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International Conference on Communications

Equilibrium Outcomes of Dynamic Games in MIMO Channels with Active Eavesdroppers

A. Mukherjee, Arnold Lee Swindlehurst

Published May 1, 2010• 19 citations
Publisher

Abstract

This paper investigates transmission strategies in a MIMO wiretap channel with a transmitter, receiver and wiretapper, each equipped with multiple antennas. The secrecy rate between the transmitter and the legitimate receiver is chosen as the performance metric. In a departure from existing work, the wiretapper is able to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data; or broadcasting artificial noise along with the information signal in order to selectively degrade the eavesdropper's channel. We model the network as a dynamic zero-sum game in extensive form with the secrecy rate as the payoff function. We first examine subgame-perfect equilibrium strategies in the extensive form of the game with perfect information. We then discuss sequential and trembling hand perfect equilibria for the case of imperfect information. Finally, numerical simulations are presented to corroborate the analytical results.

DOI
10.1109/icc.2010.5502588

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This paper investigates transmission strategies in a MIMO wiretap channel with a transmitter, receiver and wiretapper, each equipped with multiple antennas. The secrecy rate between the transmitter and the legitimate receiver is chosen as the performance metric. In a departure from existing work, the wiretapper is able to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data; or broadcasting artificial noise along with the information signal in order to selectively degrade the eavesdropper's channel. We model the network as a dynamic zero-sum game in extensive form with the secrecy rate as the payoff function. We first examine subgame-perfect equilibrium strategies in the extensive form of the game with perfect information. We then discuss sequential and trembling hand perfect equilibria for the case of imperfect information. Finally, numerical simulations are presented to corroborate the analytical results.
This paper investigates transmission strategies in a MIMO wiretap channel with a transmitter, receiver and wiretapper, each equipped with multiple antennas. In a departure from existing work, the wiretapper is able to act either as a passive eavesdropper or as an active jammer per channel use, under a half-duplex constraint. The transmitter therefore faces a choice between dynamically allocating all of its power for data; or broadcasting artificial noise along with the information signal in order to selectively degrade the eavesdropper's channel. We model the network as a zero-sum game in strategic form with the MIMO secrecy rate as the payoff function. We first carry out a detailed analysis of the various rate outcomes that result from the possible actions of the agents. We then discuss the conditions for equilibrium outcomes in the strategic form of the game. Finally, numerical simulations are presented to corroborate the analytical results.
This paper investigates reliable and covert transmission strategies in a multiple-input multiple-output (MIMO) wiretap channel with a transmitter, receiver and an adversarial wiretapper, each equipped with multiple antennas. In a departure from existing work, the wiretapper possesses a novel capability to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data, or broadcasting artificial interference along with the information signal in an attempt to jam the eavesdropper (assuming its instantaneous channel state is unknown). To examine the resulting trade-offs for the legitimate transmitter and the adversary, we model their interactions as a two-person zero-sum game with the ergodic MIMO secrecy rate as the payoff function. We first examine conditions for the existence of pure-strategy Nash equilibria (NE) and the structure of mixed-strategy NE for the strategic form of the game. We then derive equilibrium strategies for the extensive form of the game where players move sequentially under scenarios of perfect and imperfect information. Finally, numerical simulations are presented to examine the equilibrium outcomes of the various scenarios considered.
In this paper, we investigate a four single-antenna node network, constituted of a transmitter, a receiver, a cooperative node and a wiretapper. The wiretapper has the ability to eavesdrop the communication or disrupt the transmission by jamming. This results in both cases in the decrease of the secrecy rate. The cooperative node on the other hand aims to improve secrecy by either relaying or jamming. We investigate the secrecy performance of the decode-and-forward and cooperative jamming strategies against this kind of adversary. To model the interaction between the helper and the wiretapper, we define an extensive form game, for which we derive the pure and mixed strategies equilibria. Finally, we compare the performance of the schemes and we analyze the equilibrium outcomes through simulation results.
With the emergence of physical layer security, there has been an increasing interest toward its framework comprising a wiretap channel with a transmitter, a receiver, and an eavesdropper. In this paper, the eavesdropper operates in a full-duplex mode so as to reduce the secrecy rate of the transmitter-receiver pair through simultaneous wiretapping and jamming. On the other hand, the transmitter-receiver pair aims to increase its achievable secrecy rate. To examine the power decision processes between the transmitter and the eavesdropper, a two-player noncooperative game is proposed. We first provide sufficient conditions for the existence of the pure-strategy Nash equilibrium (NE), and then derive the closed-form NEs for two special cases, i.e., the eavesdropper close to and far away from the receiver. For discrete approximation of the game, we utilize a fictitious play-based algorithm to achieve the mixed-strategy NE. Based on the equilibrium, a switch policy is provided for the eavesdropper to determine its optimal mode between the full-duplex and half-duplex, depending on the self-interference and location. Numerical results show that this switch policy improves the monitoring performance in terms of utility, which is the linear combination of the secrecy rate and the power consumption.
We investigate optimal power allocation strategies over a OFDM Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and a jammer-who acts as unfriendly to both the legitimate parties and the eavesdropper. In particular, we formulate a zero-sum power allocation game between the transmitter and the jammer where the payoff function is the secrecy rate. We characterize the optimal power allocation strategies as well as the Nash equilibrium in some asymptotic regimes. We also provide a set of results that cast further insight into the problem.
This paper investigates the secrecy rate maximization problem for the multiple-input-single-output multiple-antenna-eavesdropper (MISOME) wiretap channel with multiple randomly located jammers. The multi-antenna base station (BS) transmits information signals along with artificial noise (AN) to disturb the eavesdropper. Moreover, the friendly jammers are properly selected to assist the legitimate link for better secure transmission with some payoffs. With this system model, we first formulate a Stackelberg game between the BS and the assisting jammers with full channel state information. Stackelberg equilibriums, including optimal fraction of transmit power for AN, optimal transmit power, and asking prices of assisting jammers, are first proved to exist and then analytically derived. A policy iterative algorithm is also proposed to obtain the optimal solutions. We then extend the Stackelberg game to the case of MISOME broadcast wiretap channel with channel distribution information of eavesdropper. Numerical results verify the accuracy of the derived results and the efficiency of the proposed algorithm. The results reveal that the proposed jammer-assisted secure transmission can greatly improve the secrecy performance and meanwhile save more energy for information signals, which is significant for future wireless communication.