Algorithms for Secrecy Guarantee With Null Space Beamforming in Two-Way Relay Networks

• Published in: IEEE transactions on signal processing Vol. 62; no. 8; pp. 2111 - 2126
• Main Authors: Yang, Yunchuan, Sun, Cong, Zhao, Hui, Long, Hang, Wang, Wenbo
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 15.04.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Array signal processing; Beamforming; Detection, estimation, filtering, equalization, prediction; Equivalence; Exact sciences and technology; Information, signal and communications theory; Linear programming; Mathematical analysis; Null space; Null space beamforming; physical layer security; Quadratic programming; Relay; Relay networks; Relays; Searching; semi-definite programming; sequential quadratic programming; Signal and communications theory; Signal processing algorithms; Signal, noise; Telecommunications and information theory; Vectors; Vectors (mathematics); Wireless communication; Relaying; Relay; Relay network; Cooperative systems; Equity; semi-definite programming; Iterative method; Quadratic programming; Beam forming; Search algorithm; Null space beamforming; Simulation; Sequential method; Signal processing; Safety; physical layer security; sequential quadratic programming; Newton method; Secrecy
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2303942

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.