon_J\); then, the cluster-head UAVs act as followers and choose their channel selection strategies \(\boldsymbol{\omega}=\{w_1,w_2,\ldots,w_G\}\) accordingly. The Stackelberg equilibrium is defined as a strategy pair \((\varepsilon_J^*,\boldsymbol{\omega}^*)\) such that
$$ U_J(\varepsilon_J^*,\boldsymbol{\omega}^*) \ge U_J(\varepsilon_J,\boldsymbol{\omega}^*), \quad \forall \varepsilon_J, $$
$$ U_G(\varepsilon_J^*,\boldsymbol{\omega}^*) \ge U_G(\varepsilon_J^*,w_g,\boldsymbol{\omega}_{-g}^*), \quad \forall g, w_g. $$
Since the game is a potential game, the existence of the Stackelberg equilibrium is guaranteed.
3 Solution Algorithms
3.1 Joint Power and Spectrum Resource Optimization Algorithm for Homogeneous Multi-task Scenario
To solve the MINLP problem in the homogeneous multi-task scenario, I propose an iterative algorithm that alternately optimizes the channel assignment and the transmit power. The channel assignment subproblem is an integer programming problem. I design an improved genetic algorithm (IGA) that can simultaneously optimize the channel allocation of cluster-head UAVs and member UAVs. The key steps of the IGA are as follows:
(1) Gene encoding: a binary vector is used to represent the channel assignment of cluster-head UAVs, and another binary vector is used for member UAVs. These two vectors are combined as an individual in the population.
(2) Initial population: a set of feasible individuals is randomly generated, and each individual is checked against the constraints C1–C5 in the formulated problem. If an individual violates the constraints, a repair procedure is applied.
(3) Fitness function: the objective value \(\eta\) is used as the fitness. A larger \(\eta\) indicates a better individual.
(4) Selection: roulette wheel selection is adopted to choose parents for reproduction. This method gives higher-selection probability to individuals with larger fitness, while still maintaining diversity.
(5) Crossover: single-point crossover is performed on the selected pairs with a crossover probability.
(6) Mutation: bit-flipping mutation is applied with a mutation probability to generate new individuals.
(7) Elitist preservation: the best \( \lambda-\lambda’ \) individuals from the parent population are directly copied to the next generation to avoid losing excellent solutions.
For fixed channel assignment, the power allocation subproblem is still non-convex. To handle this, I use geometric programming (GP) and a logarithmic transformation. Specifically, let \(\tilde{P}^G_{g,m}=\log(P^G_{g,m})\). Under the high SINR approximation, \(\log_2(1+\gamma)\approx \log_2(\gamma)\), the non-convex constraints become convex. Therefore, the power subproblem can be solved by the CVX toolbox. Because the cluster-head power and member power are coupled, I optimize them alternately. The complete joint algorithm is summarized as follows:
Algorithm 1: Joint Power and Spectrum Resource Optimization Algorithm
Input: \(G,N,M,P^G_{\max},P^N_{\max},\varepsilon,r_{\max}\). Initialize feasible \(\boldsymbol{\theta}^G_0,\boldsymbol{\theta}^N_0,\mathbf{P}^G_0,\mathbf{P}^N_0\). Set \(r=1\). Repeat:
1. Fix \(\mathbf{P}^G_r,\mathbf{P}^N_r\), and use the IGA to solve the channel assignment subproblem. Obtain \(\boldsymbol{\theta}^{G}_{r+1},\boldsymbol{\theta}^{N}_{r+1}\).
2. Fix \(\boldsymbol{\theta}^{G}_{r+1},\boldsymbol{\theta}^{N}_{r+1},\mathbf{P}^{N}_{r}\), and solve the convex cluster-head power subproblem. Obtain \(\mathbf{P}^{G}_{r+1}\).
3. Fix \(\boldsymbol{\theta}^{G}_{r+1},\boldsymbol{\theta}^{N}_{r+1},\mathbf{P}^{G}_{r+1}\), and solve the convex member power subproblem. Obtain \(\mathbf{P}^{N}_{r+1}\).
4. Update \(\eta_{r+1}\) and set \(r=r+1\). Until \(|\eta_{r+1}-\eta_r|\le \varepsilon\) or \(r>r_{\max}\). Output the optimal solutions.
