Joint transmit beamforming and artificial noise design for QoS discrimination inwireless downlink

This paper considers a downlink wireless system where a multiple-antenna transmitter (Alice) aims to discriminate the reception performances between a legitimate receiver (Bob) and a set of unauthorized receivers (Eves). To this end, there has been great interest in the use of artificial noise (AN) together with transmit beamforming in order to effectively interfere Eves´ reception. However, most of the existing works do not optimize the AN but simply allocate it in the left null space of the Alice-to-Bob channel. In the paper, we propose to jointly optimize the beamforming vector and the AN covariance matrix by minimizing the total transmit power subject to a target signal-to-interference-plus-noise ratio (SINR) constraint on Bob and limited SINR constraints on all Eves. While the considered beamforming problem is not convex and may be difficult to solve in general, it can be effectively handled by a convex approximation method called semidefinite program (SDP) relaxation. In addition to showing how SDP relaxation can be applied to this problem, we prove using the KKT optimality that SDP relaxation provides a global optimum solution of the proposed beamforming problem when Alice has perfect information of the channel from Alice to Bob. Simulation results are presented to demonstrate the effectiveness of the proposed beamforming method.