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IEEE Transactions on Wireless Communications

Joint Beamforming and Power Allocation for Secrecy in Peer-to-Peer Relay Networks

Chao Wang, Hui‐Ming Wang, Derrick Wing Kwan Ng, Xiang‐Gen Xia, Chaowen Liu

Published Feb 13, 2015• 88 citations
Publisher

Abstract

This paper investigates the physical-layer security of a multiuser peer-to-peer (MUP2P) relay network for amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with a multi-antenna eavesdropper and the eavesdropper can wiretap the confidential information in both two cooperative phases. Our goal is to optimize the transmit power of the source and the beamforming weights of the relays jointly for secrecy rate maximization subject to the minimum signal-to-interference-noise-ratio (SINR) constraint at each user, and the individual and total power constraints. Mathematically, the optimization problem is non-linear and non-convex, which does not facilitate an efficient resource allocation algorithm design. As an alternative, a null space beamforming scheme is adopted at the relays for simplifying the joint optimization and eliminating the confidential information leakage in the second cooperative phase, where the relay beamforming vector lies in the null space of the equivalent channel of the relay to eavesdropper links. Although the null space beamforming scheme simplifies the design of resource allocation algorithm, the considered problem is still non-convex and obtaining the global optimum is very difficult, if not impossible. Employing a sequential parametric convex approximation (SPCA) method, we propose an iterative algorithm to obtain an efficient solution of the non-convex problem. Besides, the proposed joint design algorithm requires a feasible starting point, we also propose a low complexity feasible initial points searching algorithm. Simulations demonstrate the validity of the proposed strategy.