3.2 BCD-Based Spectrum Resource Joint Optimization Method for Heterogeneous Multi-task Scenario
For the heterogeneous multi-task scenario, the objective function involves both the channel assignment and the transmit power over \(T\) time slots. I apply the block coordinate descent (BCD) method to decompose the original problem. In each iteration, I solve two subproblems: the channel assignment subproblem and the power allocation subproblem. The channel assignment subproblem is solved by the improved genetic algorithm, similar to Algorithm 1, but with the objective of minimizing the total completion time. The power allocation subproblem is divided into two parts: cluster-head power optimization and member power optimization. For each part, I first transform the non-convex problem into a convex problem using geometric programming. Then, I apply the gradient projection method to find the optimal power values. The detailed steps are described as follows:
Algorithm 2: BCD-Based Spectrum Resource Joint Optimization Method
Input: \(G,N,M,H,\mu,\varepsilon_2,r_{\max}\). Initialize feasible \(\boldsymbol{\theta}^G_0,\boldsymbol{\theta}^N_0,\mathbf{P}^G_0,\mathbf{P}^N_0\). Set \(r=1\). Repeat:
1. Given \(\mathbf{P}^G_r,\mathbf{P}^N_r\), solve the channel assignment subproblem using the improved GA and obtain \(\boldsymbol{\theta}^{G}_{r+1},\boldsymbol{\theta}^{N}_{r+1}\).
2. Given \(\boldsymbol{\theta}^{G}_{r+1},\boldsymbol{\theta}^{N}_{r+1},\mathbf{P}^{N}_{r}\), solve the cluster-head transmit power subproblem using geometric programming and the gradient projection method. Obtain \(\mathbf{P}^{G}_{r+1}\).
3. Given \(\boldsymbol{\theta}^{G}_{r+1},\boldsymbol{\theta}^{N}_{r+1},\mathbf{P}^{G}_{r+1}\), solve the member transmit power subproblem using the same approach. Obtain \(\mathbf{P}^{N}_{r+1}\).
4. Compute the objective value \(\Psi_{r+1}\). If \(|\Psi_{r+1}-\Psi_r|\le \varepsilon_2\) or \(r>r_{\max}\), stop; otherwise \(r=r+1\).
The convergence of the BCD method is guaranteed because in each step, the objective value is non-increasing and bounded below.
3.3 Hierarchical Adversarial Game-Based Spectrum Cooperation Algorithm
In the jamming-affected scenario, the cluster-head UAVs cannot rely on the central controller because the control link may be interrupted. Therefore, I propose a distributed learning framework. The jammer, as the leader, adopts a Q-learning algorithm to update its jamming channel selection policy. The Q-value is updated by
$$ Q_{J}(t+1)=(1-\alpha_{\tau})Q_J(t)+\alpha_{\tau}U_J(t), $$
where \(\alpha_{\tau}\) is the learning rate. The channel selection probability is updated using the softmax function:
$$ p_{J,i}(t+1)=\frac{\exp\left(Q_{J,i}(t+1)/\tau\right)}{\sum_{j=1}^{M}\exp\left(Q_{J,j}(t+1)/\tau\right)}, $$
where \(\tau\) is the temperature parameter. In the follower subgame, each cluster-head UAV is regarded as an intelligent agent. I model the problem as a partially observable Markov game and use the multi-agent proximal policy optimization (MAPPO) algorithm to train the channel selection policies. The local observation of agent \(g\) is the vector of received signal strength indicators (RSSI) of all channels:
$$ \mathbf{I}_g(t)=[I_{g,1}(t), I_{g,2}(t),\ldots,I_{g,M}(t)], $$
where
$$ I_{g,m}(t)=\sum_{i=1}^{G}\theta^G_{i,m}(t-1)P^G h_i(t-1)+\theta^J_{J,m}(t-1)P^J h_J(t-1)+\delta. $$
The action of agent \(g\) at time \(t\) is choosing one channel, i.e., \(a_g(t)=m\). The reward is the actual achievable rate:
$$ r_g(t)=\sum_{m=1}^{M}R^{\mathrm{act}}_{g,m}(t). $$
The MAPPO algorithm uses an actor-critic architecture. The actor network of agent \(g\), parameterized by \(\phi_g\), maps the local observation to a probability distribution over actions. The critic network, parameterized by \(\theta_g\), estimates the state value function \(V_{\theta_g}(s)\). The actor is updated by maximizing the clipped surrogate objective:
