Optimal Power Allocation for Joint Beamforming and Artificial Noise Design in Secure Wireless Communications

This paper studies the secure communication between a multiple-antenna transmitter (Alice) and a single-antenna destination (Bob) in the presence of more than one eavesdroppers (Eves). The optimal beamforming weights and the covariance matrix of artificial noise (AN) are obtained by minimizing the total transmission power of Alice, subject to a target secrecy rate constraint for Bob. We propose a two-level optimization method, where the inner-level optimization is solved by an interesting semidefinite relaxation method of W. C. Liao et al., and the outer-level optimization is solved by the golden section method. Our algorithm converges quite fast. Some properties of the optimal solution are also provided to illustrate the features of this problem.