Cooperative wideband spectrum sensing effectively overcomes the limitations of single-user sensing, which becomes unreliable in practical environments due to shadowing and multipath fading. Nowadays, most studies of cooperative wide-band signal reconstruction problem are based on thel2;1-norm regularization, which is ineffective in exploiting signal sparsity. We propose an arctangent regularization iterative thresholding (ARIT) algorithm for collaborative wideband spectrum sensing. To address the challenge of solving subproblems with the arctangent penalty, a high-dimensional matrix optimization problem is reduced toNindependent scalar problems. Consequently, a closed-form proximity operator of an arctangent penalty is derived, which is expressed as hyperbolic functions of sine and cosine. Additionally, to overcome high complexity in manual parameter optimization in ARIT, a signal reconstruction network is put forward which combines ARIT with deep learning (DL) technique through deep unfolding, called ARIT-Net. Parameters in ARIT-Net, such as regularization parameter and penalty factor, are learned in an end-to-end manner by DL rather than being adjusted manually. This network architecture not only preserves the theoretical interpretability of ARIT but also enhances reconstruction performance and efficiency through data-driven adaptive parameter optimization. Simulation results demonstrate that ARIT-Net achieves a reconstruction error reduction of 15.6% compared with ADMM-Net.

Unmanned swarms can effectively improve the utility of tasks by collaboratively executing them in dynamic environments, but the heterogeneity of tasks and scarcity of spectrum resources lead to the dynamic matching of task resources becoming the core problem of improving utility. To address the interaction characteristics between the mission layer and the spectrum layer of unmanned swarm, this paper constructs a partially overlapping coalition formation game (POCFG) model, which is proposed to be an exact potential game with at least one Nash Equilibrium (NE). Inspired by the idea of parallel search of quantum superposition states and cooperative decision making of entangled states, a dual rationality guided quantum inspired partial overlapping coalition formation game (DRGQI-POCFG) algorithm is designed. The quantum entanglement state mechanism is utilized to correlate task allocation with the decision variables of spectrum resources. The simulation results show that the efficiency of joint task spectrum allocation is improved and the computational complexity is reduced. Compared with the selfish criterion algorithm, the Pareto algorithm and the non-joint allocation algorithm, the utility has increased by 12.2%, 26.4% and 34.6% respectively.

This paper focuses on the research of anti-jamming issues for Low Earth Orbit (LEO) satellite constellations. Initially, the anti-jamming problem is modeled as a Local Interaction Markov Game (LIMG) and proven to be an Exact Potential Game (EPG), with at least one pure strategy Nash Equilibrium (NE) existing. Secondly, based on the theoretical analysis and the ”offline training and online execution” architecture, a Distributed Multi-Agent Deep Reinforcement Learning-based anti-jamming (DMDRLA) scheme is proposed, and its convergence and asymptotic optimality are theoretically analyzed. Finally, simulations validate that the proposed DM-DRLA scheme can effectively balance the training costs and performance optimization of the anti-jamming model, making it suitable for anti-jamming issues in resource-constrained LEO satellite networks.

A mega hybrid constellation comprising low Earth orbit (LEO) and geostationary orbit (GEO) satellites represents a prevalent architecture for future space-based networks. However, the emergence of mega constellations has exacerbated the shortage of spectrum resources. To address this issue, this paper investigates a method for LEO satellites within such constellations to expand their available spectrum by sharing the downlink spectrum of GEO satellites. Firstly, to avoid interference with GEO satellites and optimize the beam coverage for LEO user (LU), a coalition formation game model for LU based on cooperation criteria is constructed, and the existence of a stable coalition structure is proven. Secondly, to determine this stable coalition structure, a coalition formation game algorithm based on the best response (BR) is proposed, and its convergence is theoretically validated. Additionally, to more efficiently determine the beam radius and center covering the LU in the coalition, an improved algorithm for solving the outer circle of LU in the coalition using a K-dimensional tree is presented. Simulation results demonstrate that the proposed method effectively balances convergence time and accuracy. Without affecting GEO satellite communications, LEO satellites can share the downlink spectrum of GEO satellites, thereby enhancing the utilization of spectrum resources within the hybrid constellation.

This paper proposes a game-based anti-jamming channel selection method for satellite-terrestrial networks. Firstly, to address the insufficient consideration of user demands in existing schemes, a Mean Opinion Score (MOS)-based Quality of Experience (QoE) model is established. Secondly, the interaction between jammer and users is modeled as a one-leader multi-follower Stackelberg game, while local cooperation among users is formulated as a local altruistic game. Finally, a hierarchical Q-learning with spatial altruistic play (HQ-SAP) algorithm is proposed to obtain the game equilibrium solution. Simulations validate its convergence and effectiveness, achieving a good satisfaction rate for the network.

