Optimal transmit design for miso secrecy-rate maximization with general covariance constraints

The notion of providing secure communication via physical-layer designs has gained much attention in recent studies. This paper considers the transmit covariance design for a generalized secrecy rate maximization (SRM) problem under the scenario of a multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. This generalized SRM design encompasses various existing SRM designs, e.g., the per-antenna power constrained design and the interference temperature constrained design. While the considered generalized SRM problem is nonconvex by nature, this paper shows that the problem can actually be solved in a convex fashion, by recasting the generalized SRM problem as a semidefinite program (SDP). The development of the solution to the generalized SRM shows that transmit beamforming is generally an optimal transmit strategy. Simulation results are also provided to demonstrate the secrecy-rate performance gains of the proposed algorithm over some closed-form, but suboptimal algorithms.