Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Signal Processing

Competing for Secrecy in the MISO Interference Channel

S. Ali. A. Fakoorian, Arnold Lee Swindlehurst

Published Oct 9, 2012• 21 citations
Publisher

Abstract

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.

DOI
10.1109/tsp.2012.2223689

Related papers

MIMO interference channel with confidential messages: Game theoretic beamforming designs

S. Ali. A. Fakoorian, Arnold Lee Swindlehurst

We study the achievable rate regions of the multiple-input multiple-output (MIMO) interference channel with confidential messages sent to two receivers. Under this model, each receiver is an eavesdropper for the other link and tries to decode both its own message and the message intended for the other receiver. We describe several transmission schemes for Gaussian interference channels and derive their achievable secrecy rate regions under the assumption that the transmitters use low complexity beamforming algorithms. We also consider the trade-offs associated with their need for channel state information at the transmitter (CSIT).We approach the above topics from a game-theoretic perspective.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Nov 1, 2010•10 citations

Secure Beamforming Design in Wiretap MISO Interference Channels

Jian Zhou, Ruohan Cao, Hui Gao +2 more

In this paper, we study the secrecy communication in two-user MISO interference networks where an external eavesdropper is interested in the messages transmitted by both transmitters. We propose a beamforming design to maximize the achievable secrecy sum rate of the transmitters subject to the individual power constraint at each transmitter. To transform this complex non-convex problem into a convex one, we propose an iterative algorithm based on the constrained concave convex procedure (CCCP) and successive convex approximation (SCA). It is observed that the proposed algorithm converges fast to a stationary point within a few iterations. Furthermore, we also propose a low-complexity null-space beamforming design scheme in which the beamforming vectors have closed-form solutions. Simulation results show the effectiveness of the two proposed schemes in improving the secrecy sum rate performance.

IEEE Vehicular Technology Conference•May 1, 2015•6 citations

Signalling and Resource Allocation for Secure Communication in Gaussian Wireless Channels

Shabnam Shafiee

Gaussian wireless channels are studied under two forms of security attacks: (i) the jamming attack, where the adversary is active and transmits corruptive signal, but is not interested in the content of the communication, (ii) the eavesdropping attack, where the adversary is passive and overhears the communication and tries to obtain the message that has been transmitted. The active attack is studied in a multi-user setting. The behavior of two users and one jammer in an additive white Gaussian channel (AWGN) with and without fading is investigated, when they participate in a non-cooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop the channel and can use the information obtained to perform correlated jamming. We also differentiate between the availability of perfect and noisy information about the user signals at the jammer. Under various assumptions on the channel characteristics, and the extent of channel state information available at the users and the jammer, we show the existence, or otherwise non-existence of a simultaneously optimal set of strategies for the users and the jammer, and characterize those strategies whenever they exist. For the passive eavesdropping attack, we study multiple-input multiple-output (MIMO) AWGN channels. We first consider a multiple-input single-output (MISO) channel, where the transmitter has multiple antennas, while the receiver and the eavesdropper have single antennas each. We find achievable rates for this channel. With the channel input restricted to Gaussian signalling with no pre-processing of information, optimal transmission strategies that maximize the achievable secrecy rates are found, in terms of the input covariance matrices. It is shown that, under the optimal communication strategy, the system reduces to a single-input single-output (SISO) channel. We then extend the achievability results to fading Gaussian MISO channels. Finally, as a step toward generalizing the problem to one with multiple antennas at the receiver, we discuss the Gaussian 2-2-1 channel with a transmitter and a receiver with two antennas each, and a single antenna eavesdropper. We develop an achievability scheme similar to those of the SISO and MISO channels, and further show that in fact, it achieves the secrecy capacity of this 2-2-1 channel.

•Mar 7, 2008•1 citation

Secrecy Sum-Rate Enhancement in the Interference Channel via Price-Based Power Splitting

Atena Ebrahimkhani, Bahareh Akhbari, Babak Seyfe

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.

IEEE Communications Letters•Oct 1, 2018•3 citations

Achievable Rates in Gaussian MISO Channels with Secrecy Constraints

Shabnam Shafiee, Şennur Ulukuş

A Gaussian MISO (multiple input single output) channel is considered where a transmitter is communicating to a receiver in the presence of an eavesdropper. The transmitter is equipped with multiple antennas, while the receiver and the eavesdropper each have a single antenna. The transmitter maximizes the communication rate, while concealing the message from the eavesdropper. The channel input is restricted to Gaussian signalling, with no preprocessing of information. For these channel inputs, and under different channel fading assumptions, optimal transmission strategies are found, in terms of the input covariance matrices. It is shown that, the optimal communication strategy in all cases, is beamforming.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2007•313 citations

Maximizing the Minimum Achievable Secrecy Rate for a Two-User Gaussian Weak Interference Channel

Meysam Mirzaee, Soroush Akhlaghi

This paper is a study of the Gaussian weak interference channel in which two single-antenna sources aim to send their messages to legitimate destinations such that all messages are kept confidential from non-intended receivers. Under the Gaussian codebook assumption, the problem of secrecy rate balancing with the objective of exploring the optimal power allocation policy at the sources in an attempt to maximize the minimum achievable secrecy rate is investigated, assuming each source is subject to a transmit power constraint. It is shown that at the optimal point, the two secrecy rates are equal; hence, the problem is abstracted to maximize the secrecy rate associated with one destination, while the other is restricted to having the same secrecy rate. The optimum secrecy rate associated with the investigated max-min problem is analytically derived, leading to the solution of the secrecy rate balancing problem. An additional scenario is considered in which sources can transmit artificial noise in addition to their signals. In this case, the max-min problem is solved and a suboptimal solution is provided. Numerical results show that the proposed solution is near-optimal and can be used as a suitable alternative.

