Achievable rate region with secrecy constraints for secure communication in two-way relay networks

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 Figure1. 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 (c) 2013 John Wiley & Sons, Ltd.