A robust and distributed design for coordinated downlink beamforming for secure MISO interference channels

In this paper, we address the optimization problems of downlink coordinated beamforming over the K-user multiple-input single-output interference channel with confidential messages. Our design objective is to minimise the total transmit power subject to the constraints of individual signal-to-interference plus noise ratio and equivocation rates. For the case with perfect channel state information (CSI), by deriving the equivalent forms for the signal-to-interference plus noise ratio and the secrecy constraints, the optimization problem is reformulated as a second-order cone programme problem. Then, an optimal distributed algorithm using the partial Lagrangian duality is discussed. In addition we extend the analysis to the imperfect CSI scenario with bounded ellipsoidal errors, the centralised algorithm has been proposed by solving a semi-definite programme with the help of rank relaxation, whereas the distributed robust algorithm is devised by using ADMM. Finally, the simulation results have shown that with perfect CSI, the centralised and distributed algorithms have nearly the same performance, but in the case of imperfect CSI, the centralised algorithm shows a slightly better performance.