Unified approach for optimisation of single user and multi-user multiple input multiple output wireless systems

Multiple-input multiple-output (MIMO) systems will be applied in wireless communications in order to increase the performance, spectral efficiency, and reliability. Theoretically, the channel capacity of those systems grows linearly with the number of transmit and receive antennas. An important performance metric beneath capacity is the normalised mean square error (MSE) under the assumption of optimal linear reception. Clearly, both performance measures depend on the properties of the MIMO channel as well as on the considered system approach, e.g. on the type of channel state information which is available at the transmitter. It has been shown that even partial CSI at the transmitter can increase the performance. In this thesis, we analyse the performance and design optimal transmit strategies of single- and multiuser MIMO systems with respect to the statistical properties of the fading channel and under different types of CSI at the transmit side. In the single-user scenario, we study the average performance of the system under spatial correlated fading and with different types of CSI at the transmitter and with perfect CSI at the receiver. First, we introduce a measure of correlation which is based on Majorization. As a result, the average performance is analysed as a function of correlation in the context of Schur-convexity and Schur-concavity. Furthermore, we observe that the performance metrics belong to a general class of functions which are the trace of a matrix-monotone function. We use Löwner's representation of operator monotone functions in order to derive the optimum transmission strategies and to characterise the impact of correlation on the average performance. The optimal transmit strategy without CSI at transmitter is equal power allocation. We prove this result for spatial correlated channels by analysing the most robust transmit strategy under worst case correlation. The average performance without CSI is a Schur-concave function with respect to transmit and receive correlation. In addition to this, we derive the optimal transmission strategy with long-term statistics knowledge at the transmitter and propose an iterative algorithm. The beamforming-range is the SNR range in which only one data stream spatially multiplexed achieves the maximum average performance. This range is important, because of its simple receiver structure and well known channel coding. Finally, we derive the generalised water-filling transmit strategy for perfect CSI and characterise its properties. If the single-user MIMO link is placed into a cellular system in which multiple users at the same time on the same frequency access one common base station or in which one base station transmits to multiple users, the interference colours the noise. This means, we can continue to study a single-user link now with coloured noise as a first approach. In order to gain insights into the performance under interference conditions, we derive the worst case noise performance for three different noise scenarios. We show that the cooperation and the CSI at the transmitter get lost if some type of worst case noise is applied. If all transmit strategies of all participating users are incooperated into the analysis, we arrive at the multi-user MIMO system. Finally, we maximise the instantaneous sum performance of MIMO multiple access channels (MAC) or broadcast channels (BC) under individual or sum power constraints. The sum performance is either the sum capacity if SIC is applied in the uplink or if Costa Precoding is applied in the downlink, or the normalised sum MSE if a multiuser MMSE receiver is applied at the base. Using the Karush-Kuhn-Tucker optimality conditions, we show that the mutual covariance matrix optimisation can be decomposed into power allocation and covariance matrix optimisation under individual power constraints, which can be decomposed into a kind of modified single-user covariance matrix optimisation treating the other users as noise. The concrete structure of the single-user program depends on the performance metric. The proposed algorithms efficiently solve the multi-user MIMO sum performance optimisation problem