Abstract
This paper considers a two-way relay network, where two legitimate users exchange messages through several cooperative relays in the presence of an eavesdropper, and the Channel State Information (CSI) of the eavesdropper is imperfectly known. The Amplify-and-Forward (AF) relay protocol is used. We design the relay beamforming weights to minimize the total relay transmit power, while requiring the Signal-to-Noise-Ratio (SNRs) of the legitimate users to be higher than the given thresholds and the achievable rate of the eavesdropper to be upper-bounded. Due to the imperfect CSI, a robust optimization problem is summarized. A novel iterative algorithm is proposed, where the line search technique is applied, and the feasibility is preserved during iterations. In each iteration, two Quadratically-Constrained Quadratic Programming (QCQP) subproblems and a one-dimensional subproblem are optimally solved. The optimality property of the robust optimization problem is analyzed. Simulation results show that the proposed algorithm performs very close to the non-robust model with perfect CSI, in terms of the obtained relay transmit power; it~achieves higher secrecy rate compared to the existing work. Numerically, the proposed algorithm converges very quickly, and more than 85% of the problems are solved optimally.
Highlights
Due to the openness and the broadcast property of wireless communication, network security becomes a challenging issue
The physical layer security technique becomes appealing, because it guarantees the information being only accessed by the legitimate users rather than eavesdroppers
The main contributions of our paper are listed as follows: 1. A new model to design the relay beamforming weights is proposed with the assumption of imperfect Channel State Information (CSI) and summarized as a robust optimization problem
Summary
Due to the openness and the broadcast property of wireless communication, network security becomes a challenging issue. Assuming that no CSI of eavesdroppers is known, artificial noise is introduced in the literature, and enhances security: Wang et al proposes a cooperative artificial noise transmission-based secrecy strategy and summarizes the relay beamforming design and power allocation problems as second order cone programming and linear programming problems [14], respectively; Salem et al. By designing the relay beamforming weights, we build up the model to minimize the relay transmit power, while the QoS of the legitimate users are guaranteed, and the worst case achievable rate of the eavesdropper is upper bounded. A new model to design the relay beamforming weights is proposed with the assumption of imperfect CSI and summarized as a robust optimization problem. Diag(a) is the diagonal matrix with diagonal entries as the elements of vector a; Diag(A) is the diagonal matrix with the same diagonal entries as matrix A. x ∼ N (μ, σ2 ) represents that the random variable x obeys a Gaussian distribution with the mean as μ and variance as σ2
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