Multiple-Input Multiple-Output Channel Models: Theory and Practice

2

MULTIPLE ANTENNA CHANNELS AND CORRELATION

In this chapter, we define the terms wideband and MIMO channel. Here, we summarize several different classes of channels, starting with the narrowband SISO channel and leading to the wideband MIMO channel. We also define correlation in a multi-antenna channel. We discuss the H-tensor, which is an elegant way of representing the channel gains in a wideband MIMO channel. Characterizing the wideband MIMO channel as a third-order tensor is a small but significant step; we use tensor calculus to compute the correlation between paths in the wideband MIMO channel. The correlation is expressed as a sixth-order wideband correlation tensor. Expressing the channel correlation using tensor calculus maintains more of the channel structure.

In Appendix A, we provide a brief introduction to tensor calculus. We also introduce notation that is used throughout the rest of the text. Whereas it is not necessary to have a complete understanding of tensor calculus, it is important to be familiar with the notation and operations covered in Appendix A to appreciate the following discussion.

2.1 THE RADIO CHANNEL: DEFINITIONS

2.1.1 The Physical Channel

Communication systems are designed to convey information from a transmitter, across a channel, to a receiver. There are many possible physical channels. Some examples include an air interface, a coaxial cable, a telephone twisted pair, an optical cable, a waveguide, and so forth. In the following, we are concerned ...