MIMO Wireless Communications: From Real-World Propagation to Space-Time Code Design

Chapter 6: Error Probability in Real-World MIMO Channels

Overview

Chapter 5 has dealt with the design of space-time codes in i.i.d. Rayleigh fading channels. However, as highlighted in Chapters 2 and 3, real-world channels span a large variety of propagation conditions and some environments may highly deviate from the i.i.d. Rayleigh fading scenario. It is thus of great importance to understand

  • how codes developed under the i.i.d. Rayleigh assumption behave in more realistic propagation conditions, i.e. how these codes are affected by non-ideal propagation conditions

  • how a more adapted design criterion might significantly improve their performance.

In Section 6.1, we start from a physical perspective to understand how the channel scattering richness at the transmitter affects the performance of space-time codes. Through the application of intuitive concepts, we point out the problems faced by classical designs. These concepts are then formalized in Sections 6.2 to 6.5 corresponding to various realistic fading channels. Finally, Section 6.6 summarizes the important ideas of this chapter, which form the basis for developing the design criteria of Chapter 7.

6.1 A Conditional Pairwise Error Probability Approach

6.1.1 Degenerate Channels

On the one hand, we know from (5.3) in Chapter 5 that the conditional pairwise error probability (PEP) is a function of

(6.1)

On the other hand, the conditional channel energy is a function of

(6.2)

In order to understand how propagation mechanisms affect the performance of space-time coding, let us get some insight into how (6.1) and (6.2) behave as a function of the scattering richness around the transmitter. As noted in...

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