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A Game Theoretic Design of Artificial-Noise Aided Transmissions in MIMO Wiretap Interference Network

Peyman Siyari, Marwan Krunz, Diep Ngoc Nguyen

Published Dec 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1109/glocom.2016.7841504

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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 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.
We consider an interference network tapped by external eavesdropper(s) in which each legitimate transmit-receive pair conceals its communications by using joint transmit-based friendly jamming (TxFJ) and receiver-based friendly jamming (RxFJ). Specifically, TxFJ is realized at the transmit side using MIMO precoding while RxFJ is achieved at the receiver side of each link by leveraging the state-of-the-art self-interference-suppression techniques (allowing a radio to cancel the self-interference effect of its transmit signal). We show that with a careful power allocation between the information signal and TxFJ at the transmit side of each link, the corresponding receiver is able decide on using RxFJ independent of any multi-user interference factor. This ability sets the receivers free from having to measure multi-user interference at eavesdropper(s). With every link following such strategy, we model this interaction as a non-cooperative game. We derive sufficient conditions under which the game admits a unique Nash equilibrium. We then propose a robust version of the game that requires only statistical knowledge of eavesdropping channel.
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.
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.
We propose a distributed artificial noise-assisted precoding scheme for secure communications over wiretap multi-input multi-output (MIMO) interference channels, where K legitimate transmitter-receiver pairs communicate in the presence of a sophisticated eavesdropper having more receive-antennas than the legitimate user. Realistic constraints are considered by imposing statistical error bounds for the channel state information of both the eavesdropping and interference channels. Based on the asynchronous distributed pricing model, the proposed scheme maximizes the total utility of all the users, where each user’s utility function is defined as the secrecy rate minus the interference cost imposed on other users. Using the weighted minimum mean square error, Schur complement and sign-definiteness techniques, the original non-concave optimization problem is approximated with high accuracy as a quasi-concave problem, which can be solved by the alternating convex search method. Simulation results consolidate our theoretical analysis and show that the proposed scheme outperforms the artificial noise-assisted interference alignment and minimum total mean-square error-based schemes.
Secure precoding superimposed with artificial noise (AN) is a promising transmission technique to improve security by harnessing the superposition nature of the wireless medium. However, finding a jointly optimal precoding and AN structure is very challenging in downlink multi-user multiple-input multiple-output wiretap channels with multiple eavesdroppers. The major challenge in maximizing the secrecy rate arises from the non-convexity and non-smoothness of the rate function. Traditionally, an alternating optimization framework that identifies beamforming vectors and AN covariance matrix has been adopted; yet this alternating approach has limitations in maximizing the secrecy rate. In this paper, we put forth a novel secure precoding algorithm that jointly and simultaneously optimizes the beams and AN covariance matrix for maximizing the secrecy rate when a transmitter has either perfect or partial channel knowledge of eavesdroppers. To this end, we first establish an approximate secrecy rate in a smooth function. Then, we derive the first-order optimality condition in the form of the nonlinear eigenvalue problem (NEP). We present a computationally efficient algorithm to identify the principal eigenvector of the NEP as a suboptimal solution for secure precoding. Simulations demonstrate that the proposed methods improve secrecy rate significantly compared to the existing methods.