Up to this point in the book, we have assumed that the receiver (and the transmitter in the case of eigenbeamforming) have perfect knowledge of the channel matrix. The theoretical performance results we have shown thus far have been based on that assumption. In practice, of course, the channel matrix must be estimated, and there is always some error associated with knowledge of the channel. This chapter introduces the basic concepts associated with channel estimation (CE) and presents results that illustrate how MIMO performance is affected by channel estimation errors.

Introduction

In general, there are two types of MIMO channel estimation methods: a) training-based, which uses known training symbols; and b) blind-based approaches, that perform CE without the benefit of known training symbols. In training-based CE, known training symbols are transmitted at certain prescribed times and frequencies that are known by the receiver. Since the receiver knows the training symbols, as well as when and where (i.e., at which frequencies) they are transmitted, it uses that information to estimate the gain and phase rotation imparted by the channel at each point in time and frequency based on the characteristics of the received training symbols. Although blind-based methods have higher bandwidth efficiencies because they do not use any resources for transmitting training symbols, they tend to have lower speed and poorer performance than training-based methods. For this reason, training-based CE is used more than blind-estimation, and it is the method we focus on in this chapter.

In this chapter, we turn our attention to the second major class of MIMO processing techniques: spatial multiplexing. As we discussed in Chapter 1, spatial multiplexing refers to transmitting multiple independent data streams over multipath channels, without the need to increase the bandwidth. Unlike space-time coding, which is used to achieve spatial diversity and which transmits at most one modulation symbol per modulation symbol period (i.e., rs ≤ 1), spatial multiplexing techniques are capable of achieving spatial rates equal to min {Nt,Nr}; that is, rather than only transmitting one or fewer modulation symbols per symbol period, spatial multiplexing involves transmitting up to min{Nt, Nr} modulation symbols per symbol period, resulting in a concomitant increase in throughput relative to spatial diversity schemes. This improvement in throughput, however, is achieved at the expense of diversity gain, so the diversity gains associated with spatial multiplexing methods are normally significantly less than NtNr. This chapter describes several fundamental, practical techniques that are used to achieve spatial multiplexing.

The chapter is divided into four sections. The first section presents an overview of spatial multiplexing concepts and reviews the major types of spatial multiplexing methods that have been proposed. The second section describes the transmit architectures associated with the class of SM schemes known as BLAST. Section 3 describes four spatial demultiplexing methods that can be used with H-BLAST and V-BLAST.

This book is an outgrowth of a graduate course I have taught for the past four years on MIMO Wireless Communications in the Engineering for Professionals (EP) Program within the Whiting School of Engineering at The Johns Hopkins University. When I began to develop the course in the spring of 2006, I initially thought I would simply choose a textbook from the collection of numerous books that had been written on MIMO communications at that time. As I began studying these books, however, I found that, although they were each excellent in various ways, none of them was as accessible to the average practicing communications engineer or early level electrical engineering graduate student as I had hoped. Many of these books were written by experts in the field, researchers who had made seminal contributions in the area of MIMO communications, but the prerequisites needed to follow and understand the details in their presentations were often above the level of expertise of those being introduced to MIMO for the first time.

This book is my attempt to remedy this problem. In developing the course and in writing this book, I have tried to make the concepts and techniques associated with MIMO communications accessible to an average communications engineer with an undergraduate degree in electrical engineering. I assume that readers are familiar with digital communication techniques and that they have had a formal course (or its equivalent) in digital signal processing; however, I do not assume readers are familiar with information theory or are proficient in advanced matrix mathematics, areas of expertise that are normally assumed in the MIMO literature and in many of the books that have been published on this topic. When knowledge in these areas is required to understand MIMO concepts, I have attempted to include the necessary information on those topics in the book so that it is not necessary to consult external resources. In this sense, the book has been designed to be as self-contained as possible.

Now that the basic concepts of MIMO communications have been introduced, we conclude the book with a chapter that describes how those concepts are applied in real-world wireless communications systems. For this purpose, we focus on two popular wireless families of standards, WiFi and LTE/LTE-advanced, which are used extensively for wireless LAN applications and conventional cellular communications, respectively. Although these communication standards are extremely complex, we focus primarily on the MIMO aspects of these technologies.

