This letter proposes a game-theoretic model to jointly optimize artificial noise and information signals in a two-user weak Gaussian interference channel. In this channel, each receiver not only is interested in its related transmitter's message, but also it is an eavesdropper for the other link. Transmitters may broadcast noise in addition to data in order to confuse eavesdroppers. In this context, the secrecy rate is referred to as the utility, and the Nash equilibrium outcome in the related non-cooperative power splitting game is inefficient. By introducing a novel price-based potential game, we obtain Pareto improvement in the secrecy sum-rate. Numerical results confirm our analytical development.
This letter proposes a game-theoretic model to jointly optimize artificial noise and information signals in a two-user weak Gaussian interference channel. In this channel, each receiver not only is interested in its related transmitter's message, but also it is an eavesdropper for the other link. Transmitters may broadcast noise in addition to data in order to confuse eavesdroppers. In this context, the secrecy rate is referred to as the utility, and the Nash equilibrium outcome in the related non-cooperative power splitting game is inefficient. By introducing a novel price-based potential game, we obtain Pareto improvement in the secrecy sum-rate. Numerical results confirm our analytical development.
A secure communication game is considered for the two-user MISO Gaussian interference channel with confidential messages, where each transmitter aims to maximize the difference between its secrecy rate and the secrecy rate of the other transmitter. In this novel problem, the weaker link tries to minimize the extra secret information obtained by its adversary, while the stronger link attempts to maximize it. We provide an information theoretic formulation for this non-cooperative zero-sum game scenario and determine that, under the assumption of Gaussian signaling at the transmitters, there exists a unique Nash equilibrium solution for the proposed problem. Moreover, we obtain in closed-form the optimal strategies (beamformers) at the transmitters that result in the Nash equilibrium. While the NE strategies are achievable in one shot when full channel state information is available at the transmitters (CSIT), we also propose an iterative step-by-step algorithm that converges to the NE point, but only requires limited CSIT. Numerical results are presented to illustrate the analytical findings and to study the role of different channel parameters on the NE strategies.
The broadcast nature of wireless communication makes it vulnerable to Eavesdropping. To enhance the communication security, cooperative jamming (CJ) is applied and studied in many previous works. However, jamming signal may also decrease the signal-to noise ratio (SNR) of legal receivers, and degrade the overall performance of networks. Therefore, the jammer power must be reasonably controlled. In this paper, the jamming power control over two-user Gaussian interference wiretap channel is investigated. We aim to establish the optimal scheme for each communication pair with game theory. To maximize secrecy rate with minimal jamming power, we first derive the pure and mixed strategies Nash Equilibrium (NE) in non-cooperative game frame. Then given the overall utility and fairness, we establish a cooperative game. In cooperative game frame, time-sharing mechanism is used. In both frames, we derive best equilibrium strategy for each transmitter. Numerical results demonstrate that the system utility is really improved with jamming power control based on game theory.
The article considers the joint optimization of artificial noise (AN) and information signal precoders in a MIMO wiretap interference network where the transmission of each user may be overheard by several MIMO-capable eavesdroppers. We use the theory of non-cooperative games to propose a distributed framework to optimize the covariance matrices of the information signal and AN at each link. To tackle the non-convexity of each link/player's optimization problem, we recruit a relaxed equilibrium concept in game theory, called quasi-Nash equilibrium (QNE). Under the assumption of no coordination between links, we derive sufficient conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness of QNE is not always guaranteed, especially in the case of high interference. Hence, multiple QNEs might exist, and an ordinary updating process (e.g., Gauss-Seidel, Jacobi, or asynchronous update) does not guarantee the convergence to a QNE. Instead, by using the Tikhonov regularization method for variational inequality problems, we modify our algorithm to guarantee the game's convergence to a QNE even in the case of having multiple QNEs. The modified algorithm also allows the links to select between multiple QNEs so as to reduce the received interference at the legitimate receivers. Simulations are then used to confirm the above theoretical findings and the efficacy (in terms of secrecy sum-rate, convergence guarantee, and energy efficiency) of the latter algorithm.
We propose a distributed interference management method for a single-stream MIMO interference network that is tapped by an external eavesdropper. Along with its information signal, each legitimate transmitter creates a bogus signal, known as transmit-based friendly jamming (TxFJ), to confuse the eavesdropper. Although generating TxFJ protects the link from eavesdropping, it creates interference at other unintended but legitimate links. Using non-cooperative game theory, we design a distributed method for maximizing the sum of secrecy rates. Each link is a player in the game. It seeks to maximize its secrecy rate subject to a given information-rate constraint and power budget. The strategy profile of each player is to control the amount of TxFJ it generates. Because a pure non-cooperative game may not have Nash equilibria that result in (Pareto-)optimal secrecy sum-rate, we propose a modified price-based game, in which each link is penalized for generating interference on other legitimate links. Under the exact knowledge of eavesdropping channels, we show that the price-based game has a comparable secrecy sum-rate to a centralized approach. We then relax the assumption of knowledge of eavesdropping channels and leverage mixed-strategy games to provide robust solutions to the distributed secrecy sum-rate maximization problem.
We consider joint optimization of artificial noise (AN) and information signals in a MIMO wiretap interference network, wherein the transmission of each link may be overheard by several MIMO-capable eavesdroppers. Each information signal is accompanied with AN, generated by the same user to confuse nearby eavesdroppers. Using a noncooperative game, a distributed optimization mechanism is proposed to maximize the secrecy rate of each link. The decision variables here are the covariance matrices for the information signals and ANs. However, the nonconvexity of each link's optimization problem (i.e., best response) makes conventional convex games inapplicable, even to find whether a Nash equilibrium (NE) exists. To tackle this issue, we analyze the proposed game using a relaxed equilibrium concept, called quasi-NE (QNE). Under a constraint qualification condition for each player's problem, the set of QNEs includes the NE of the proposed game. We also derive the conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness conditions are too restrictive, and do not always hold in typical network scenarios. Thus, the proposed game often has multiple QNEs, and convergence to a QNE is not always guaranteed. To overcome these issues, we modify the utility functions of the players by adding several specific terms to each utility function. The modified game converges to a QNE even when multiple QNEs exist. Furthermore, players have the ability to select a desired QNE that optimizes a given social objective (e.g., sum rate or secrecy sum rate). Depending on the chosen objective, the amount of signaling overhead as well as the performance of resulting QNE can be controlled. Simulations show that not only can we guarantee the convergence to a QNE, but also due to the QNE selection mechanism, we can achieve a significant improvement in terms of secrecy sum rate and power efficiency, especially in dense networks.
In this paper, we investigate the performance of artificial noise assisted secure communication in the presence of a full-duplex active eavesdropper who can simultaneously perform eavesdropping and jamming. An approximate closed-form expression for the secrecy rate is derived. With this result, we obtain a new result for the optimal power allocation factor maximizing the secrecy rate, and analyze the impact of self-interference coefficient and jamming power on it. We further consider a more practical scenario where the legitimate user aims to maintain a given target data rate and uses all remaining power for artificial noise (AN) to interfere with the eavesdropper. While the eavesdropper tries to compel the transmitter to reduce the AN by sending jamming signals to the legitimate receiver. To solve this conflict, we introduce a power cost parameter to describe the impact of jamming on the eavesdropper itself and then formulate a game-theoretic framework. We also derive the closed-form equilibrium solutions for both sides. These results show the optimal jamming strategy of the eavesdropper and provide insights into the low bound secrecy performance. Finally, simulation results are provided to verify our analytical results.