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IEEE Transactions on Wireless Communications

A Proactive Eavesdropping Game in MIMO Systems Based on Multiagent Deep Reinforcement Learning

Delin Guo, Hui Ding, Lan Tang, Xinggan Zhang, Lüxi Yang, Ying‐Chang Liang

Published May 6, 2022• 22 citations
Publisher

Abstract

This paper considers an adversarial scenario between a legitimate eavesdropper and a suspicious communication pair. All three nodes are equipped with multiple antennas. The eavesdropper, which operates in a full-duplex model, aims to wiretap the dubious communication pair via proactive jamming. On the other hand, the suspicious transmitter, which can send artificial noise (AN) to disturb the wiretap channel, aims to guarantee secrecy. More specifically, the eavesdropper adjusts jamming power to enhance the wiretap rate, while the suspicious transmitter jointly adapts the transmit power and noise power against the eavesdropping. Considering the partial observation and complicated interactions between the eavesdropper and the suspicious pair in unknown system dynamics, we model the problem as an imperfect-information stochastic game. To approach the Nash equilibrium solution of the eavesdropping game, we develop a multi-agent reinforcement learning (MARL) algorithm, termed neural fictitious self-play with soft actor-critic (NFSP-SAC), by combining the fictitious self-play (FSP) with a deep reinforcement learning algorithm, SAC. The introduction of SAC enables FSP to handle the problems with continuous and high dimension observation and action space. The simulation results demonstrate that the power allocation policies learned by our method empirically converge to a Nash equilibrium, while the compared reinforcement learning algorithms suffer from severe fluctuations during the learning process.

DOI
10.1109/twc.2022.3170308

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This paper considers an adversarial scenario between a legitimate eavesdropper and a suspicious communication pair. All three nodes are equipped with multiple antennas. The eavesdropper, which operates in a full-duplex model, aims to wiretap the dubious communication pair via proactive jamming. On the other hand, the suspicious transmitter, which can send artificial noise (AN) to disturb the wiretap channel, aims to guarantee secrecy. More specifically, the eavesdropper adjusts jamming power to enhance the wiretap rate, while the suspicious transmitter jointly adapts the transmit power and noise power against the eavesdropping. Considering the partial observation and complicated interactions between the eavesdropper and the suspicious pair in unknown system dynamics, we model the problem as an imperfect-information stochastic game. To approach the Nash equilibrium solution of the eavesdropping game, we develop a multi-agent reinforcement learning (MARL) algorithm, termed neural fictitious self-play with soft actor-critic (NFSP-SAC), by combining the fictitious self-play (FSP) with a deep reinforcement learning algorithm, SAC. The introduction of SAC enables FSP to handle the problems with continuous and high dimension observation and action space. The simulation results demonstrate that the power allocation policies learned by our method empirically converge to a Nash equilibrium, while the compared reinforcement learning algorithms suffer from severe fluctuations during the learning process.
This paper considers an adversarial scenario between a legitimate eavesdropper and a suspicious communication pair. All three nodes are equipped with multiple antennas. The eavesdropper, which operates in a full-duplex model, aims to wiretap the dubious communication pair via proactive jamming. On the other hand, the suspicious transmitter, which can send artificial noise (AN) to disturb the wiretap channel, aims to guarantee secrecy. More specifically, the eavesdropper adjusts jamming power to enhance the wiretap rate, while the suspicious transmitter jointly adapts the transmit power and noise power against the eavesdropping. Considering the partial observation and complicated interactions between the eavesdropper and the suspicious pair in unknown system dynamics, we model the problem as an imperfect-information stochastic game. To approach the Nash equilibrium solution of the eavesdropping game, we develop a multi-agent reinforcement learning (MARL) algorithm, termed neural fictitious self-play with soft actor-critic (NFSP-SAC), by combining the fictitious self-play (FSP) with a deep reinforcement learning algorithm, SAC. The introduction of SAC enables FSP to handle the problems with continuous and high dimension observation and action space. The simulation results demonstrate that the power allocation policies learned by our method empirically converge to a Nash equilibrium, while the compared reinforcement learning algorithms suffer from severe fluctuations during the learning process.
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.
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.
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.
Self-interference cancellation technologies enable full-duplex operation at the eavesdropper. In addition to wiretapping, the eavesdropper simultaneously tries to reduce the secrecy rate of the illegitimate transmitter-receiver pair by jamming its receiver. On the other hand, the transmitter-receiver pair aims to increase its secrecy rate. To examine the power decision processes between the transmitter and the eavesdropper, we propose a novel physical layer security game in the wiretap channel, where the eavesdropper operates in a full-duplex mode. To analyse the game outcome, a distributed learning algorithm is adopted to achieve the mixed-strategy Nash equilibrium. Based on the equilibrium, we provide a switch strategy for the eavesdropper to determine the optimal operation mode between the full-duplex and half-duplex, depending on its location and self-interference. Numerical results show that the switch strategy improves the eavesdropper's performance in the sense of decreasing the secrecy rate.
We consider a multi-link interference network that is tapped by an external eavesdropper. To conceal information from the eavesdropper, legitimate links are equipped with transmitter-based friendly jamming (TxFJ) and receiver-based friendly jamming (RxFJ). Each link seeks to maximize its secrecy rate by determining the best power assignment (PA) for the information, TxFJ, and RxFJ signals. Joint optimization of these parameters is a non-convex problem. Hence, we seek sub-optimal solutions. Specifically, we find a lower bound on the allocated power to TxFJ above which positive secrecy is achievable for a given link. Once positive secrecy is achieved, the secrecy rate becomes monotonically increasing in the power at the transmitter (Alice). Therefore, the rest of Alice's power is allocated to the information signal. Despite its sub-optimality, such an approach precludes the possibility of employing successive interference cancellation by the eavesdropper. The RxFJ PA of a link is adjusted using an on-off PA that depends only on the link's local channel state information (CSI). With every link following such a strategy, we model this interaction as a non-cooperative game. We derive sufficient conditions for the uniqueness of the resulting Nash equilibrium. We then propose an algorithm to implement the PA game. Lastly, we relax knowledge of eavesdropper's CSI (E-CSI) and propose a framework that is robust to unknown E-CSI. Our results indicate that this robust framework performs close to when E-CSI is fully known to legitimate links. Moreover, empirically it is shown that the secrecy sum-rate scales with the power budget of transmitters.