LAUSR

This article studies robust artificial noise-aided beamforming for correlated multiple-input-single-output eavesdropping channels under Gaussian channel uncertainties. In the case of high reception correlation, under a secrecy outage probability constraint, the achievable secrecy rate is very small and does not satisfy the requirements of some high-rate applications. In view of this, optimization designs on the premise of quality-of-service (QoS) assurance are considered. By exploiting the correlation and employing a novel QoS criterion of the signal-to-noise ratio (SNR) outage probability, two optimization problems, namely minimization of the target SNR at eavesdroppers and maximization of the loose secrecy rate, are formulated. Despite less rigorous secrecy, a much lower target SNR at eavesdroppers and a higher loose secrecy rate are achieved. Compared with the conventional SNR-QoS, SNR-outage-QoS is a more flexible criterion that can be applied to Gaussian channel uncertainties, although challenging probabilistic constraints are introduced into the optimization problems. To make the optimization problems feasible, two approaches, namely, the Bernstein-type inequality approach and ellipsoid bounding approach, are applied to approximate the probabilistic constraints. Simulation results show that the robust transmit designs contribute to a secrecy performance gain from the perspective of SNR-outage-QoS.