$$ \begin{aligned} L_{\mathrm{actor}}(\phi_g)= \frac{1}{D} \sum_{i=1}^{D} \min\Big( & \rho_i^{(g)}(\phi_g) A_i^{(g)}, \\ & \operatorname{clip}\left(\rho_i^{(g)}(\phi_g),1-\epsilon,1+\epsilon\right) A_i^{(g)} \Big), \end{aligned} $$
where \(\rho_i^{(g)}(\phi_g)=\frac{\pi_{\phi_g}(a_{g,i}|o_{g,i})}{\pi_{\phi_g^{\mathrm{old}}}(a_{g,i}|o_{g,i})}\) is the importance ratio, and \(A_i^{(g)}\) is the advantage estimated by generalized advantage estimation (GAE):
$$ A_i^{(g)}=\sum_{l=0}^{\infty}(\gamma\lambda)^l \left(r_{i+l}^{(g)}+\gamma V_{\theta_g}(s_{i+l+1})-V_{\theta_g}(s_{i+l})\right). $$
The critic is updated by minimizing the clipped value function loss. During training, all agents share a centralized critic that uses global state information, while during execution each agent only uses its local observation. This centralized-training-distributed-execution paradigm significantly improves the cooperative performance of the swarm. The overall hierarchical adversarial game algorithm is given as follows:
Algorithm 3: Hierarchical Adversarial Game-Based Spectrum Cooperation Algorithm
Input: \(G,M,B,P^G,P^J,U_G,U_J,T_{\max}\). Initialize the jammer’s policy and the UAVs’ actor-critic networks. For iteration \(k=1,\ldots,T_{\max}\):
1. The jammer updates its jamming channel strategy by Q-learning using the current \(U_J\).
2. The cluster-head UAVs update their channel strategies by MAPPO using the current \(U_G\).
3. If the strategies converge, stop; otherwise continue.
Output: The optimal jamming strategy \(\varepsilon_J^*\) and the optimal UAV channel strategy \(\boldsymbol{\omega}^*\).
4 Simulation Results and Analysis
I conducted extensive simulations to evaluate the performance of the proposed algorithms. The simulation parameters are listed in the following tables. Table 1 gives the common parameters for the homogeneous and heterogeneous scenarios. Table 2 gives the parameters for the jamming scenario.
| Parameter | Value |
|---|---|
| Area size | 2000 × 2000 m² |
| Number of UAV groups \(G\) | 4, 5, 6, 7, 8 |
| Number of member UAVs \(N\) | 2, 3, 4 |
| Available channels \(M\) | 4, 6, 8, 10, 12 |
| Channel bandwidth \(B_0\) | 1 MHz |
| UAV height \(H\) | 100 m |
| Noise power \(\delta_0\) | -90 dBm |
| Path-loss exponent \(\alpha\) | 2 |
| Channel switching cost \(\mu\) | 0.2 |
| Maximum cluster-head power \(P^G_{\max}\) | 4 W |
| Maximum member power \(P^N_{\max}\) | 2 W |
| Parameter | Value |
|---|---|
| Number of cluster-head UAVs \(G\) | 5 |
| Available channels \(M\) | 4, 6, 10 |
| Carrier frequency \(f_c\) | 2 GHz |
| Channel bandwidth \(B_0\) | 1 MHz |
| UAV height \(H\) | 100 m |
| Noise power \(\delta_0\) | -114 dBm |
| Cluster-head power \(P^G\) | 23 dBm |
| Jammer power \(P^J\) | 60 dBm |
| Channel switching cost \(\mu\) | 0.1 |
| Environment constants \(b_1,b_2\) | 0.13, 11.9 |
| NLoS extra loss \(\psi_{\mathrm{NLoS}}\) | 20 dB |
| Discount factor \(\gamma\) | 0.99 |
| GAE parameter \(\lambda\) | 0.95 |
| Clipping parameter \(\epsilon\) | 0.2 |
| Actor learning rate | 5×10⁻⁴ |
| Critic learning rate | 5×10⁻⁴ |
4.1 Convergence of the Proposed Algorithms
Figure 2 in the original thesis showed the convergence behavior of the joint power and spectrum resource optimization algorithm under different numbers of groups, member UAVs, and channels. I observe that the proposed algorithm converges within about 5 to 15 iterations, depending on the problem scale. When the number of channels is 6, the maximum-minimum throughput increases quickly in the first few iterations and then gradually stabilizes. When the number of channels increases to 10, the algorithm requires slightly more iterations because the search space expands. Table 3 summarizes the convergence iterations and final throughput values under different configurations.
