In recent years there has been growing interest in study of multi-antennatransmit designs for providing secure communication over the physical layer.This paper considers the scenario of an intended multi-input single-outputchannel overheard by multiple multi-antenna eavesdroppers. Specifically, weaddress the transmit covariance optimization for secrecy-rate maximization(SRM) of that scenario. The challenge of this problem is that it is a nonconvexoptimization problem. This paper shows that the SRM problem can actually besolved in a convex and tractable fashion, by recasting the SRM problem as asemidefinite program (SDP). The SRM problem we solve is under the premise ofperfect channel state information (CSI). This paper also deals with theimperfect CSI case. We consider a worst-case robust SRM formulation underspherical CSI uncertainties, and we develop an optimal solution to it, againvia SDP. Moreover, our analysis reveals that transmit beamforming is generallythe optimal transmit strategy for SRM of the considered scenario, for both theperfect and imperfect CSI cases. Simulation results are provided to illustratethe secrecy-rate performance gains of the proposed SDP solutions compared tosome suboptimal transmit designs.
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