Fundamental capacity limits of multiple antenna wireless systems

Multiple input multiple output (MIMO) systems using multiple transmit and receive antennas are widely recognized as the vital breakthrough that will allow future wireless systems to achieve higher data rates with limited bandwidth and power resources. However, the capacity benefits of MIMO systems depend strongly on how well the channel can be tracked at the transmitter and the receiver; whether the fades associated with different transmit and receive antennas are correlated; whether the channel is a point-to-point channel or a multi-user channel. This thesis presents the progress we have made towards determining the capacity benefits of multiple antennas under different assumptions about the underlying channel and what is known about this channel at the transmitters and receivers.; The thesis contains five main results. First, for a single user MIMO channel with perfect channel knowledge at the receiver and a knowledge of only the channel mean or correlations at the transmitter we characterize the optimal input strategy and find a necessary and sufficient condition under which capacity can be achieved with beamforming, i.e., using the well developed scalar codec technology. Second, we show that with only the knowledge of spatial correlations at both the transmitter and the receiver and a T symbol block fading model, adding correlated transmit antennas increases the capacity and the capacity is only a function of the T largest eigenvalues of the transmit fade covariance matrix. Third, for the multiuser broadcast channel we propose an outer bound for the general broadcast channel (BC) that is shown to be achievable with dirty paper coding for the multiantenna Gaussian BC if Gaussian codebooks are assumed, leading to the conjecture that the dirty paper coding achievable rate region is the capacity region of the non-degraded MIMO BC. We also propose two algorithms to compute the sum capacity of the MIMO BC and extend the results to the cellular downlink. Fourth, we determine an upperbound on the capacity region of a vector fading broadcast channel in terms of the capacity region of a scalar vector fading broadcast channel when the channel is unknown to the transmitter and known perfectly to the receiver and prove that the bound is tight for many interesting cases including some non-degraded broadcast channels. Fifth, we apply the Kailath-Schalkwijk coding scheme to determine the previously unknown feedback capacity region of the two user vector Gaussian MAC with multiple receive antennas at the base station and a single transmit antenna at each user.