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This paper considers an artificial noise (AN) aided secrecy rate maximization(SRM) problem for a multi-input single-output (MISO) channel overheard bymultiple single-antenna eavesdroppers. We assume that the transmitter hasperfect knowledge about the channel to the desired user but imperfect knowledgeabout the channels to the eavesdroppers. Therefore, the resultant SRM problemis formulated in the way that we maximize the worst-case secrecy rate byjointly designing the signal covariance ${\bf W}$ and the AN covariance ${\bf\Sigma}$. However, such a worst-case SRM problem turns out to be hard tooptimize, since it is nonconvex in ${\bf W}$ and ${\bf \Sigma}$ jointly.Moreover, it falls into the class of semi-infinite optimization problems.Through a careful reformulation, we show that the worst-case SRM problem can behandled by performing a one-dimensional line search in which a sequence ofsemidefinite programs (SDPs) are involved. Moreover, we also show that theoptimal ${\bf W}$ admits a rank-one structure, implying that transmitbeamforming is secrecy rate optimal under the considered scenario. Simulationresults are provided to demonstrate the robustness and effectiveness of theproposed design compared to a non-robust AN design.

A Robust Artificial Noise Aided Transmit Design for Miso Secrecy