Matrix-Monotonic Optimization $-$ Part I: Single-Variable Optimization

Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for matrix variables matrix-variable problems. Based on derived, associated problems can be substantially simplified and underlying physical insights also revealed. In our work, a comprehensive framework applications matrix-monotonic multiple-input multiple-output (MIMO) transceiver design is provided series specific performance metrics under various linear constraints. This consists two parts, i.e., Part-I single-variable Part-II multi-variable optimization. this paper, investigated power constraints types channel state information (CSI) condition. Specifically, three cases are investigated: 1) both transmitter receiver have imperfect CSI; 2) perfect CSI available at but has no 3) estimation error norm-bounded. all cases, used deriving variables.