WiFi

WiFi is a virtually ubiquitous wireless technology that is designed to allow electronic devices to exchange data wirelessly at rates ranging from 1 Mbps to as much as 600 Mbps over distances of typically 10s to 100s of feet. The most common application of WiFi technology today is the use of wireless routers in homes and businesses for the purpose of enabling computers, cellular phones, and a growing list of personal wireless devices to connect to the Internet without cables. The version of WiFi that employs MIMO is defined by the IEEE 802.11 n standard, which is the latest in a series of amendments to the original 802.11 standard that was developed in the late 1990s. The current version of the 802.11n standard at the time of this writing is called IEEE 802.11n-2009, which was published in October 2009. The information in this section is primarily gleaned from that standard [77].

In the previous chapter, we considered Alamouti space-time coding, which enables transmit diversity with optimum performance. As we saw, although Alamouti coding works with any number of receive antennas, it is restricted to cases where there are only two transmit antennas. In this chapter, we broaden our discussion and consider space-time codes that support more than two transmitters.

Since Alamouti's code was introduced in 1998, much research has been conducted in the area of space-time coding for MIMO applications, and space-time coding is now a broad field encompassing many different types of coding schemes. Space-time codes fall into one of two primary classes: space-time block codes (STBCs) and space-time trellis codes (STTCs). STBCs, in turn, fall into two subclasses called orthogonal space-time block codes (OSTBCs) and non-orthogonal space-time block codes (NOSTBCs). In this chapter we focus on OSTBCs because they have simple decoding schemes and are used in practical wireless systems.

The chapter begins with a general discussion of space-time coding concepts and terminology, followed by a section that derives criteria for designing space-time codes. Next, we describe OSTBCs in detail and describe how to decode them. After that, we include a brief section on NOSTBCs, listing some specific ones that have been proposed and giving references for further reading. We conclude the chapter with a section on STTCs.

In the previous chapters we examined some of the implications of the MIMO capacity formula. As we have seen, the statistics of the MIMO capacity are dependent on the statistics of the channel matrix and the average signal-to-noise ratio at the receiver, which we denote by ρ. Both the statistics of H and the value of ρ depend on the propagation characteristics of the channel; thus, an understanding of propagation is important in order to predict and understand the performance of MIMO communication systems. Because MIMO techniques are designed to operate in a scattering environment, we focus on channel phenomena that give rise to scattering and multipath. Without scattering and multipath, the channels between the various combinations of transmit and receive antennas are correlated, which results in poor MIMO performance. In this chapter, the fundamental concepts and terminology of multipath propagation are reviewed.

Phenomenology of multipath channels

In any wireless communications path between a transmitter and a receiver, signals arrive at the receiver through various propagation mechanisms. In general, RF energy propagates between two points in one of two ways: directly or indirectly. Direct propagation refers to transmission of RF energy along a direct path between the transmitter and the receiver that does not involve any reflections, scattering, ducting, or diffractive bending. Direct propagation is called free space propagation and is said to undergo free space attenuation. Indirect propagation, in contrast, involves any one or a combination of the following: reflection, diffraction, scattering, or refraction.

This chapter lays the foundations for the remainder of the book by presenting an overview of MIMO communications. Fundamental concepts and key terminology are introduced, and a summary of important matrix properties is provided, which will be referred to throughout the book. Some experimental results showing the benefits of MIMO are also presented.

What is MIMO?

Multiple Input Multiple Output communications, abbreviated MIMO,and normally pronounced like “My-Moe,” refers to a collection of signal processing techniques that have been developed to enhance the performance of wireless communication systems using multiple antennas at the transmitter, receiver, or both. MIMO techniques improve communications performance by either combating or exploiting multipath scattering in the communications channel between a transmitter and receiver. MIMO techniques in the first category combat multipath by creating what is called spatial diversity, and those techniques that exploit multipath do so by performing spatial multiplexing. These two concepts are introduced in this chapter, and we will have much more to say about them throughout the remainder of the book. The subject of MIMO communications is the study of spatial diversity and spatial multiplexing techniques.

