Secure transmission for wireless collaborative systems based on second-order channel statistics

In this article, we investigate the maximum secrecy rates (SRs) and the optimal beamforming schemes for a collaborative wireless network under uncertain channel levels of available second-order statistics. Both decode-and-forward (DF) and amplify-and-forward (AF) strategies under the aggregate and individual power constraints are considered. We have derived the maximum SRs and the optimal beamforming vectors under aforementioned conditions and an efficient cooperation paradigm to provide secrecy in a multirelay environment. A closed-form maximum SR in the DF scheme under aggregate power constraint is presented. Next, the upper and lower bounds for the maximum SR under aggregate power constraint in the AF scheme is derived. The optimization problem in the AF scheme can be converted into a convex semidefinite programming problem, which is efficiently solved by the bisection method. Moreover, the optimal beamforming weights are also obtained to maximize the SRs under both aggregate and individual relay power constraints. Numerical results are provided to demonstrate the effectiveness of proposed algorithms.