IEEE Transactions on Information Forensics and Security•Jan 24, 2019•5 citations
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.
We study the achievable rate regions of the multiple-input multiple-output (MIMO) interference channel with confidential messages sent to two receivers. Under this model, each receiver is an eavesdropper for the other link and tries to decode both its own message and the message intended for the other receiver. We describe several transmission schemes for Gaussian interference channels and derive their achievable secrecy rate regions under the assumption that the transmitters use low complexity beamforming algorithms. We also consider the trade-offs associated with their need for channel state information at the transmitter (CSIT).We approach the above topics from a game-theoretic perspective.
In this paper, we study the secrecy communication in two-user MISO interference networks where an external eavesdropper is interested in the messages transmitted by both transmitters. We propose a beamforming design to maximize the achievable secrecy sum rate of the transmitters subject to the individual power constraint at each transmitter. To transform this complex non-convex problem into a convex one, we propose an iterative algorithm based on the constrained concave convex procedure (CCCP) and successive convex approximation (SCA). It is observed that the proposed algorithm converges fast to a stationary point within a few iterations. Furthermore, we also propose a low-complexity null-space beamforming design scheme in which the beamforming vectors have closed-form solutions. Simulation results show the effectiveness of the two proposed schemes in improving the secrecy sum rate performance.
Gaussian wireless channels are studied under two forms of security attacks: (i) the jamming attack, where the adversary is active and transmits corruptive signal, but is not interested in the content of the communication, (ii) the eavesdropping attack, where the adversary is passive and overhears the communication and tries to obtain the message that has been transmitted. The active attack is studied in a multi-user setting. The behavior of two users and one jammer in an additive white Gaussian channel (AWGN) with and without fading is investigated, when they participate in a non-cooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop the channel and can use the information obtained to perform correlated jamming. We also differentiate between the availability of perfect and noisy information about the user signals at the jammer. Under various assumptions on the channel characteristics, and the extent of channel state information available at the users and the jammer, we show the existence, or otherwise non-existence of a simultaneously optimal set of strategies for the users and the jammer, and characterize those strategies whenever they exist. For the passive eavesdropping attack, we study multiple-input multiple-output (MIMO) AWGN channels. We first consider a multiple-input single-output (MISO) channel, where the transmitter has multiple antennas, while the receiver and the eavesdropper have single antennas each. We find achievable rates for this channel. With the channel input restricted to Gaussian signalling with no pre-processing of information, optimal transmission strategies that maximize the achievable secrecy rates are found, in terms of the input covariance matrices. It is shown that, under the optimal communication strategy, the system reduces to a single-input single-output (SISO) channel. We then extend the achievability results to fading Gaussian MISO channels. Finally, as a step toward generalizing the problem to one with multiple antennas at the receiver, we discuss the Gaussian 2-2-1 channel with a transmitter and a receiver with two antennas each, and a single antenna eavesdropper. We develop an achievability scheme similar to those of the SISO and MISO channels, and further show that in fact, it achieves the secrecy capacity of this 2-2-1 channel.
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 Gaussian MISO (multiple input single output) channel is considered where a transmitter is communicating to a receiver in the presence of an eavesdropper. The transmitter is equipped with multiple antennas, while the receiver and the eavesdropper each have a single antenna. The transmitter maximizes the communication rate, while concealing the message from the eavesdropper. The channel input is restricted to Gaussian signalling, with no preprocessing of information. For these channel inputs, and under different channel fading assumptions, optimal transmission strategies are found, in terms of the input covariance matrices. It is shown that, the optimal communication strategy in all cases, is beamforming.
This paper is a study of the Gaussian weak interference channel in which two single-antenna sources aim to send their messages to legitimate destinations such that all messages are kept confidential from non-intended receivers. Under the Gaussian codebook assumption, the problem of secrecy rate balancing with the objective of exploring the optimal power allocation policy at the sources in an attempt to maximize the minimum achievable secrecy rate is investigated, assuming each source is subject to a transmit power constraint. It is shown that at the optimal point, the two secrecy rates are equal; hence, the problem is abstracted to maximize the secrecy rate associated with one destination, while the other is restricted to having the same secrecy rate. The optimum secrecy rate associated with the investigated max-min problem is analytically derived, leading to the solution of the secrecy rate balancing problem. An additional scenario is considered in which sources can transmit artificial noise in addition to their signals. In this case, the max-min problem is solved and a suboptimal solution is provided. Numerical results show that the proposed solution is near-optimal and can be used as a suitable alternative.