Optimum Transmit Strategies for Gaussian Multi-user MIMO Systems with Partial CSI and Noisy Channel Estimation
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Multiple antenna wireless communications systems are known to provide very large data rates, when perfect channel state information (CSI) is available at the receiver and the transmitter. Availability of perfect CSI at the receiver requires the receiver to perform a noise-free, multi-dimensional channel estimation, without using communication resources. Similarly, availability of perfect and instantaneous CSI at the transmitter requires a feedback scheme that sends the estimated CSI to the transmitter in its entirety and error-free. However, in practice, any channel estimation is noisy and uses system resources, and any feedback scheme is limited. This thesis is devoted to the study of the effects of noisy channel estimation at the receiver and partial CSI at the transmitters on the optimum transmit strategies for Gaussian multi-input multi-output (MIMO) systems. The main focus of the thesis is on achievable rate maximization problems, solutions of which give the optimum resource allocation and channel estimation schemes for single-user and multi-user MIMO systems. In the first part of the thesis, we focus on the effects of having non-perfect CSI at the transmitter side when the receiver is assumed to estimate the channel perfectly. We consider the capacity of a point-to-point channel and the sum-capacity of a MIMO multiple access channel (MAC). We analyze both the single-user and the multi-user MIMO systems from three different viewpoints. First, we consider a finite-sized system, and find the optimum transmit directions, and optimum power allocations along these directions, as well as beamforming optimality conditions. Second, we analyze the effects of increasing the number of users in the system, and show that the region where beamforming is optimal gets larger with the increasing number of users. Third, we consider the asymptotic case where the number of users is large, and show that beamforming is always optimal. In the second part of the thesis, we consider the effects of channel estimation error at the receiver when partial CSI, in the form of covariance feedback, is available at the transmitter side. We solve the trade-off between estimating the channel better and increasing the achievable data rate. We consider a block fading MIMO channel, where each block is divided into training and data transmission phases. The receiver has a noisy CSI that it obtains through a channel estimation process. In both single-user and multi-user cases, we optimize the achievable rate jointly over the parameters of the training and data transmission phases. In particular, we first choose the training signal to minimize the channel estimation error, and then, we develop an iterative algorithm to solve for the optimum training duration, the optimum allocation of power between training and data transmission phases, and the optimum allocation of power over the antennas during the data transmission phase.