Figures 1.1 and 1.2 show block diagrams of generic MIMO communication systems. As indicated, the characteristics of the system depend on whether the focus of the MIMO processing is on creating spatial diversity, which improves reliability by combating fading, or if the purpose is to maximize throughput by performing spatial multiplexing.

This chapter describes the Alamouti space-time coding scheme [6] for achieving transmit diversity. As discussed in Chapter 1, Alamouti coding was one of the first space-time codes to be developed, and it is now included in the definition of all modern wireless standards that employ MIMO techniques. Although other transmit diversity techniques were proposed in the 1990s prior to Alamouti's seminal paper (e.g. see [81], [82], and [79]), Alamouti's technique has the following advantages over alternative schemes: a) it requires CSIR only (as opposed to requiring both CSIT and CSIR); b) it does not involve any bandwidth expansion, which some of the competing techniques do; and c) Alamouti coding has relatively low computational complexity due to the fact that its decoding rules are quite simple.

Prior to the development of transmit diversity techniques in the 1990s, of which Alamouti coding is the most famous example, diversity benefits in fading environments were achieved using receive diversity only. In cellular applications, this meant that it was only possible to perform diversity combining at the base station because of the impracticality (due to lack of physical space and battery power limitations) of having multiple antennas on small hand-held devices. Therefore, prior to the development of space-time coding, which made transmit diversity possible, diversity gains were only available on the reverse links of cellular systems.

In 1948 Claude Shannon published his famous paper titled “A mathematical theory of communications,” which was published in the July and October 1948 issues of the Bell Technical Journal [65, 66]. In that paper, he presented the fundamental concepts of what would later become the field of information theory, and derived mathematical expressions for the maximum theoretical data rate that could be transmitted over a communication system without errors. This maximum data rate, called the communications capacity, was derived for a conventional SISO system; however, the concepts he introduced in his landmark paper provided the framework for generalizing to MIMO systems. In 1999 Emre Telatar derived an expression for the theoretical capacity of a MIMO system using the concepts from information theory first developed by Shannon half a century earlier [70]. This chapter derives the MIMO capacity formula based on Telatar's arguments. The expression we develop in this chapter will be used to quantify the throughput enhancement that is possible with spatial multiplexing, as well as to provide a useful way of conceptualizing how MIMO systems work.

What is information?

In its most fundamental sense, the capacity of a communication system is defined as the maximum amount of information that can be conveyed per unit of time between two points over a communications channel. I assume that readers are familiar with digital communication techniques and that they have had a formal course (or its equivalent) in digital signal processing; however, I do not assume readers are familiar with information theory or are proficient in advanced matrix mathematics, areas of expertise that are normally assumed in the MIMO literature and in many of the books that have been published on this topic. When knowledge in these areas is required to understand MIMO concepts, I have attempted to include the necessary information on those topics in the book so that it is not necessary to consult external resources. In this sense, the book has been designed to be as self-contained as possible.

A common assumption in MIMO analyses is that the channel matrix consists of independent identically distributed complex Gaussian gains (i.e., H = Hw). In the real world, however, this is not always the case. In particular, correlation between the received or emitted signals to or from antenna pairs, or the existence of a direct LOS component in the signal at each receive antenna causes H ≠ Hw. In this chapter, we introduce several analytical models for H that incorporate the effects of antenna correlation and the impact of LOS propagation. These models often appear in the MIMO literature and provide a convenient means to compute the impact of antenna correlation and Rician fading (as opposed to pure Rayleigh fading) on the capacity of a MIMO system.

MIMO channels in LOS geometry

We begin this chapter by considering the case where the transmit and receive antenna arrays are within line-of-sight of each other and there is no scattering in the channel, as illustrated in Figure 5.1. Under this assumption, we seek a mathematical expression for H and a criterion that assures a high MIMO capacity, despite the fact that scattering is normally assumed to be required to support spatial multiplexing.