An optimal transmission strategy in zero-sum matrix games under intelligent jamming attacks Senthuran Arunthavanathan 1 • Leonardo Goratti 2 • Lorenzo Maggi 3 • Francesco de Pellegrini 2 • Sithamparanathan Kandeepan 1 • Sam Reisenfield 4 Ó Springer Science+Business Media, LLC, part of Springer Nature 2017 Abstract Cognitive radio networks are more susceptible to jamming attacks due to the nature of unlicensed users accessing the spectrum by performing dynamic spectrum access. In such a context, a natural concern for operators is the resilience of the system. We model such a scenario as one of adversity in the system consisting of a single legitimate (LU) pair and malicious user (MU). The aim of the LU is to maximize throughput of transmissions, while the MU is to minimize the throughput of the LU completely. We present the achievable transmission rate of the LU pair under jamming attacks taking into account mainly on the transmission power per channel. Furthermore, we embed our utility function in a zero-sum matrix game and extend this by employing a fictitious play when both players learn each other’s strategy over time, e.g., such an equilibrium becomes the system’s global operating point. We further extend this to a reinforcement learning (RL) approach, where the LU is given the advantage of incorporating RL methods to maximize its throughput for fixed jamming strategies. Keywords Anti-jamming game  Zero-sum games  Reinforcement learning  Fictitious play 1 Introduction Communication systems that provide dynamic spectral access (DSA), tends to promise intelligence and autono- mous functionality in terms of learning the environment and performing decisions to provide successful spectral access and transmission to the relevant destination. Cog- nitive radios (CRs) are described to perform DSA and comprises of two users: the unlicensed users termed as secondary users (SU), and licensed users termed as primary users (PU). The first objective in a cognitive radio network (CRN) is to allow SUs to perform access on the available spectrum on a noninterference basis to the PUs, in which the SUs are subject to power and range constraints [1, 2]. This paper does not look upon the relationship between the PU and SU, rather it discusses the interactions between the authorized SUs termed as legitimate users (LUs) and unauthorized SUs known as malicious users (MUs). The authorization of spectral access to the LUs means that SUs are informed of the channel availability by the PU, albeit it does not ensure that the channels are secure for the SU access. An exacerbated issue is when the SUs are inten- tionally inflicting harm upon other competing SUs. Such types of attacks are termed as jamming attacks in the physical (PHY) layer. In the recent decade, game theory models were con- sidered as a viable approach to model the resilience of the physical link itself, in a variety of system models and environments. The general approach of resilience in CRNs lies in the access scheme, frequency hopping pattern, power allocation, and selection of control and data chan- nels at a given time. An equilibrium is approached through iterative updates, hence leading to the application of a & Senthuran Arunthavanathan Senthuran.A.1989@ieee.org 1 Electrical and Computer Engineering, RMIT University, Melbourne, VIC 3001, Australia 2 CREATE-Net, 31628 Trento, Italy 3 Huawei Technologies, Lannion, France 4 Department of Engineering, Macquarie University, Sydney, NSW 2109, Australia 123 Wireless Networks https://doi.org/10.1007/s11276-017-1629-4