On Duality of MIMO Relays and Performance Limits of Full-Duplex MIMO Radios

In the first part of this thesis, linear transmitters and receivers (i.e., transceivers) are designed for bi-directional and/or relay multiple input multiple output (MIMO) full-duplex (FD) systems. The transmitters and receivers are designed under imperfect channel state information (CSI) and transmitter/receiver impairments at the FD nodes. Different metrics, like ergodic sum-rate maximization, weighted sum-rate maximization, sum mean-squared-error (MSE) minimization and maximum per-node MSE minimization are considered subject to individual and/or total power constraints in the system.;The proposed sum-rate maximization algorithms exploit both spatial and temporal freedoms of the source covariance matrices of the MIMO links between transmitters and receivers to achieve a higher achievable sum-rate. It is observed through simulations that the algorithms reduce to a FD scheme when the nominal self-interference is low, or to a half-duplex (HD) scheme when the nominal self-interference is high.;As for the MSE based transceiver designs, we studied the sum-MSE and Min-Max MSE transceiver design problems for a FD MIMO bi-directional system that suffers from self-interference under the imperfect CSI knowledge and limited dynamic ranges at the transmitters and receivers. Since the globally optimal solution is difficult to obtain due to the non-convex nature of the problems, algorithms that iterate between transmit precoding and receive filtering matrices while keeping the other fixed are proposed. It is shown in simulations that sum-MSE minimization scheme achieves the minimum sum MSE over two FD nodes, and the Min-Max MSE minimization scheme almost achieves the same MSE for the two FD nodes.;In the second part of this thesis, we establish the uplink-downlink duality in terms of signal-to-interference-plus-noise ratio (SINR), MSE, and capacity for uplink and downlink multi-hop amplify-and-forward (AF) MIMO relay channels, which is a generalization of several previously established uplink-downlink duality results. And an interesting perspective to the relation of the uplink-downlink duality based on the Karush-Kuhn-Tucker (KKT) conditions of sum-MSE transceiver optimization problems for uplink and downlink multi-hop AF MIMO relay channels is provided.