DOI
10.1109/twc.2015.2403367

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This paper investigates the physical-layer security of a multiuser peer-to-peer (MUP2P) relay network for amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with a multi-antenna eavesdropper and the eavesdropper can wiretap the confidential information in both two cooperative phases. Our goal is to optimize the transmit power of the source and the beamforming weights of the relays jointly for secrecy rate maximization subject to the minimum signal-to-interference-noise-ratio (SINR) constraint at each user, and the individual and total power constraints. Mathematically, the optimization problem is non-linear and non-convex, which does not facilitate an efficient resource allocation algorithm design. As an alternative, a null space beamforming scheme is adopted at the relays for simplifying the joint optimization and eliminating the confidential information leakage in the second cooperative phase, where the relay beamforming vector lies in the null space of the equivalent channel of the relay to eavesdropper links. Although the null space beamforming scheme simplifies the design of resource allocation algorithm, the considered problem is still non-convex and obtaining the global optimum is very difficult, if not impossible. Employing a sequential parametric convex approximation (SPCA) method, we propose an iterative algorithm to obtain an efficient solution of the non-convex problem. Besides, the proposed joint design algorithm requires a feasible starting point, we also propose a low complexity feasible initial points searching algorithm. Simulations demonstrate the validity of the proposed strategy.
In this paper, physical layer security is studied for multiuser peer-to-peer (MUP2P) relay networks using amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with an eavesdropper. Though the beamforming design has been previously investigated with perfect channel state information (CSI) in the presence of an eavesdropper, this paper focuses on researching the robust relay beamforming mechanism for MUP2P relay networks. The worst-case secrecy rate is maximized, while subject to the worst-case signal-to-interference-noise ratio constraint at each user and the total power constraint at relays under a bounded spherical region for the norm of the CSI error vector from the relays to the destination. Mathematically, the optimization problem is nonlinear and nonconvex. We propose an iterative algorithm to obtain an efficient solution of the nonconvex problem by employing S-Procedure and rank relaxation techniques. The convergence of the proposed robust algorithm is proved and its complexity is analyzed. Simulations show that the proposed design can significantly improve the performance of secure wireless communications.
We address a robust beamforming design and power allocation problem for a multi-pair one-way relay network, where the single-antenna users of each pair implement communication via a decode-and-forward multi-antenna relay. In this network, a secure user and other unclassified users coexist with a multi-antenna eavesdropper, and only the imperfect eavesdropper's channel state information (ECSI) is available. We aim to maximize the worst-case secrecy rate of the secure user while guaranteeing the quality of service of the unclassified users with a total power constraint. Motivated by this challenge, we explore the beamforming design and power allocation among the sources and the relay with the channel matrix error. Unfortunately, the proposed design constitutes a non-convex problem, which involves an infinite number of constraints because of the imperfect ECSI. To this end, we propose an efficient algorithm by using the techniques of semidefinite relaxation, successive convex approximation and S-procedure techniques. Following a similar optimization framework, we further investigate the scheme with the channel covariance matrix error. Simulation results validate the effectiveness of the proposed algorithm.
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.
This paper considers secure communication for amplify-and-forward (AF) relay networks with finite alphabet input. The joint optimization of power selection and beamforming design for improving the physical layer security of AF relay networks with single and multiple eavesdroppers is investigated. For the case with one eavesdropper, we transform the problem of multi-variable beamforming design into a single-variable optimization problem through semi-definite programming and solve it with one-dimensional optimization techniques. Moreover, the corresponding source power is obtained by utilizing the relation between the mutual information and minimum mean square error. Then, an iterative two-step algorithm is proposed to maximize the achievable secrecy rate. In the presence of multiple eavesdroppers, a zero-forcing beamforming scheme, where the confidential signal is nulled out in the direction of all eavesdroppers, is proposed to enhance the physical layer security. We decouple the source power and the beamforming vector by transforming the achievable secrecy rate into a single-variable function of the source power. Then, the suboptimal source power and the corresponding beamforming vector with low-complexity are derived. Numerical examples show that the proposed schemes significantly enhance the secrecy performance of the AF relay networks.
In this paper, we investigate the secure relay beamforming problem for simultaneous wireless information and power transfer (SWIPT) in an amplify-and-forward (AF) two-way relay network. We consider scenarios that the eavesdropper's channel state information (CSI) is and is not available. When the eavesdropper's CSI is available, our objective is to maximize the achievable secrecy sum rate under transmit power constraint and energy harvesting constraint. Since the optimization problem is nonconvex, we derive its performance upper bound, which requires 2-D search, where a semidefinite programming is solved in each step. We also propose an upper bound-based rank-one solution by employing the Gaussian randomization method. To reduce computational complexity, we transform the optimization problem into a difference-of-convex programming and propose a sequential parametric convex approximation (SPCA)-based iterative algorithm to find a locally optimal solution. Furthermore, we also propose a zero-forcing (ZF)-based suboptimal solution. Simulation results demonstrate that the upper bound-based rank-one solution archives the performance almost the same as the upper bound that has high computational complexity. The low-complexity SPCA-based locally optimal solution performs close to the upper bound. The ZF-based suboptimal solution has the lowest computational complexity among the proposed solutions. When the eavesdropper's CSI is not available, we propose an artificial noise-aided secure relay beamforming scheme.
In this paper, we consider a two-way relay network with two sources and multiple cooperative relays in the presence of an eavesdropper. To guarantee the secrecy, a null space beamforming scheme is applied, where the relay beamforming vector lies in the nullspace of the equivalent channel of relay link from two sources to the eavesdropper. Our goal is to obtain the optimal beamforming vector as well as two sources' transmit power subject to various criteria. We propose three different approaches and solve them in an alternating iterative way, where subproblems for solving beamforming and sources' power are formulated in each iteration, respectively. First, we minimize the total transmit power under secrecy rate constraint at two sources. For beamforming vector subproblem, two different methods, semi-definite programming (SDP) and sequential quadratic programming (SQP), are proposed, where we analyze and verify SQP has lower complexity than SDP. Second, we maximize the secrecy sum rate, subject to total transmit power constraint. The beamforming vector subproblem is equivalent to a generalized Rayleigh quotient problem with rank constraint. Third, the problem of minimum per-user secrecy rate maximization under the total power constraint is investigated for user fairness. An iterative procedure utilizing the SDP with bisection search method is proposed to solve beamforming subproblem. In each approach the subproblem with two sources' power is formulated as a single variable problem and solved by Newton's method with line search. Simulation results demonstrate the validity of proposed approaches and algorithms for both symmetric and asymmetric scenarios.