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For a multiple antenna Gaussian broadcast channel, we look for inputs that facilitate secret transmission between authorized communication parties in the presence of passive eavesdroppers. In this work, we assume all channel information is known at the transmitter. For the general multiple antenna system, we find that the problem of optimizing over Gaussian inputs for achievable secrecy rate is not convex, making it difficult to solve. However, for the simpler case where multiple transmit antennas are deployed with only a single receive antenna used at both the intended receiver and the eavesdropper, the problem can be solved easily. The analytical solution for this case is presented.
Zang et al. (Thu,) studied this question.