| In recent years, to improve the quality of communication at a relative low cost,linear precoding/decoding techniques have been applied in the multi-antenna transceiver designs. However, these linear transceiver designs are all based on the perfect channel state information(CSI) assumption. Considering the fact that perfect CSI is difficult to obtain in a practical system due to many factors such as inaccurate estimate, feedback errors and feedback delays, it is necessary to investigate the robust design which takes the CSI errors into account. Robustness refers to the health or fault tolerance of the system. In the wireless communication area, robustness is used to measure the reliability of data transmission in the unexpected cases. In this dissertation, robust transceiver design aims to achieve the optimality of the worst case performance under the imperfect CSI assumption.In the current cellular systems, the joint optimal transceiver is still a challenging problem either for the uplink/downlink system or the multipoint-to-multipoint system. In the literatures, the researchers only focused on the transmitter or receiver design, which cannot fully exploits the advantages of joint transceiver design; or they only proposed suboptimal algorithms with high complexity. To simplify the problem formulation, and to provide insights for the more general system, we discuss the point-to-point multi-antenna system in this paper. By considering the minimum total mean-square error criterion, the joint optimal linear transceiver design is shown to have the channel-diagonalizing structure in chapter 3, which converts the transmission over multi-antenna channels into some interference-free eigenmode subchannels.Based on this property, the original design problem with matrix-valued variables is simplified into a power allocation problem, which can be efficiently solved by its convexity. Simulation results validates the superior performance of the proposed method over the existing method.To further extend the coverage of the wireless communication with lower costs,data transmission in the long distance is completed with the aid of the relays. Considering the per-antenna power constraints, the robust transceiver design becomes more difficult. Even with perfect CSI assumption, the existing work only proposed the alternating optimization methods for the design. In chapter 4, we consider the multi-antenna system with single user and single relay, and derive the optimal joint transceiver design in a semi-closed form. A low-complexity iterative algorithm is also proposed for determining the remaining unknown variable. Finally, the method proposed in this paper is verified to have the same performance but with lower complexity than the existing method.Multiple relays can improve the throughput of the system and also extend the coverage. Especially, for the beamforming case(transmitting single data stream), under the maximum receiver signal-to-noise ratio criterion, it has been proved that the optimal relay processing matrices can be computed in a distributed manner, promoting the use of multiple relays in a practical system. For the single-user multi-antenna multiple relay system, the optimal structure of the relay precoding matrix is derived in Chapter5. In particular, we discover that the robust design and the nonrobust design have the similar structure with different power allocation. Based on this found, the problem for determining the optimal beamforming vector is reformulated as a monotonic optimization problem, and thus can be efficiently solved by the polyblock outer approximation algorithm. Simulation results show that the proposed robust design can significantly reduce the sensitivity of the channel uncertainty to the system performance.In summary, low-complexity algorithms and optimal benchmarks are proposed and closed-form solutions are derived in this paper. Our study not only enriches the state-of-art results of the linear transceiver design, but also provides guidelines for the practical system.
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