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Abstract-Various spectrum management schemes have been proposed in recent years to improve the spectrum utilization in cognitive radio networks. However, few of them have considered the existence of cognitive attackers who can adapt their attacking strategy to the time-varying spectrum environment and the secondary users' strategy. In this paper, we investigate the security mechanism when secondary users are facing the jamming attack, and propose a stochastic game framework for anti-jamming defense. At each stage of the game, secondary users observe the spectrum availability, the channel quality, and the attackers' strategy from the status of jammed channels. According to this observation, they will decide how many channels they should reserve for transmitting control and data messages and how to switch between the different channels. Using the minimax-Q learning, secondary users can gradually learn the optimal policy, which maximizes the expected sum of discounted payoffs defined as the spectrum-efficient throughput. The proposed stationary policy in the anti-jamming game is shown to achieve much better performance than the policy obtained from myopic learning, which only maximizes each stage's payoff, and a random defense strategy, since it successfully accommodates the environment dynamics and the strategic behavior of the cognitive attackers.

Abstract-Crucial to the successful deployment of cognitive radio networks, security issues have begun to receive research interests recently. In this paper, we focus on defending against the jamming attack, one of the major threats to cognitive radio networks. Secondary users can exploit the flexible access to multiple channels as the means of anti-jamming defense. We first investigate the situation where a secondary user can access only one channel at a time and hop among different channels, and model it as an anti-jamming game. Analyzing the interaction between the secondary user and attackers, we derive a channel hopping defense strategy using the Markov decision process approach with the assumption of perfect knowledge, and then propose two learning schemes for secondary users to gain knowledge of adversaries to handle cases without perfect knowledge. In addition, we extend to the scenario where secondary users can access all available channels simultaneously, and redefine the anti-jamming game with randomized power allocation as the defense strategy. We derive the Nash equilibrium for this Colonel Blotto game which minimizes the worst-case damage. Finally, simulation results are presented to verify the performance.

Fusion-evaporation cross sections were measured in the two systems 48 Ca + 90,96 Zr in an energy range from well below to well above the Coulomb barrier. The sub-barrier fusion of 48 Ca + 90 Zr is reproduced by coupled-channels calculations including the lowest quadrupole and octupole vibrations of 90 Zr, and using a Woods-Saxon potential with a standard diffuseness parameter a = 0.68 fm. However, the fusion cross sections are overestimated above the barrier. The low-energy slope of the excitation function for 48 Ca + 96 Zr is steeper. This implies a larger diffuseness parameter a = 0.85 fm. Fusion cross sections are well fit in the whole energy range, and the effect of the strong octupole vibration in 96 Zr is predominant. The extracted fusion barrier distributions are reasonably well reproduced by calculations for both systems. A comparison with previous data for 40 Ca + 90,96 Zr is made in an attempt to clarify the role of transfer couplings in sub-barrier fusion.

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