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International Conference on Wireless Communications and Signal Processing (WCSP)

Precoder design for secrecy rate maximization in the DF-based MIMO relay networks

Bing Fang, Zuping Qian, Zhong Wei, Wei Shao

Published Oct 1, 2015• 1 citation
Publisher

Abstract

In this paper, we study the precoder design problem for secrecy rate maximization in a decode-and-forward (DF)-based multiple-input multiple-output (MIMO) relay network. The system model considered here consists of a source, a trusted relay, a legitimate receiver and an eavesdropper, all mounted with multiple antennas. Our objective is to maximize the achievable secrecy rate of this DF-based MIMO relay wiretap system subject to a total transmit power constraint. Since the formulated secrecy rate maximization (SRM) problem is nonconvex in general, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the formulated problem is linearized to its first-order Taylor expansion. Then, the nonconvex SRM problem can be iteratively solved through successive convex programming of its convexified version, and thus an iterative precoding algorithm is developed. Moreover, the theoretical result is further extended to the case when multiple eavesdroppers are simultaneously present. Finally, numerical simulations are provided to evaluate the performance of the proposed algorithm. Results show that our algorithm can converge fast to a near-optimal solution.

DOI
10.1109/wcsp.2015.7341097

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In this paper, we study the precoder design problem for secrecy rate maximization in a decode-and-forward (DF)-based multiple-input multiple-output (MIMO) relay network. The system model considered here consists of a source, a trusted relay, a legitimate receiver and an eavesdropper, all mounted with multiple antennas. Our objective is to maximize the achievable secrecy rate of this DF-based MIMO relay wiretap system subject to a total transmit power constraint. Since the formulated secrecy rate maximization (SRM) problem is nonconvex in general, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the formulated problem is linearized to its first-order Taylor expansion. Then, the nonconvex SRM problem can be iteratively solved through successive convex programming of its convexified version, and thus an iterative precoding algorithm is developed. Moreover, the theoretical result is further extended to the case when multiple eavesdroppers are simultaneously present. Finally, numerical simulations are provided to evaluate the performance of the proposed algorithm. Results show that our algorithm can converge fast to a near-optimal solution.
In this paper, we investigate the security issue of a two-hop amplify-and-forward multiple-input multiple-output wireless relay network in the existence of a multiantenna eavesdropper. The optimal scheme to achieve the secrecy capacity involves a nonconvex optimization and is still an open problem. Aiming to find an efficient way to enhance the secrecy rate with a tractable complexity, we propose a suboptimal joint source and relay linear precoding and power allocation scheme. In the scheme, the source node adopts a generalized singular value decomposition (SVD)-based precoding to transmit the signal in the first phase, and the relay node forwards the received signal based on the SVD precoding in the null-space of the wiretap channel in the second phase. Power allocations in both phases are optimized to maximize the secrecy rate by an alternating iterative optimization algorithm. Each iteration involves two subproblems. One has a water-filling solution and the other has a closed-form solution or a water-filling-like solution as well, both of which are computationally very efficient. The iteration converges fast and we prove that it guarantees to find a stationary optimum. Furthermore, we show that when the eavesdropper has equal or more antennas than the source does, the secrecy rate is a quasi-concave function of the source power so that allocating all the source power is generally not optimal. Numerical evaluation results are provided to show the effectiveness of the iterative algorithm and the proposed secrecy scheme.
In this paper, we propose a joint source-relay precoding scheme to secure an amplify-and-forward multiple-input multiple-output wireless relay network in the existence of a multi-antenna eavesdropper. Different from existing works that only consider some specific signal design to simplify the problem, we take both the direct links from the source to the destination and to the eavesdropper into account, and investigate the general joint signal covariance matrices optimization problem to maximize the secrecy rate, which leads to a difficult non-convex optimization problem. To handle it, we propose a group alternating optimization algorithm to find a solution, which alternately optimizes the signal covariance matrix and the linear precoding matrix at the source and the relay, respectively. For optimizing the linear precoding matrix at the relay, the problem is still non-convex, and we propose a minorization-maximization (MM) method to handle it. The MM method transforms the original non-convex problem into a series of convex problems and guarantees the convergence of a local optimum. For optimizing the signal covariance matrix at the source, we reveal the convex-concave property of the problem, and find its global optimum using a barrier method combined with the Newton iteration. We also provide an initialization method to trigger the algorithm and analyze the convergence and complexity. The numerical results show the computational efficiency and the prominent performance of the proposed algorithm.
In this paper, we investigate the security issue of a two-hop amplify-and-forward MIMO wireless relay networks in the existence of a multi-antenna eavesdropper. The optimal scheme to achieve the secrecy capacity involves a non-convex optimization and is still an open problem. Aiming to find an efficient way to enhance the secrecy rate, we propose a suboptimal joint source and relay linear precoding scheme. In the scheme, the source node adopt a generalized singular value decomposition (GSVD) based precoding to transmit the signal in the first phase, and the relay node forwards the received signal based on SVD in the null-space of the wiretap channel in the second phase. Power allocations in both phases are optimized to maximize the secrecy rate. An alternating iterative optimization algorithm is proposed to solve the problem. The algorithm is computationally efficient and guarantees to converge to a local optimum. Numerical evaluation results are provided to show the effectiveness of the iterative algorithm and the proposed secrecy scheme.
In this paper, we study the energy-efficient secrecy precoding problem for a general multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel. The system model considered here consists of a common transmitter, a legitimate receiver, and multiple eavesdroppers, all mounted with multiple antennas. In order to improve the energy efficiency (EE) performance of the proposed system, an artificial noise (AN)-aided precoding scheme is adopted. Because the formulated EE maximization problem is of huge nonconvex complexity, we solve it by employing a two-tier optimization structure. Although the outer-tier optimization problem is quite simple and can be efficiently solved by the famous golden section searching method, the inner-tier optimization problem turns out to be nonconvex and cannot be easily solved. To solve it, we relax it to a secrecy rate maximization (SRM) problem, which naturally constitutes a difference convex (DC)-type programming problem and can be iteratively solved by employing a successive convex approximation (SCA) method. Numerical simulations are further provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a near-optimal solution.
In this paper, we study the precoding problem for physical layer security in a general multiple-input multiple-output (MIMO) wiretap channel. Since the resultant secrecy capacity maximization (SCM) problem is nonconvex in general, we solve it by employing a successive convex approximation method, where the nonconvex part of the formulated problem is approximated by its first-order Taylor expansion. Thus, the SCM problem can be iteratively solved through convex programming of its convexified version. Finally, an iterative precoding algorithm with provable convergence is presented. Numerical simulations are also provided to verify the proposed algorithm.
We address a robust beamforming design and power allocation problem for a one-way multi-antenna relay network, where the multi-antenna source implements communication with the multi-antenna destination via a decode-and-forward (DF) relay in the presence of the multiple single-antenna eavesdroppers. The eavesdroppers can only overhear the information flowed from the relay to the destination in the second hop. We aim to maximize the worst-case secrecy rate in the condition that the global channel state information (CSI) is imperfect. To this end, we propose the joint beamforming and power allocation design for the worst-case secrecy rate maximization. However, our proposed design constitutes a non-convex problem, which involves an infinite number of constraints because of the imperfect CSI. To make the problem more tractable, we approximate the problem into several tractablesemidefinite programs by semidefinite relaxation, successive convex approximation, and S-procedure techniques, and we propose an iterative algorithm to solve the problem. Furthermore, we show that the proposed algorithm is also applicable for the case the Gaussian wiretap model, where only the eavesdroppers' CSI is imperfect. Simulation results validate the effectiveness of the proposed algorithm.