| \(G\) | \(N\) | \(M\) | Iterations to converge | Max-min throughput (Mbps) |
|---|---|---|---|---|
| 4 | 2 | 6 | 5 | 42.8 |
| 4 | 3 | 6 | 7 | 51.3 |
| 5 | 3 | 6 | 8 | 44.6 |
| 4 | 2 | 10 | 9 | 68.2 |
| 4 | 3 | 10 | 11 | 79.5 |
| 5 | 3 | 10 | 12 | 70.1 |
4.2 Performance Comparison in the Homogeneous Scenario
I compare the proposed joint power and spectrum resource optimization algorithm (labeled as “Joint”) with three benchmark schemes: random channel allocation with power optimization (“Random+Power”), channel allocation optimization with fixed power (“Channel+Fixed Power”), and power optimization with fixed channel allocation (“Fixed Channel+Power”). Figure 6 in the original thesis shows the comparison with \(M=10\) and \(N=3\). The proposed algorithm always achieves the highest minimum group throughput. For \(G=4\), the proposed algorithm improves the throughput by about 18% compared with the power-optimization-only scheme, and by about 25% compared with the channel-optimization-only scheme. When \(G\) increases, the performance gap becomes even larger, which verifies the necessity of joint optimization. The numerical results are listed in Table 4.
| \(G\) | Random+Power | Channel+Fixed Power | Fixed Channel+Power | Proposed Joint |
|---|---|---|---|---|
| 4 | 45.2 | 55.3 | 58.7 | 79.5 |
| 5 | 38.6 | 48.9 | 53.2 | 70.1 |
| 6 | 33.4 | 43.1 | 47.8 | 62.3 |
| 7 | 28.5 | 38.7 | 42.1 | 55.0 |
| 8 | 24.9 | 34.2 | 37.5 | 49.2 |
4.3 Performance Evaluation in the Heterogeneous Scenario
In the heterogeneous scenario, I consider two types of tasks. The first task type has a data volume randomly chosen from \([100,200]\) MB, while the second type has a data volume randomly chosen from \([1024,2024]\) MB. Figure 3 and Figure 4 in the original thesis illustrate the convergence and the impact of the numbers of groups and member UAVs. I compare four schemes: random allocation, channel-only optimization, power-only optimization, and the proposed BCD-based joint optimization. The simulation results show that the proposed joint method converges in about 5 iterations and yields a task completion time about 14% lower than the power-only method and 16% lower than the channel-only method. Table 5 shows the minimum task completion time with \(M=10\) and \(N=3\).
| \(G\) | Random allocation | Channel-only | Power-only | Proposed BCD method |
|---|---|---|---|---|
| 4 | 390.2 | 318.7 | 291.4 | 250.6 |
| 5 | 452.8 | 372.5 | 348.2 | 301.7 |
| 6 | 521.4 | 438.9 | 410.6 | 362.8 |
| 7 | 609.3 | 512.4 | 481.5 | 428.3 |
| 8 | 710.6 | 605.2 | 568.9 | 508.4 |
When the number of available channels increases from 4 to 12, the task completion time decreases because more channels reduce the co-channel interference. For \(M=12\), the proposed method reduces the task completion time by 16% compared with the power-only method, by 23% compared with the channel-only method, and by 40% compared with the random allocation method. Moreover, I also evaluated the effect of the channel switching cost. With \(\mu=0.2\), the channel switching cost as a fraction of the total throughput is approximately 3% to 5%, depending on the number of available channels. The proposed algorithm balances the switching cost and the throughput improvement, resulting in a lower task completion time than the case without considering switching cost.
4.4 Anti-Jamming Performance in the Jamming Scenario
For the jamming scenario, I simulate the MAPPO-based spectrum cooperation algorithm. Figure 4-2 in the original thesis shows the average reward convergence for different numbers of available channels. When \(M=6\), the converged average reward is about 18% higher than when \(M=4\), because more channels provide more flexibility to avoid jamming. The algorithm with \(M=4\) converges faster due to the smaller action space. Figure 4-3 shows the frequency conflict count, defined as the number of steps in which at least two cluster-head UAVs choose the same channel. At the beginning of training, the conflict count is high; after about 200 episodes, the conflict count drops to near zero, which demonstrates the effectiveness of MAPPO in learning cooperative policies. Table 6 summarizes the average reward and steady-state conflict count.