A mega hybrid constellation of low-Earth orbit (LEO) and geosynchronous orbit (GEO) satellites represents a typical architecture for future space networks. However, the emergence of such large constellations exacerbates the shortage of spectrum resources. To address this issue, this article investigates a hierarchical optimization method for beam scheduling and power control of LEO satellites, aiming to extend the available spectrum by sharing the downlink spectrum of GEO satellites. In the upper layer optimization, a many-to-one matching game model is constructed to achieve optimal matching of LEO satellite beams and LEO users (LUs). A distributed beam matching learning algorithm (DBMLA) is designed to find a stable matching solution for the model, with the convergence of the algorithm theoretically proven. In the lower layer optimization, an LEO beam power level optimization game model is developed for discrete LEO beam power levels. This model is demonstrated to be an exact potential game with at least one Nash equilibrium (NE). To solve this NE, a dynamic power allocation logarithmic learning algorithm (DPALLA) is proposed. Simulation results verify that the proposed DBMLA-DPALLA hierarchical optimization scheme effectively balances convergence time and accuracy compared to traditional independent optimization strategies. By leveraging the combined effects of the two optimization strategies, it better mitigates the co-channel interference experienced by GEO satellites and improves the average network satisfaction of the LUs.

In agricultural and food production, sensors are widely used for real-time monitoring of the production process. These sensors transmit data to access points (APs) in wireless sensor networks (WSNs), forming an Internet of Things-empowered advanced production paradigm. Due to limited power, sensors have constrained transmission ranges, necessitating unmanned ground vehicles (UGVs) to assist in timely sensor data collection. A critical problem is the intelligent coordination among multiple UGVs to realize safe path planning, as well as fair and timely data collection. However, it encounters the following challenges: 1) real-time monitoring introduces the dynamics in the volume of sensor data; 2) unknown obstacles, such as mobile packaging containers and vehicles, complicate safe path planning and fair data collection in WSNs; and 3) inefficient action explorations deteriorate action selection. To address these challenges, we propose a multiagent path planning algorithm based on coalition formation game and Bayesian optimization (BO) (MAPP-CFGBO) to optimize UGVs paths and sensor association in industrial WSNs. First, we construct a dynamic data caching model and design a fairness index. Second, a cooperative communication coalition formation (C3F) algorithm is proposed to facilitate cooperation among UGVs. Next, the safe path planning problem is solved with our proposed BO algorithm, which addresses challenges 2 and 3. Extensive simulations are performed. Compared with the benchmark algorithms, the proposed algorithm improves the fairness of communication services by$\rm 39.20{\,}\% $and increases the amount of collected data by$\rm 142.07{\,}\%$.

Large-scale satellite constellations lead to a scarcity of spatial spectrum resources, especially for the overlapped spectrum between Low Earth Orbit (LEO) and Geostationary Orbit (GEO)satellites in hybrid constellations. Hence, based on game theory, a distributed spectrum-sharing method is proposed for downlink spectrum sharing in large-scale hybrid satellite constellations. Specifically, the system cycle is divided into equal-spaced topological periods, and the beams ofLEOsatellites are assigned toLEOground stations (LGS) during every topological period. A system model based on game theory is also developed to describe the mutual interference of links established betweenLEOsatellites andLGS. Subsequently, the formulated game is proven to be an exact potential game, with at least one pure strategic Nash equilibrium (NE). Along the line, to obtain the NE solution, a dynamic channel allocation algorithm is proposed based on stochastic learning theory, and the convergence is proven. Finally, the simulation results demonstrate the proposed DCASLA’s effectiveness, which can balance the convergence speed and overall network satisfaction.

Abstract In view of the diverse jamming environment, the single‐level anti‐jamming method faces some challenges such as poor timeliness, high cost and poor effect. In this paper, routing delay, cost overhead and diversified jamming threats are comprehensively considered. In addition, a cross‐layer anti‐jamming method is proposed in the scenario of busy satellite Internet communication. The proposed cross‐layer anti‐jamming method involves two levels: link‐layer anti‐jamming based on path repair and network‐layer anti‐jamming based on path reconstruction. On the one hand, the channel is selected based on the improved Q‐learning anti‐jamming algorithm to confront common jamming. On the other hand, the route from the source to the destination node is selected based on the cross‐layer anti‐jamming algorithm to confront high‐intensity jamming. Finally, the simulation results show that, compared with other anti‐jamming algorithms, the proposed algorithm can achieve higher efficiency, lower cost, and more robust anti‐jamming routing.

