Efficient algorithms for physical layer security in one-way relay systems

In this paper, we solve two problems aiming at improving the secure communications in a one-way relay system. The system under consideration consists of one source, one destination, N cooperative relays that use amplify and forward, and one eavesdropper. First, we minimize the relays power under information rate constraints for both the legitimate destination and the eavesdropper. When the source power is given, the problem is formulated as a non-convex quadratically constraint quadratic programming, which can be solved using a semidefinite programming (SDP). However, since SDP suffers from high complexity, we propose a novel approach, using generalized eigenvalue, that provides a closed form of the optimal solution in most cases. Then we prove that the relays power can be further decreased as the source power increases. Second, we solve the problem of maximizing the secrecy rate by looking for the optimal relays beamforming vector. We show that the optimization problem of the beamforming vector is a product of two correlated generalized Rayleigh quotients. For this problem, we show that the optimal beamforming vector can be obtained using a series of SDPs, then we significantly simplify the problem by solving it using a series of eigenvalue problem. Numerical results show that the proposed approaches achieve the optimal solution of the relay beamforming vector and enhance the physical layer security with power allocation.