IEEE Signal Processing Letters

A Full-Duplex Bob in the MIMO Gaussian Wiretap Channel: Scheme and Performance

Lingxiang Li, Zhi Chen, Duo Zhang, Jun Fang

Published Nov 30, 2015• 64 citations

Abstract

This letter considers secrecy communication from an information-theoretic perspective, and studies the secrecy capacity of a multi-input multi-output (MIMO) Gaussian wiretap channel with a source (Alice), an eavesdropper (Eve) and a Full-Duplex (FD) legitimate receiver (Bob). Bob can allocate part of his antennas to transmit jamming signals to impair Eve’s channel. Our goal is to identify the secrecy capacity behavior in the high signal-to-noise ratio (SNR) regimes, i.e., the maximal achievable secure degrees of freedom (S.D.o.F). Such S.D.o.F maximization is generally difficult to solve since it requires to face a nonlinear fractional problem. To deal with this issue, we first propose a cooperative secrecy transmission scheme, and prove its optimality in the sense of achieving the maximal S.D.o.F.. By studying this proposed transmission scheme, we obtain the maximal achievable S.D.o.F. in closed form for any given antenna allocation at Bob. Based on this closed-form result, we further analytically derive the optimal antenna allocation at Bob. To the best of our knowledge, this is the first time that the benefit brought by using the FD jamming Bob has been quantified.

DOI: 10.1109/lsp.2015.2504396

Related papers

Linear Precoder Design for an MIMO Gaussian Wiretap Channel With Full-Duplex Source and Destination Nodes

Lingxiang Li, Zhi Chen, Athina P. Petropulu +1 more

This paper investigates and quantifies the advantages of a Full-Duplex (FD) transmitter/receiver pair in improving the secrecy rate of the system. We consider a linear precoder design for a multiple-input multiple-output Gaussian wiretap channel, which comprises two legitimate nodes, i.e., Alice and Bob, operating in FD mode and exchanging confidential messages in the presence of a passive eavesdropper. Using the sum secrecy degrees of freedoms (sum SDoFs) as metric, we formulate an optimization problem with respect to Alice's and Bob's precoding matrices. In order to solve this problem, we first propose a cooperative secrecy transmission scheme, whose feasible set is sufficient to achieve the maximum sum SDoF. Based on that feasible set, we then determine in closed form the maximum achievable sum SDoF and also provide a method for constructing the precoding matrix pair, which achieves the maximum sum SDoF. The latter pair would be near-optimal in terms of the achievable secrecy sum rate in the high signal-to-noise ratio (SNR) regime. By providing the maximum achievable sum SDoF as a function of the number of antennas, one could select the optimal system parameters to further maximize the achievable sum SDoF. We use simulations to evaluate the performance of the proposed precoding matrices in realistic channel scenarios and at various levels of the SNR.

IEEE Transactions on Information Forensics and SecuritySep 25, 20179 citations

MIMO Secret Communications Against an Active Eavesdropper

Lingxiang Li, Athina P. Petropulu, Zhi Chen

This paper considers a scenario in which an Alice-Bob pair wishes to communicate in secret in the presence of an active Eve, who is capable of jamming as well as eavesdropping and operates in full-duplex (FD) mode. As countermeasure, Bob operates in FD mode, using a subset of its antennas to receive, and the remaining antennas to transmit jamming noise. Alice and Bob employ linear precoding, and all nodes use Gaussian code books. In that context, our goal is to maximize the achievable secrecy degrees of freedom (S.D.o.F.) of the system. We provide the optimal receive/transmit antennas allocation at Bob, based on which we determine in closed form the maximum achievable S.D.o.F. We also provide a method for constructing the precoding matrices of Alice and Bob, based on which the maximum S.D.o.F. can be achieved. We further investigate the adverse scenario in which Eve knows Bob's transmission strategy and optimizes its transmit/receive antennas allocation in order to minimize the achievable S.D.o.F. For that case, we find the worst case achievable S.D.o.F. Numerical results validate the theoretical findings and demonstrate the performance of the proposed method.

arXiv:1612.01564IEEE Transactions on Information Forensics and SecurityMay 18, 201751 citations

Linear Precoder Design for a MIMO Gaussian Wiretap Channel with Full-Duplex Source and Destination Nodes

Lingxiang Li, Zhi Chen, Athina P. Petropulu +1 more

We consider linear precoder design for a multiple-input multiple-output (MIMO) Gaussian wiretap channel, which comprises two legitimate nodes, i.e., Alice and Bob, operating in Full-Duplex (FD) mode and exchanging confidential messages in the presence of a passive eavesdropper. Using the sum secrecy degrees of freedoms (sum S.D.o.F.) as reliability measure, we formulate an optimization problem with respect to the precoding matrices. In order to solve this problem, we first propose a cooperative secrecy transmission scheme, and prove that its feasible set is sufficient to achieve the maximum sum S.D.o.F.. Based on that feasible set, we then determine the maximum achievable sum S.D.o.F. in closed form, and provide a method for constructing the precoding matrix pair which achieves the maximum sum S.D.o.F.. Results show that, the FD based network provides an attractive secrecy transmission rate performance.

arXiv:1611.05015Nov 15, 20160 citations

Application of Full-Duplex Wireless Technique into Secure MIMO Communication: Achievable Secrecy Rate based Optimization

Yongkai Zhou, Zheng Zheng Xiang, Yan Mei Zhu +1 more

This letter considers the secure MIMO transmission in a wireless environment, in which one transmitter (Alice), one receiver (Bob) and one eavesdropper (Eve) are involved. Apart from the artificial noise (AN) generated by Alice, Bob can also exploit his remaining antenna resources to emit AN to further impair Eve's channel. Such kind of AN can be cancelled by Bob himself by applying the Full-Duplex wireless communication technique. A computable secrecy rate is obtained for this model over a Rayleigh-fading eavesdropping channel. In order to maximize the secrecy rate, a joint optimization scheme is proposed to assign the TX/RX antennas for Bob and to design the beamforming and power allocation for Alice's information and AN signal. Simulation is carried out to illustrate the process of the proposed optimization scheme.

IEEE Signal Processing LettersApr 11, 201471 citations

On the Secrecy Capacity of a MIMO Gaussian Wiretap Channel with a Cooperative Jammer

Lingxiang Li, Zhi Chen, Jun Fang +1 more

We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.

arXiv:1509.04624Sep 15, 20152 citations

Cooperative Jamming for MIMO Wiretap Channels

Shuiyin Liu, Yi Hong, Emanuele Viterbo

Abstract—This paper addresses secure communications over MIMO wiretap channels with the help of multiple cooperative jammers. The worst-case scenario for Alice, Bob and jammers is considered: Eve has the knowledge of all channel matrices, while neither her channel matrix nor her location is known to the remaining terminals. We propose an artificial noise aided cooperative jamming (AN-CJ) scheme, allowing the total jamming signals to be nulled at Bob. The new scheme is valid for the case where the eavesdropper has more antennas than the transmitter. To evaluate the performance of the AN-CJ scheme, we first derive a closed-form expression for the achievable ergodic secrecy rate with Gaussian input alphabets. Then, we show how Gaussian input alphabets achieve the ergodic secrecy capacity. I.

Jan 18, 20166 citations