The log-sum minimization has been widely employed in signal and image processing . In this paper, in order to analyze its applicable conditions and achievable boundary for compressed sensing (CS) scenarios, some theoretical derivations of the log-sum minimization are studied based on the mutual incoherence property (MIP) of a measurement matrix . Firstly, the existing condition of the global minimum is demonstrated for the log-sum minimization without noise perturbation. Secondly, for the iterative threshold log-sum (ITL) algorithm, the theoretical performance guarantee of recovering sparse signals disturbed by noise is proposed. Additionally, comprehensive experimental results verify the theoretical analysis for the log-sum item and display the advantages and disadvantages of five sparse estimation algorithms, i.e., the ITL algorithm, ℓ 1 / 2 regularization , ℓ 1 regularization , ℓ 0 regularization and orthogonal matching pursuit (OMP).

The log-sum function as a penalty has always been drawing widespread attention in the field of sparse problems. However, it brings a non-convex, non-smooth and non-Lipschitz optimization problem that is difficult to tackle. To overcome the problem, an iterative threshold algorithm for the sparse optimization problems with log-sum function is proposed in this paper. For brevity, the sparse optimization problems with log-sum function are named log-sum regularization. Firstly, by introducing an intermediate function to construct another new function, a property theorem about solution for log-sum regularization is established. Secondly, based on the above theorem, the optimal setting rules of the compromising parameters are elaborated, and an iterative log-sum threshold algorithm is proposed. Thirdly, under the situation that the compromising parameters of log-sum regularization are relatively small, it can be proven that the proposed algorithm converges to a local minimizer of log-sum regularization. Finally, a series of simulations are implemented to examine performance of the proposed algorithm, and the results exhibit that the proposed algorithm outperforms the state-of-the-art algorithms.

Abstract Although unmanned aerial vehicle (UAV) relay can provide auxiliary communication due to its flexible mobility, it is vulnerable to jamming attacks. This paper considers the UAV relay anti‐jamming communication issue under the threat of a malicious jammer with beam‐forming jamming capability. To prevent the relay link from deteriorating, UAV trajectory adjustment and transmission mode switching between half‐duplex and full‐duplex are two available schemes, while they will incur the additional flying costs and continuous mode switching, respectively. To balance the trade‐off between trajectory optimization and mode selection, this paper investigates the joint trajectory optimization and mode selection anti‐jamming approach. First, an anti‐jamming utility considering the cost‐efficient and end‐to‐end capacity gains is designed. Second, to model the bounded rationality of both the UAV relay and the jammer due to the adversarial context, a biased Stackelberg game to analyse the competitive system interactions is proposed. Moreover, the existence of Stackelberg equilibrium (SE) in the problem is proved. Finally, a joint mode selection and trajectory optimization (JMSTO) algorithm based on the multi‐armed bandit is proposed to obtain the SE. It is further demonstrated that the JMSTO algorithm has a logarithmic regret. The results show that our proposed JMSTO algorithm is superior to non‐joint optimization methods.

Abstract In this paper, the dynamic spectrum access is investigated in satellite internet. Firstly, to describe the confrontation characteristics of the electromagnetic environment, two opposing teams denoted as the blue team (BT) and red team (RT), are designed. In addition, an “electromagnetic barrier” jamming strategy is proposed to achieve the effect of promoting approach defence with the attack. Precisely, the “electromagnetic barrier” can significantly weaken the communication ability of enemies (i.e. RT) while protecting the (i.e. BT) communication quality. Secondly, internal interference, external interference and malicious jamming of BT and RT are considered, and expected weighted aggregate interference and jamming (EWAIJ) are introduced to integrate these interference. Moreover, minimising interference is taken as the optimisation goal. Thirdly, Game theory is introduced to describe the combinatorial optimisation problem. The process of each team finding the optimal spectrum access strategy is proved to be an exact potential energy game. These two sub‐games together constitute the Stackelberg game framework. Finally, a distributed hierarchical confrontation channel selection algorithm (DHCCSA) is proposed to find the Stackelberg equilibrium solution. The simulation results show that the proposed algorithm can converge to a better effect compared with other algorithms. In addition, with the assistance of the “electromagnetic barrier,” BT is more robust than RT in terms of convergence rate, total utility, and total network throughput.

Recently, the development of unmanned aerial vehicle (UAV) mobile-edge computing (MEC) networks has brought unprecedented gains and opportunities. In this article, the joint computation offloading, UAV role, and location selection problem in hierarchical multicoalition UAV MEC network is investigated. To capture the hierarchical feature and discrete optimization, the discrete Stackelberg game with multiple leaders and followers is formulated. We prove that both the leader-level and member-level subgames are ordinal potential games (OPGs) with Nash equilibrium (NE). Thus, the Stackelberg equilibrium (SE) is guaranteed. To achieve the SE, the log-linear-based hierarchical learning algorithm (LHLA) is proposed and analyzed. The simulation results show that the LHLA can converge fast and achieve better performance compared with the existing schemes.

