Secure Communication for Two-Way Relay Networks with Imperfect CSI

Cong Sun, Ke Liu, Dahu Zheng, Wenbao Ai
2017 Entropy  
This paper considers a two-way relay network, where two source nodes exchange messages through several relays in the presence of an eavesdropper, and the channel state information (CSI) of the eavesdropper is imperfectly known. The amplify-and-forward relay protocol is used and the relay beamforming weights are designed. The model is built up to minimize the total relay transmit power while guaranteeing the quality of service at users and preventing the eavesdropper from decoding the signals.
more » ... ding the signals. Due to the imperfect CSI, a semi-infinite programming problem is obtained. An algorithm is proposed to solve the problem, and the iterative points are updated through the linesearch technique, where the feasibility are preserved during iterations. The optimality property is analyzed. The obtained subproblems are quadratic constrained quadratic programming problems, either with less than 4 constraints or with only one variable, which are solved optimally. Simulation results demonstrate the importance of the proposed model, and imply that the proposed algorithm is efficient and converges very fast, where more than 85% of the problems are solved optimally. All the aforementioned references suppose that the CSI from users and from relays to eavesdroppers are perfectly known. In fact, it is very difficult to obtain the perfect CSI of the eavesdroppers. Assuming that no CSI of eavesdroppers is known, artificial noise is introduced in the literatures, and enhances security: [14] 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, respectively; [15] sends the artificial noise in the nullspace of the legitimate channel, and compares the cases that all relays are working and that only the best relay is used. In [26] , no CSI of eavesdroppers and imperfect CSI between users and jammers are assumed, and the secrecy performance is analyzed for the cooperative jamming (CJ) technique. Networks with imperfect CSI are often considered, too. The multi-user downlink channel is considered in [27] , where the lower bound of the sum secrecy rate is maximized, and semi-definite relaxation and first order Tailor extension techniques are applied. In [28] , it considers a multiple-antenna AF relay network with partial CSI and bounded error region, and maximizes the worst case secrecy rate, where a rank 2 relay beamformer is constructed via singular value decomposition (SVD). The secure communication switches between the DF relay protocol and the CJ technique in [29] , and the authors provide robust designs for the secrecy rate maximization and secrecy outage probability minimization problems. In [30] , both the source and the relay have multiple antennas, where it jointly designs source and relay beamforming matrices, to minimize the relay power with quality of service (QoS) constraints. The worst case Signal-to-Noise-Ratio (SNR) at the eavesdropper is considered, which is approximated by its upper bound. As listed above, models to design relay beamforming weights with imperfect CSI are usually formulated as semi-infinite programming optimization problems. That is, some constraints should be satisfied with infinite choices of parameters [31] . Almost all the references in the wireless communication literatures deal with such problems by relaxing or tightening the corresponding constraints, so as to eliminate the semi-infinite parts and to solve the approximated problem with classical optimization techniques. This makes the optimization problem much easier. However, the approximation cuts off parts of the feasible region of the original problem, and consequently loses optimality property or even feasibility. This paper also builds up a model with imperfect CSI and formulates a semi-infinite programming problem. But the idea of the propose algorithm is quite different from the usual way, which will be introduced in detail. In this paper, we consider a two-way relay network, with imperfect CSI from user nodes and from relays to the eavesdropper, where the eavesdropper receives signals from both user nodes and relays, and decodes signals combining the two phases. 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 rate of the eavesdropper is upper bounded. Rather than solving an approximated problem directly, we propose an algorithm, to solve the problem iteratively and keep the feasibility during iterations. The optimality property is analyzed. Simulations show that the curves representing the imperfect and perfect CSI models have similar trends. It is also demonstrated that the proposed model is meaningful, and the proposed algorithm is efficient and converges very fast. Numerically more than 85% of the problems are solved optimally. The rest of the paper is organized as follows. The system model of the two-way relay network with one eavesdropper is shown in Section 2. In Section 3, the corresponding optimization problem is summarized and an algorithm is proposed to solve the problem. Simulation results are shown in Section 4. The conclusion is summarized in Section 5. Notations: Uppercase and lowercase bold-faced letters denote matrices and column vectors, respectively. (·) H , (·) T and (·) * represent the Hermitian, transpose and conjugate of a matrix, respectively. · F is the Frobenius norm of a matrix. E(·) is the mathematical expectation of a random variable. Tr(·) represents the trace of a matrix. Re(·) means the real part of a scaler, a vector or a matrix. λ max (·) represents for the largest eigenvalue of a Hermitian matrix. Diag(a) is the diagonal Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 31
doi:10.3390/e19100522 fatcat:ktujsilww5ayrj4euwqspratj4