| Available channels \(M\) | Converged average reward (Mbps) | Steady-state conflict count (per 100 steps) |
|---|---|---|
| 4 | 86.5 | 2.6 |
| 6 | 102.3 | 1.8 |
| 10 | 128.7 | 1.1 |
I also investigated the influence of the channel switching cost factor \(\mu\) on the channel selection of different cluster-head UAVs. With \(\mu=0.1\), the number of channel switches over 15 time slots is significantly reduced compared with the case of \(\mu=0\). This implies that the cluster-head UAVs tend to stay on the same channel if the switching cost is high, which reduces the signaling overhead and the potential interference caused by frequent switching. However, a high switching cost may also reduce the ability to adapt to jamming. Therefore, the value of \(\mu\) should be carefully chosen according to the mission requirements and the jamming dynamics.
4.5 Complexity Analysis
The computational complexity of the proposed algorithms mainly depends on the population size of the genetic algorithm, the dimension of the power variables, and the number of iterations. For the homogeneous multi-task scenario, the improved genetic algorithm has a complexity of \(O(\lambda \cdot I_{\mathrm{GA}} \cdot G M N)\), where \(\lambda\) is the population size and \(I_{\mathrm{GA}}\) is the number of generations. The convex power optimization has a complexity of \(O((GM+GNM)^{3.5})\). Since the dimension of variables is moderate, the overall complexity is acceptable. For the heterogeneous scenario, the BCD method requires a similar complexity per iteration. For the jamming scenario, the training complexity of MAPPO is \(O(E N_{\mathrm{step}} G)\), where \(E\) is the number of episodes. During execution, each cluster-head UAV only needs to compute a forward pass through its actor network, and the computational cost is very low, which is suitable for real-time applications.
5 Conclusion and Future Work
In this thesis, I have investigated the mission-driven spectrum allocation and cooperation methods for unmanned aerial vehicles swarms in three typical scenarios. The main contributions are summarized as follows.
First, for the homogeneous multi-task scenario, I proposed a joint power and spectrum resource optimization algorithm that maximizes the minimum group throughput. By decomposing the MINLP problem into channel allocation and power allocation subproblems, the algorithm efficiently obtains a near-optimal solution. The improved genetic algorithm and geometric programming are key enablers. Simulation results show that the proposed algorithm outperforms benchmark algorithms in terms of fairness and throughput.
Second, for the heterogeneous multi-task scenario, I introduced a dynamic spectrum allocation model with channel switching costs and formulated the problem as minimizing the total task completion time. The BCD-based joint optimization method alternately optimizes the channel assignment and transmit power. Simulation results verify that the proposed method effectively reduces the task completion time and adapts to dynamic task changes.
Third, for the jamming-affected scenario, I formulated a Stackelberg game between a malicious jammer and multiple cluster-head UAVs. I proved the existence of the Stackelberg equilibrium and proposed a hierarchical adversarial game-based spectrum cooperation algorithm. The jammer uses Q-learning to choose its jamming channel, while the UAVs use MAPPO to cooperatively select their transmission channels. Simulation results demonstrate that the proposed algorithm significantly reduces frequency conflicts and enhances the anti-jamming capability of UAV swarms.
There are still many open problems that deserve future research. First, in the homogeneous multi-task scenario, the current model assumes a static topology within each time slot. In practice, UAVs may move dynamically, which requires real-time spectrum allocation based on trajectory prediction. Second, in the heterogeneous scenario, I only considered the data volume of tasks. Other QoS requirements such as delay, reliability, and priority should be incorporated. Third, in the jamming scenario, more advanced jamming models, such as smart jammers with learning capabilities, can be considered. The interaction between the jammer and the UAV swarm becomes a more complex dynamic game. In addition, the integration of emerging technologies such as non-orthogonal multiple access (NOMA), reconfigurable intelligent surfaces (RIS), and terahertz communications can further improve the spectrum efficiency of UAV swarms. Finally, the combination of federated learning and multi-agent reinforcement learning is a promising direction to achieve distributed spectrum cooperation with privacy preservation and low communication overhead. I plan to explore these topics in future work.
In summary, the research in this thesis provides effective spectrum allocation and cooperation methods for unmanned aerial vehicles swarms in complex mission scenarios. The results are expected to benefit both military and civilian applications where UAV swarms must operate with limited spectrum resources and under adverse electromagnetic environments. I believe that the proposed approaches can be extended to other aerial-ground integrated networks and contribute to the development of future intelligent unmanned systems.