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IET Communications

MMSE‐based secure precoding in two‐way relaying systems

Hang Long, Wei Xiang, Luyuan Zhang, Li Qun Huang

Published Dec 1, 2020• 1 citation
Publisher

Abstract

In this study, secure communications in a two‐way relaying wiretap system with a silent eavesdropper are studied. Under the assumption that the channel state information relating to the eavesdropper is unknown at legitimate nodes, the precoding vectors at the two source nodes are jointly designed to decrease the wiretap capacity at the eavesdropper. The derived relationship between the two precoding vectors is partially similar in nature to the linear minimum mean squared error (MMSE) equaliser. An iterative process is proposed to jointly achieve two precoding vectors, and its convergence is proved. Simulation results are presented to demonstrate that the proposed MMSE‐based precoding algorithm can be used for source nodes with any number of antennas, and outperforms its conventional zero‐forcing‐ and matched‐filter‐based counterparts. Signal leakage from the relay node to the eavesdropper is nearly completely suppressed by the proposed precoding design.

DOI
10.1049/iet-com.2020.0379

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In this study, secure communications in a two‐way relaying wiretap system with a silent eavesdropper are studied. Under the assumption that the channel state information relating to the eavesdropper is unknown at legitimate nodes, the precoding vectors at the two source nodes are jointly designed to decrease the wiretap capacity at the eavesdropper. The derived relationship between the two precoding vectors is partially similar in nature to the linear minimum mean squared error (MMSE) equaliser. An iterative process is proposed to jointly achieve two precoding vectors, and its convergence is proved. Simulation results are presented to demonstrate that the proposed MMSE‐based precoding algorithm can be used for source nodes with any number of antennas, and outperforms its conventional zero‐forcing‐ and matched‐filter‐based counterparts. Signal leakage from the relay node to the eavesdropper is nearly completely suppressed by the proposed precoding design.
This paper studies secrecy communications in a multi-antenna two-way relaying wiretap system. Each source node transmits user and jamming signals with distinct precoding vectors. Based on the assumption that the channel state information relating to the eavesdropper is unknown by the legitimate nodes, new precoding design algorithms are proposed. The jamming signals are designed to ensure that minimum interference is perceived by the other source node. The precoding vectors of the user signals are designed to form two parallel vectors in the equivalent wiretap channel at the eavesdropper. Two algorithms are proposed based upon the zero-forcing and matched-filter schemes, which are dubbed the selective zero-forcing-based precoding (SZFP) and matched-filter-based precoding schemes. Analytical and simulation results are presented to demonstrate that the SZFP algorithm is more applicable when the eavesdropper is equipped with a large number of antennas or the eavesdropper's channels are in good condition.
In this paper, secrecy communications with cooperative jamming in a two-hop one-way untrusted relay system is studied. Assuming that all nodes are equipped with multiple antennas, new precoding designs are proposed to increase the secrecy capacity. Two situations are considered, namely only designing precoding vector for jamming signal when user signal has been determined, and designing precoding vectors for both user and jamming signals by jointly considering the source node. For each situation, two alignment algorithms are proposed, namely zero-forcing-based (ZF) alignment algorithm and minimum-mean-squared-error-based (MMSE) alignment algorithm. Both algorithms are designed to ensure that the equivalent wiretap channel matrix forms two aligned vectors. The channel vector from the destination node is designed to be aligned with that from the source node, so that the eavesdropping node cannot decode user signals. Analytical and simulation results show that all proposed scheme can achieve secure communication, and the MMSE algorithm performs better than the ZF. In addition, the destination-relay link has greater impact on the secrecy performance than the relay-destination link.
In this paper, we investigate the problem of jointly designing optimum linear precoder and decoder with secrecy constraints, where two legitimate parties communicate in the presence of an eavesdropper over multiple-input multiple-output (MIMO) Gaussian channels. In particular, we focus on optimizing the linear transceiver to guarantee a certain quality of service (QoS) level for the legitimate receiver in terms of mean square error (MSE), whilst employing the artificial noise to maximally degrade the MSE for the eavesdropper. We assume that the transmitter may not or may have the channel state information (CSI) for the eavesdropper, and then propose two design formulations. With the aid of majorization theory, we characterize the forms of optimal transmit precoder when both the legitimate receiver and the eavesdropper employ the optimal linear MMSE receiver. Numerical results illustrate main conclusions.
In this paper, cooperative jamming in the multiantenna two-way relaying wiretap system is investigated. Under the assumption that all the channel state information related to the eavesdropper is unknown at legitimate nodes, and the jamming signals generated by the two source nodes can not be shared with each other, the precoding vectors for the user and jamming signals at each source node are designed. Additionally, the power allocation between the user and jamming signals at each source node is also discussed. Simulation results are given to verify the proposed cooperative jamming design.
In this paper, we investigate the precoding scheme for multiple-input multiple-output multiple antennas eavesdropper (MIMOME) channels under the constraint of finite-alphabet inputs to ensure secure transmission between the source and the destination in the presence of an eavesdropper. With finite-alphabet inputs, there are no closed-form solutions for mutual information (MI) and its gradient-minimum mean-square error (MMSE) matrix. Therefore traditional precoding schemes based on direct calculation of MI and MMSE matrix through numerical integration involve prohibitive computational burden. To address this problem, this paper first derives asymptotically optimal lower bounds of MI and ergodic MI with which the computational complexity can be significantly reduced compared with the direct computation of MI. With the derived lower bounds, a low-complexity precoding scheme is proposed to maximize the secrecy rate, wherein a gradient descent based algorithm is used to obtain the precoding result. In the low and high signal-to-noise ratio (SNR) regions, we demonstrate that the proposed precoding scheme gives the same result as directly maximizing the secrecy rate, which indicates that the proposed low-complexity precoding scheme is asymptotically optimal.
In this study, security schemes at the physical layer are proposed for an amplify‐and‐forward relay system in the presence of a passive eavesdropper. We focus on maximising the transmit power of the artificial noise (AN) to degrade the minimum mean square error (MMSE) level at the eavesdropper, while achieving MMSE constraint for the desired receiver. Assuming that the desired receiver and the passive eavesdropper possess perfect channel state information (CSI), AN is designed to lie in the null space of legitimate channels. However, the available CSI is impossible to be perfect in practice. Therefore the authors present a robust beamforming scheme which maximises the worst‐case transmit power of the AN under the condition of imperfect CSI and recovers a large fraction of the performance in the perfect CSI case. A classical alternating optimisation algorithm is proposed to obtain the relay beamforming weights, and simulation results show the benefit of proposed schemes.