An optimization approach to signalling strategies in MIMO and CDMA fading channels

In the first part of this thesis, we consider the problem of finding the sum capacity of a wireless CDMA channel. The optimal spreading sequences that achieve sum capacity in a Gaussian CDMA channel are well-known for fading chanels. We thoroughly analyze the optimization problem and support with simulations the conjecture that generalized WBE sequences are the optimal spreading sequences in achieving sum capacity in a frequency non-selective (flat fading) multiple access channel. We also consider the problem of maximizing mutual information and hence the data rates in a multi-input multi-output(MIMO) fading channel for general fading distributions under rank constraint on the input covariance. Such a problem formulation enables us to find optimal low-rank signalling strategies (like beamforming schemes with a covariance of rank one). The natural equivalence of the two above-mentioned optimization problems is also established.; The second part of the thesis concerns space-time code design for the so-called UIU MIMO channel model. Our approach will be to leverage existing high performance space-time codes for the spatially i.i.d channel, through suitable precoding and power allocation. We show that asymptotically with high SNR the power allocated to each antenna is directly proportional to the number of non-zero channel channel gains that exist from each transmit antenna to the receiver. The optimal power allocation strategy is shown, in general, to be the solution of a convex optimization problem.