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arXiv:1611.05015

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

Lingxiang Li, Zhi Chen, Athina P. Petropulu, Jun Fang

Published Nov 15, 2016• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1611.05015

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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.
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.
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.
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.
This paper considers secrecy communication from a signal processing point of view, and studies the maximal achievable secrecy degrees of freedoms (S.D.o.F.) of a helper-assisted Gaussian wiretap channel, consisting of a source, a legitimate receiver, an eavesdropper and an external helper. Each terminal is equipped with multiple antennas. We first propose a cooperative secrecy transmission scheme, and show that it achieves the maximal secrecy degrees of freedom. We then propose a heuristic method, through which, we solve analytically the optimization problem associated with the proposed cooperative secrecy transmission scheme. By this way, we obtain the maximal achievable S.D.o.F. and also the precoding matrices which achieve the maximal S.D.o.F. in closed-form.
We study the achievable rate regions of the multiple-input multiple-output (MIMO) interference channel with confidential messages sent to two receivers, assuming the transmitters use linear precoding. Each receiver is assumed to be an eavesdropper for the other link, and the transmitters employ various techniques to increase the secrecy rate of their own link or that of the network. We describe both cooperative and noncooperative transmission schemes for Gaussian interference channels, and derive their achievable secrecy rate regions. Cooperation is made possible if the transmitters share a portion of their channel state information, allowing them to appropriately adjust their precoders and improve the overall secrecy performance of the network. A game-theoretic formulation of the problem is adopted to allow the transmitters to find an operating point that balances network performance and fairness. The benefit of cooperation is demonstrated via several numerical examples.
This paper considers a Gaussian multi-input multi-output (MIMO) multiple access wiretap (MAC-WT) channel, where an eavesdropper (Eve) wants to extract the confidential information of all users. Assuming that both the legitimate receiver and Eve jointly decode their interested messages, we aim to maximize the sum secrecy rate of the system by precoder design. Although this problem could be solved by first using the iterative majorization minimization (MM) based algorithm to get a sequence of convex log-determinant optimization subproblems and then using some general tools, e.g., the interior point method, to deal with each subproblem, this strategy involves quite high computational complexity. Therefore, we propose a simultaneous diagonalization based low-complexity (SDLC) method to maximize the secrecy rate of a simple one-user wiretap channel, and then use this method to iteratively optimize the covariance matrix of each user. Simulation results show that in contrast to the existing approaches, the SDLC scheme achieves similar secrecy performance but requires much lower complexity.