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This paper studies different secrecy rate optimization problems for a multiple-input–multiple-output (MIMO) secrecy channel. In particular, we consider a scenario where a communication through a MIMO channel is overheard by a multiple-antenna eavesdropper. In this secrecy network, we first investigate two secrecy rate optimization problems: 1) power minimization and 2) secrecy rate maximization. These optimization problems are not convex due to the nonconvex secrecy rate constraint. However, by approximating this secrecy rate constraint based on Taylor series expansion, we propose iterative algorithms to solve these secrecy rate optimization problems. In addition, we provide the convergence analysis for the proposed algorithms. These iterative optimization approaches are developed under the assumption that the transmitter has perfect channel state information. However, there are practical difficulties in …