During the past decades, there has been an increasing demand of high-rate services to be supported by wireless communications. Among different solutions that have been proposed to meet this demand, the utilization of multiple antennas, which leads to multi-input multi-output (MIMO) transmissions, arises as one of the best candidates. Fundamentally, MIMO channels constitute a unified way to model a wide range of different physical channels, for example wireless multi-antenna channels and wireline Digital Subscriber Line (DSL) channels. The full potential of MIMO channels is achieved by exploring the channel state information (CSI)....[ Read more ]

During the past decades, there has been an increasing demand of high-rate services to be supported by wireless communications. Among different solutions that have been proposed to meet this demand, the utilization of multiple antennas, which leads to multi-input multi-output (MIMO) transmissions, arises as one of the best candidates. Fundamentally, MIMO channels constitute a unified way to model a wide range of different physical channels, for example wireless multi-antenna channels and wireline Digital Subscriber Line (DSL) channels. The full potential of MIMO channels is achieved by exploring the channel state information (CSI).

It is well known that the performance of MIMO systems depends, to a substantial extent, on the quantity and quality of CSI that is available at the communication ends. However, in wireless communications, CSI, especially CSI at the transmitter (CSIT), is seldom perfectly known, due to many issues such as estimation or feedback errors. Therefore, a practical MIMO system must utilize CSI and at the same time has the ability to combat against the imperfectness of CSI, or, in other words, is robust to imperfect CSI. In this thesis, we apply the philosophy of worst-case robustness, which originates from robust optimization in mathematical programming, to designing wireless communication systems, especially MIMO systems.

Firstly, we focus on designing robust transmit strategies for a MIMO link by optimizing the worst-case received signal-to-noise ratio (SNR) or the error probability if a space-time block code (STBC) is used. The attention is not only on finding the numerical solutions to the formulated maximin and quality-of-service (QoS) problems through convex optimization, but also on searching the optimal transmit directions of the robust precoder, which lead to a closed-form solution that provides important insights.

Secondly, we investigate the robustness of beamforming, a simple strategy that transmits data along only one spatial direction. Because of its simplicity, beamforming has been doubted to be sensitive to inaccuracies of CSIT. However, we show, from the perspective of worst-case robustness, that beamforming is actually robust in some sense, and thus has the ability to combat against the imperfectness of CSIT, especially when channel dimensions or channel errors are small.

Thirdly, we design robust precoders for MIMO communication systems with pre-fixed receivers under the minimum mean square error (MMSE) criterion. Different types of CSI are taken into account through either the stochastic model or the deterministic (worst-case) model. Our focus is on the worst-case robust design. The optimal transmit directions are found in all considered situations, hence simplifying the matrix-valued problems to scalar power allocations problems, for which either closed-form solutions or efficient numerical methods are provided.

Finally, we consider a robust design of a cognitive radio (CR) system, consisting of multiple primary users (PUs) and multiple secondary users (SUs) over either (single-input single-output) SISO frequency-selective or MIMO channels, by taking into account the imperfectness of SU-to-PU CSI. The SUs compete over the resource made available by the PUs, forming an ad-hoc network, which is modeled a noncooperative game with robust strategy sets. We study the properties of the Nash equilibrium (NE) of the formulated robust game, and propose distributed and asynchronous algorithms along with their convergence properties to achieve the NE. The robust transmit strategy of each SU is also provided.