6.1 INTRODUCTION

We turn now our attention to closed-loop systems, where the transmitter has some knowledge about the channel. This knowledge, whether partial or complete, can be advantageously exploited to design the transmission strategy in order to optimize the system performance. The idea of using (partial or full) channel knowledge in multiantenna systems to synthesize the radiation pattern accordingly is not novel. That information can be used in fact to steer the antenna beam electronically toward the direction of interest or by nulling the radiation pattern toward some specific directions. This approach is known as beamforming. However, beamforming is only a specific example, as it works only in the space domain and it assumes that the system is either MISO (transmit beamforming) or SIMO (receive beamforming). Improvements with respect to classical beamforming can be achieved by incorporating time as a further independent variable, that is by working in the joint space-time domain, and generalizing the beamforming idea to MIMO systems.

In this chapter, we provide a very general framework for designing the optimal transmission strategy, according to alternative criteria and constraints. In section 6.2 we provide the basic mathematical tools, namely convex optimization and majorization theory. Then, we formulate the optimization problem in a very general framework, in Section 6.3, where we provide alternative solutions. In Section 6.4, 6.5, and 6.6, we specialize the solution to SISO time-varying channels, MISO frequency-selective, and MIMO systems, respectively. We consider the impact of imperfect channel knowledge in Section 6.7. In...