On the Achievable Rate in a D2D Cognitive Secondary Network Under Jamming Attacks †♭ S. Arunthavanathan, ♭ L. Goratti, ♭ L. Maggi, ♭ F. De Pellegrini, † S. Kandeepan † School of Electrical Engineering, RMIT University, Melbourne, Australia, ♭ CREATE-NET, Trento, Italy, Email: s3391760@student.rmit.edu.au, kandeepan@ieee.org, {leonardo.goratti,lorenzo.maggi,francesco.depellegrini}.create-net.org Abstract—Ongoing developments of the LTE standard will allow for device-to-device (D2D) communications, which will enable direct connection of user equipments (UEs). Since UEs are becoming increasingly more powerful both in computational power and in the role they have in the network, a concrete threat is that a hand-held D2D-enabled device could be deployed to jam intentionally ongoing transmissions of other D2D users. In this context, a natural concern for operators will be the resilience of the legitimate user (LU) against a jammer’s (J) attack. In this work, we model an LTE D2D system made of a pair of LUs and a J that tries to impair their communication. We model the adversarial scenario between the transmitting LU and J as a zero-sum game: in this game, J’s target is to minimize the throughput of the legitimate D2D pair. We show the achievable channel rate of the D2D pair under jamming attacks and the existence of a Nash equilibrium. Finally, when both players learn each other strategy over time, e.g., employing fictitious play, such equilibrium becomes the system’s operating point. I. I NTRODUCTION The Third Generation Partnership Project (3GPP) has stan- dardized the next generation of cellular technology, known as LTE and its advanced version (LTE-A), which is now ap- proaching the mass market. The 3GPP community is currently defining the new features of LTE for communications systems beyond 4G. One promising innovation that is expected to come with newer releases of LTE, namely Release 12 and 13, is provided by the D2D communication mode. D2D appears promising in order to enable short range proximity services, offload traffic and perform efficient spectrum utilization. However, this new paradigm will likely introduce strong re- quirements of coordination for legitimate D2D users. In partic- ular handing over control of radio access to local UEs requires preventing destructive interference due to local transmissions that can potentially interfere with one another. Furthermore, with the increased programmability and computational power of UE terminals, a general threat in this scenario is represented by malicious users performing jamming attacks. The aim in this paper is to provide a theoretical framework and novel performance evaluation tools able to quantify the impact of jamming for the emerging D2D paradigm. We con- sider the case of a legitimate transmitter/receiver pair subject to jamming attacks operated via the D2D communication mode. The transmitter is termed hereafter “legitimate”, as it can access only the slots leased out locally by the primary communication system (i.e., cellular network). The malicious user, namely the jammer, attempts to interfere with the physical resource blocks (PRBs) that the D2D trans- mitter exploits in the LTE radio frame. We hence consider the adversarial situation between J and the transmitting legitimate user, simply called LU. In the D2D scenario we assume that J and LU are both UEs and have similar type of cognitive capabilities, computational power, and radio characteristics. In addition, each of them may decide how to plan the transmis- sion over each transmission time interval (TTI) in order to maximize their utility. In the rest of the paper we provide a performance analysis based on the fundamental tradeoff that arises from combining physical layer considerations and link layer considerations. In particular, at each LTE radio frame, LU can select a subset of PRBs at random according to a frequency-time hopping scheme known by the receiver. The jammer, in turn, will try to hit a certain subset of PRBs with no prior knowledge on the hopping scheme. Actually, they both need to span the largest possible number of slots in order to escape/pursue the transmission of the opponent. But, under a finite power budget, they need at the same time to allocate a large enough power over each PRB to be effective, i.e., to transmit/interfere with enough energy per PRB. The situation above represents a jamming game [1], [2] where the players’ action is the number of PRBs randomly selected per frame. We formulate first the PHY layer analysis for the static case under fixed strategies for J and LU. Hence, the game between LU and J is described as a zero-sum game. Finally, we describe the system’s dynamics under a learning scheme by which players react to each other strategy. The remainder of this paper is organized as follows. Section II provides an in-depth explanation of the problem we aim to solve. Section III provides the system model and analysis. In Section IV we formulate the game theoretical approach considered in this paper. Section V illustrates and describes the simulation results obtained. Section VI shows the concluding remarks of the paper. II. PROBLEM FORMULATION In this work, we study a communication network in which a legitimate transmitter (or LU as mentioned before) is willing to communicate with the intended destination using D2D communication mode in the presence of a malicious device