This letter investigates the problem of anti-jamming communications in dynamic and intelligent jamming environment through machine learning. Different from existing studies which need to know (estimate) the jamming patterns and parameters, we use the temporal and spectral information, i.e., the spectrum waterfall, directly. Firstly, to cope with the challenge of infinite state of spectrum waterfall, a recursive convolutional neural network is designed. Then, an anti-jamming deep reinforcement learning algorithm is proposed to obtain the optimal antijamming strategies. Finally, simulation results validate the the proposed approach. The proposed algorithm does not need to model the jamming patterns, and naturally has the ability to explore the unknown environment, which implies that it can be widely used for combating dynamic and intelligent jamming.

In this letter, we investigate the anti-jamming defense problem in multi-user scenarios, where the coordination among users is taken into consideration. The Markov game framework is employed to model and analyze the anti-jamming defense problem, and a collaborative multi-agent anti-jamming algorithm (CMAA) is proposed to obtain the optimal anti-jamming strategy. In sweep jamming scenarios, on the one hand, the proposed CMAA can tackle the external malicious jamming. On the other hand, it can effectively cope with the mutual interference among users. Moreover, we consider the impact of sensing errors due to miss detection and false alarm. Simulation results show that the proposed CMAA is superior to both sensing based method and independent Q-learning method, and has the highest normalized rate.

The smart jammers pose a severe threat to wireless communications due to their abilities of learning the users' transmission strategies. A Stackelberg game can be formulated to model and analyze the hierarchical interactions between the user and the smart jammer. In this letter, an antijamming Bayesian Stackelberg game with incomplete information is proposed. In the proposed game, the user who acts as the leader has the privilege over the smart jammer and takes actions first, whereas the smart jammer acting as the follower moves subsequently. Moreover, the Stackelberg equilibrium (SE) is derived, and the existence and the uniqueness of SE are demonstrated. Simulation results are presented to validate the effectiveness of the proposed antijamming Bayesian Stackelberg game.

This paper focuses on the anti-jamming transmission problem in unmanned aerial vehicle (UAV) communication networks. Considering the incomplete information constraint and the co-channel mutual interference, a Bayesian Stackelberg game is proposed to formulate the competitive relations between UAVs (users) and the jammer. Specifically, the jammer acts as the leader, whereas users act as followers of the proposed game. Based on their utility functions, the jammer and users select their optimal power control strategies respectively. In addition, the observation error is also investigated in this paper. Due to the incomplete information constraint and the existence of co-channel mutual interference, it is challenging to obtain Stackelberg equilibrium (SE) of the proposed game. Thus, a sub-gradient based Bayesian Stackelberg iterative algorithm is proposed to obtain SE. Finally, simulations are conducted to demonstrate the performance of the proposed algorithm, and the impact of incomplete information and observation error on users' utilities are also presented.

Due to the inherently open and shared nature of the wireless channels, wireless communication networks are vulnerable to jamming attacks, and effective anti-jamming measures are of utmost importance to realize reliable communications. Game theory and reinforcement learning (RL) are powerful mathematical tools in anti-jamming field. This article investigates the anti-jamming problem from the perspective of game theory and RL. First, different anti-jamming domains and anti-jamming strategies are discussed, and technological challenges are globally analyzed from different perspectives. Second, an in-depth systematic and comprehensive survey of each kind of anti-jamming solutions (i.e., game theory and RL) is presented. To be specific, some game models are discussed for game theory based solutions, including Bayesian anti-jamming game, Stackelberg anti-jamming game, stochastic anti-jamming game, zero-sum anti-jamming game, graphical/hypergraphical anti-jamming game, etc. For RL-based anti-jamming solutions, different kinds of RL are given, including Q-learning, multi-armed bandit, deep RL and transfer RL. Third, the strengths and limitations are analyzed for each type of anti-jamming solutions. Finally, we discuss the deep integration of the game theory and RL in solving anti-jamming problems, and a few future research directions are illustrated.

In this paper, we investigate the anti-jamming channel selection problem for interference mitigation (IM)-based dense wireless networks in dynamic environment, in which the active user set is variable due to their specific traffic demands. We jointly consider the mutual interference among users and external jamming in IM-based dense wireless networks, and propose a generalized maximum protocol interference and jamming (GMPIJ) model to accurately capture the mutual interference and external jamming. Then, the anti-jamming channel selection problem is formulated as an anti-jamming dynamic game, and subsequently it is proved to be an exact potential game, which has at least one pure strategy Nash equilibrium (NE). Based on the stochastic learning theory, a distributed anti-jamming channel selection algorithm (DACSA) is proposed to find the NE solution. Moreover, the simulation results are presented to demonstrate the effectiveness of the proposed DACSA algorithm.