Matrix-Monotonic Optimization $-$ Part II: Multi-Variable Optimization

In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in paper, we investigate application matrix-monotonic framework multiple variables. It is revealed still works even for matrix-variate based problems, provided certain conditions are satisfied. Using framework, optimal structures variables can be derived and substantially simplified. several specific examples given, which essentially open problems. Firstly, multi-user multiple-input multiple-output (MU- MIMO) uplink communications under various power constraints. proposed precoding matrices at each user constraints derived. Secondly, considered signal compression sensor distributed networks. Finally, transceiver multi-hop amplify-and-forward (AF) MIMO relaying networks imperfect channel state information (CSI) At end simulation results given demonstrate accuracy theoretical results.