In this paper we consider the robust secure beamformer design for MISO wiretap channels. Assume that the eavesdroppers' channels are only partially available at the transmitter, we seek to maximize the secrecy rate under the transmit power and secrecy rate outage probability constraint. The outage probability constraint requires that the secrecy rate exceeds certain threshold with high probability.Therefore including such constraint in the design naturally ensures the desired robustness. Unfortunately, the presence of the probabilistic constraints makes the problem non-convex and hence difficult to solve.In this paper, we investigate the outage probability constrained secrecy rate maximization problem using a novel two-step approach. Under a wide range of uncertainty models, our developed algorithms can obtain high-quality solutions, sometimes even exact global solutions, for the robust secure beamformer design problem. Simulation results are presented to verify the effectiveness and robustness of the proposed algorithms. DRAFT Recently, considerable research has investigated optimization algorithms for improving secrecy rate in wiretap channels with multiple antennas [5]- [11].There are roughly two approaches for designing transmission schemes in the presence of multiple transmit antennas: 1) single-stream transmit beamforming, in which the transmit signal is steered towards the legitimate receiver, while the power leakage to the eavesdroppers is reduced at the same time; 2) joint beamforming and artificial noise (AN) generation, in which the transmit power is split into a data stream and an AN [12]- [15]. The AN is used to generate interference DRAFT
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