|Ph.D Thesis||Department of Electrical Engineering|
|Supervisors:||Prof. Eldar Yonina|
|Distinguished Prof. Shamai )Shitz( Shlomo|
|Full Thesis text|
We consider the application of modern convex optimization methods in multiple input multiple output communication systems. We apply these methods to receiver and transmitter design and provide efficient numerical solutions as well as insight and structure via Lagrange duality theory. We pay special attention to the availability of channel state information and consider the design problems with and without uncertainty conditions.
The first part of this thesis addresses the design of linear precoders for multiuser systems using multiple antennas. We concentrate on finding simple and efficient methods for maximizing throughput or ensuring fairness among the users, and consider both total power constraints and individual per-antenna power constraints as required in state of the art communication systems. In particular, we begin with the design of precoders based on signal to interference plus noise ratio measures. We transform these problems into standard conic optimization programs, analyze their structure and derive simple methods for finding the optimal solutions based on the Lagrange optimality conditions. As a byproduct, we examine the optimality of the conventional minimum mean squared error precoder. Next, we turn to the design of zero forcing precoders which promise zero interference between users. Here, the conventional approach is to base the precoders on the well known pseudo-inverse. We reformulate the design problem using convex optimization theory and question the optimality of this specific generalized inverse.
A second contribution of this thesis is in understanding multiple input multiple output systems under uncertainty conditions. We consider various uncertainty models and discuss their similarities and differences. The main idea is to compare the use of deterministic unknown parameters with the use of random parameters, i.e., the Bayesian philosophy vs. the deterministic approach. We apply this idea in two applications: transmitter design and estimation theory. Using the power of convex optimization, we define two competing uncertainty models in each of the applications and compare them conceptually and algorithmically.