Unified Overview of Matrix-Monotonic Optimization for MIMO Transceivers
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Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrix-variate optimization problems. Based on the optimal structures derived, the associated optimization problems can be substantially simplified and underlying physical insights can also be revealed. In this paper, a comprehensive overview of the applications of matrix-monotonic optimization to multiple-input multiple-output (MIMO) transceiver design is provided under various power constraints, and matrix-monotonic optimization is investigated for various types of channel state information (CSI) condition. Specifically, three cases are investigated: 1) both the transmitter and receiver have imperfect CSI; 2) perfect CSI is available at the receiver but the transmitter has no CSI; 3) perfect CSI is available at the receiver but the channel estimation error at the transmitter is norm-bounded. In all three cases, the matrix-monotonic optimization framework can be used for deriving the optimal structures of the optimal matrix variables. Furthermore, based on the proposed framework, three specific applications are given under three types of power constraints. The first is transceiver optimization for the multi-user MIMO uplink, the second is signal compression in distributed sensor networks, and the third is robust transceiver optimization of multi-hop amplify-and-forward cooperative networks.
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