This paper investigates the anti-jamming problems for multi-user scenarios. On the one hand, users in the networks should coordinate their channel selection strategies to avoid spectrum conflicts among different users. On the other hand, because of the openness characteristic of wireless communications, malicious jammers can disrupt the legitimate communications of legitimate users by sending jamming signals, thus users also need to fully consider how to defend against malicious jamming attacks. To cope with the internal coordination and external confrontation problem, a context-aware dynamic spectrum coordinated anti-jamming approach is proposed. In detail, the multiuser anti-jamming scenario is modeled as an anti-jamming local altruistic game, and the existence of Nash Equilibrium (NE) is demonstrated. Besides, the proposed game model is proved to be an exact potential game. To obtain NEs, a multi-pattern stochastic learning algorithm (MSLA) is designed. Through local information exchange and distributed learning, users can achieve global optimization under the dynamic jamming environment.

Abstract This paper investigates the problem of multi‐user anti‐jamming channel access with partially overlapping channels (POC). Compared with traditional anti‐jamming systems that use non‐overlapping channels, POC improve the spectral efficiency. However, the partial overlap of channels also brings more serious interference. For this, physical distance and channel separation on the interference intensity under partially overlapping channels are first considered and the malicious jamming and interference among users are formulated as a hierarchical binary model. Secondly, to cope with multi‐user decisions under dynamic jamming conditions, the Markov game framework is adopted to analyse the problem. Thirdly, a multi‐user collaborative anti‐jamming channel selection algorithm based on reinforcement learning is proposed as well as the optimal anti‐jamming strategy can be obtained. Finally, the simulation results validate that the proposed algorithm helps users cope with jamming and eliminate mutual interference. Compared with the non‐overlapping channel access scheme, the POC access scheme achieves higher network throughput.

In adversarial scenarios, it is crucial to timely monitor what tactical messages that opponent transmitters are sending to intended receiver(s), and disrupt the transmissions immediately if in need. The issue becomes more challenging in face of an intelligent transmitter. To address the above-stated issue, a full-duplex (FD) technique is utilized to enable simultaneous jamming and eavesdropping (SJE) at a friendly jammer node. In particular, the “Two Birds with One Stone” strategy is utilized at the jammer node to realize effective rate degradation and information eavesdropping. A confrontation game between an intelligence-empowered FD jammer and its opponent is investigated. Specifically, to capture their adversarial relationship in an environment with incomplete information, a power-domain Bayesian-Stackelberg game is proposed. The existence of a Stackelberg equilibrium (SE) power solution is proved. The semi-closed-form solutions of SE are derived, which are proved to be asymptotically optimal (have a gap of less than 1% with the exact utility), and improves the jammer node 10% utility compared with the Nash equilibrium. Additionally, the SJE strategy outperforms the half-duplex (HD) and other benchmark schemes.

This paper investigates the anti-jamming problems in wireless communication networks. In these networks consisted of multiple devices (users), there exist two critical problems. On the one hand, users with various transmission requirements should coordinate their channel selection strategies distributedly to avoid spectrum conflicts and satisfy transmission demands. On the other hand, they also need to fully consider how to eliminate the effects of malicious attacks. To cope with the internal coordination and external confrontation challenges and accommodate the dynamic changing jamming attacks, a context-aware distributed coordinated anti-jamming channel access mechanism is proposed, which means for different cases of jamming attacks, different access strategies are adopted. In detail, to reflect the heterogeneous communication demands of users, the transmission satisfaction function is firstly introduced. Then, the multi-user anti-jamming scenario is modeled as a context-aware multi-pattern dynamic anti-jamming game, which can be decomposed into two sub-games. Here, for the case that the control channel is available, a local altruistic sub-game is introduced. While for the case that the control channel has been jammed, an anti-jamming congestion sub-game is designed. Besides, the existence of Nash Equilibriums is demonstrated. To obtain NEs, a context-aware distributed channel access (CDCA) algorithm is designed. Through game-theoretic analysis and distributed learning, global transmission satisfaction can be improved under the dynamic jamming environment. Furthermore, the fairness of the network can also be guaranteed.

This paper mainly investigates the unmanned aerial vehicle (UAV) communication networks under the threat of a static malicious jammer. While taking the flying process of the user (UAV transmitter-receiver pair) into consideration, we propose a joint power and trajectory optimization method. Moreover, a Stackelberg framework is formulated to solve the proposed optimization problem. In addition, a joint power and trajectory optimization algorithm (JPTOA) based on best-response (BR) is designed to obtain the user's strategy as well as Stackelberg equilibrium (SE) in each time stage. Furthermore, as an extension of single stage optimization, the I-step exploration and one-step decision (IEOD) scheme is designed to enhance the user's cumulative utility. Finally, simulation results are presented to show the performance of the proposed JPTOA scheme.