TABLE OF CONTENTS In this chapter we describe the fundamental performance limits of MIMO wireless systems. We assume that there is no feedback from the receiver to the transmitter so that the transmitter does not have any knowledge about the channel. We denote this kind of system as an open-loop system to distinguish it from closed-loop systems, where there is some kind of feedback, from the receive to the transmit side, that allows the transmitter to acquire knowledge about the channel. This knowledge can be properly exploited to optimize the transmission strategy. Closed-loop systems will be the subject of chapter 6.
Open loops are commonly found in wireless communication systems, where the channel fluctuations make complicated the knowledge (prediction) of the channel at the transmit side. Furthermore, in broadcast systems, where the transmitter sends data to several receivers simultaneously, it does not even make sense to optimize the transmission strategy with respect to a specific channel. We start by reviewing the statistical properties of random matrices, as they have a straightforward impact on the performance of random channels. Then, we will introduce the fundamental performance parameters, in a very general setup. After reviewing the basic properties of SISO systems, we will study in detail the diversity gain and the rate gain of MIMO systems. For most of the chapter, we will assume that the transmitter has no knowledge about the channel but that the receiver knows the channel perfectly. In the last section, we will relax this assumption, reviewing...
