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IEEE Wireless Communications and Networking Conference

Iterative algorithm for secrecy guarantee with null space beamforming in two-way relay networks

Yunchuan Yang, Hui Zhao, Cong Sun, Wenbo Wang

Published Apr 1, 2013• 3 citations
Publisher

Abstract

In this paper, we investigate a two-way relay networks consisted of two sources, multiple cooperative relays, and an eavesdropper. To guarantee the secure communication, a null space beamforming strategy is applied, where the relay beamforming vector is design to lie in the null space of the equivalent channel from two sources to the eavesdropper. Aiming to minimize the total transmit power under individual secrecy rate constraint at two sources, an alternating iteration method is proposed to calculate the relay beamforming vector as well as sources' transmit power. For relay beamforming vector optimization subproblem, two different approaches, semi-definite programming (SDP) relaxation and sequential quadratic programming (SQP) method, are proposed. Subproblem with two sources' transmit power optimization is formulated as a single variable problem and solved by Newton method with line search effectively. Through the numerical simulations, we verify the effectiveness of proposed algorithm. Moreover, with computational complexity analysis, we show that the SQP method has lower complexity than SDP, and further verify it in terms of executing time.

DOI
10.1109/wcnc.2013.6555113

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In this paper, we investigate a two-way relay networks consisted of two sources, multiple cooperative relays, and an eavesdropper. To guarantee the secure communication, a null space beamforming strategy is applied, where the relay beamforming vector is design to lie in the null space of the equivalent channel from two sources to the eavesdropper. Aiming to minimize the total transmit power under individual secrecy rate constraint at two sources, an alternating iteration method is proposed to calculate the relay beamforming vector as well as sources' transmit power. For relay beamforming vector optimization subproblem, two different approaches, semi-definite programming (SDP) relaxation and sequential quadratic programming (SQP) method, are proposed. Subproblem with two sources' transmit power optimization is formulated as a single variable problem and solved by Newton method with line search effectively. Through the numerical simulations, we verify the effectiveness of proposed algorithm. Moreover, with computational complexity analysis, we show that the SQP method has lower complexity than SDP, and further verify it in terms of executing time.
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.
Abstract Here, the issue of physical layer security in a two‐way multi‐antenna relay network) is studied. In such a network, two multi‐antenna transceivers attempt to exchange their secret messages via a multi‐antenna relay node in the presence of an eavesdropper. Throughout the first hop, two sources send their messages to the relay node, while an eavesdropper tries to overhear these messages. Then, in the second hop, the relay attempts to send its signal in the null‐space direction of relay‐to‐eavesdropper channel to prevent eavesdropping. The main goal is to obtain effective receive and transmit beamforming vectors at transceivers as well as the beamforming matrix at the relay node to address the secrecy rate balancing problem. The underlying problem is not convex in general. To overcome this issue, the original problem is divided into three subproblems. In the first subproblem the beamforming design at the relay is optimized while in the second subproblem the receive beamforming in a closed form solution is obtained. Finally, in the last subproblem the transmit beamforming is solved using the semi‐definite relaxation and Taylor series expansion. Numerical results represent the effectiveness of the proposed method compared to the previous works in the literature.
In this paper, we consider a two-way relay network system which contains multiple cooperative relays transmitting information between two sources with attendance of an eavesdropper. A null space beamforming scheme is applied to ensure the secrecy in system. Our goal is achieving maximal secrecy sum rate with a certain level power transmit. In [1], authors propose an approach to solve Secrecy Sum Rate Maximization (SSRM) problem, whereas we use another approach based on Different of Convex Functions Algorithm (DCA).
This letter studies cooperative secure beamforming for amplify-and-forward (AF) relay networks in the presence of multiple eavesdroppers. Under both total and individual relay power constraints, we propose two schemes, namely secrecy rate maximization (SRM) beamforming and null-space beamforming. In the first scheme, our design problem is based on SRM. Using a suboptimal, but convex, technique-semidefinite relaxation (SDR), we show that this problem can be handled by performing a one-dimensional search which involves solving a sequence of semidefinite programs (SDPs). To reduce the complexity, in the second scheme, we instead maximize the information rate at the destination while completely eliminating the information leakage to all eavesdroppers. We prove that this problem can be exactly solved by SDR with one SDP only. Simulation results demonstrate the performance gains of the two proposed designs.
SUMMARY In this paper, we consider a two‐way relay network consisted of two sources and multiple relays in the presence of an eavesdropper, where the cooperative beamforming strategy is applied to exploit the cooperative diversity to support the secure communication as illustrated in Figure 1. Naturally, we are interested in the beamforming strategy and power allocation to maximize the achievable sum secrecy rate. However, the corresponding problem is equivalent to solve a product of three correlated generalized Rayleigh quotients problem and difficult to solve in general. Because of the openness of wireless medium, the information rate leakage to the eavesdropper cannot be canceled perfectly. To some extent, ‘almost perfect secrecy’, where the rate leakage to the eavesdropper is limited, is more interesting from the practical point of view. In this case, we concern ourself mainly the achievable rate region for general case where the rate at the eavesdropper is regarded as the measurement of secrecy level. Two beamforming approaches, optimal beamforming and null space beamforming, are applied to investigate the achievable rate region with total power constraint and the rate constraint at the eavesdropper, which can be obtained by solving a sequence of the weighted sum inverse‐signal‐to‐noise‐ratio minimization (WSISM) problem. Because of the non‐convexity of WSISM problem, an alternating iteration algorithm is proposed to optimize the relay beamforming vector and two sources' transmit power, where two subproblems need to be solved in each iteration. Meanwhile, we provide the convergence analysis of proposed algorithm. Through the numerical simulations, we verify the effectiveness of proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.
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.