Introduction

Following the initial assignment of spectrum rights and obligations to users, whether by auction or other means, circumstances may change causing initial licence holders to want to trade their rights and obligations with others. Today this is not possible in many countries. However, in a few countries secondary trading – the trading of spectrum rights after the primary assignment – is possible. The possibility to trade radio spectrum is argued by many commentators to be a critical factor in the promotion of more efficient radio spectrum use. Furthermore, it is increasingly recognised that the flexibility afforded by trading is helpful for innovation and competitiveness.

Spectrum trading is a powerful way of allowing market forces to manage the assignment of radio spectrum rights and associated obligations and it is a significant step towards a market-based spectrum management regime. The trading of radio spectrum rights has been discussed as a policy option for many years and dates back to the seminal contribution of Coase [1]. It is widely accepted by economists and increasingly by spectrum policy makers that appropriately supervised market forces can be superior to the widely used but more inflexible command-and-control methods.

Trading of spectrum is made much more powerful when it is combined with policies aimed at promoting liberalisation in use; that is allowing users to choose the use to which a frequency band is put – subject perhaps to some constraints regarding the interference that can be caused (see Chapter 7).

Introduction

This chapter starts by considering whether market mechanisms could be used to determine the appropriate amount of spectrum commons. It then addresses two possible approaches that the regulator might use to make this decision, namely (1) the “total spectrum needed” approach and (2) the “band-by-band” approach.

The use of market mechanisms to determine the amount of spectrum commons

The standard market mechanisms are difficult to apply directly to unlicensed spectrum. Because there is no single user body, it is not possible for the unlicensed users to directly buy the spectrum under auction or trading.

A possibility is for a third party (the “unlicensed spectrum manager”) to buy spectrum and to make it a private commons. Users wishing to access this would pay the unlicensed spectrum manager by some mechanism. The difficultly is in envisaging an appropriate mechanism. Ideally, the payment should reflect the level of usage, but for many unlicensed devices keeping account of the amount of usage and periodically returning the information would impose such a major increase in complexity and hence cost, that much of the revenue opportunity would be lost in subsidising devices. An alternative is to impose a royalty-like fee on the manufacture of each device, with the fee level coarsely reflecting the expected usage (e.g. a garage door opener would pay less than a W-LAN node). This is more plausible as similar mechanisms are used today to collect royalty payments on patents.

MIMO wireless communication

The use of multiple antennas at the transmitter and receiver in wireless systems, popularly known as MIMO (multiple-input multiple-output) technology, has rapidly gained in popularity over the past decade due to its powerful performance-enhancing capabilities. Communication in wireless channels is impaired predominantly by multi-path fading. Multi-path is the arrival of the transmitted signal at an intended receiver through differing angles and/or differing time delays and/or differing frequency (i.e., Doppler) shifts due to the scattering of electromagnetic waves in the environment. Consequently, the received signal power fluctuates in space (due to angle spread) and/or frequency (due to delay spread) and/or time (due to Doppler spread) through the random superposition of the impinging multi-path components. This random fluctuation in signal level, known as fading, can severely affect the quality and reliability of wireless communication. Additionally, the constraints posed by limited power and scarce frequency bandwidth make the task of designing high data rate, high reliability wireless communication systems extremely challenging.

MIMO technology constitutes a breakthrough in wireless communication system design. The technology offers a number of benefits that help meet the challenges posed by both the impairments in the wireless channel as well as resource constraints. In addition to the time and frequency dimensions that are exploited in conventional single-antenna (single-input single-output) wireless systems, the leverages of MIMO are realized by exploiting the spatial dimension (provided by the multiple antennas at the transmitter and the receiver).

Armed with the theoretical limits of MIMO wireless performance from Chapter 2, we now embark on the design of specific system blocks. At the transmitter, two major MIMO processing components at the symbol level are precoding and spacetime coding. Precoding, the last digital processing block at the transmitter (see Figure 1.2), is a technique that exploits the channel information available at the transmitter. Such information is generally referred to as transmit channel side information, or CSIT (this definition is more general than that in Chapter 2). In MIMO wireless, spatial CSIT is particularly useful in enhancing system performance. Space-time coding, on the other hand, assumes no CSIT and focuses on enhancing reliability through diversity. In addition to these two components, regular channel coding is required for bit-level protection. This chapter focuses on precoding design, and space-time coding is discussed in Chapter 4.

CSIT helps to increase the transmission rate, to enhance coverage, and to reduce receiver complexity in MIMO wireless systems. Many forms of CSIT exist. Exact channel knowledge at each time instance, or perfect CSIT, is ideal; but it is often difficult to acquire in a time-selective fading channel. CSIT is more likely to be available as a channel estimate with an associated error covariance, which reduce in the limit to the channel statistics, such as the channel mean and covariance. Such CSIT encompasses several models discussed in Chapter 2, including perfect CSIT and CDIT. Other partial CSIT forms can involve only parametric channel information, such as the channel condition number or the Ricean K factor.

Introduction

Chapter 1 introduced the basic concepts behind multiple-input multiple-output (MIMO) communications along with their performance advantages. In particular, we saw that MIMO systems provide tremendous capacity gains, which has spurred significant activity to develop transmitter and receiver techniques that realize these capacity benefits and exploit diversitymultiplexing trade-offs. In this chapter we will explore in more detail the Shannon capacity limits of single- and multi-user MIMO systems. These fundamental limits dictate the maximum data rates that can be transmitted over the MIMO channel to one or more users (not in outage) with asymptotically small error probability, assuming no constraints on the delay or the complexity of the encoder and decoder. Much of the initial excitement about MIMO systems was due to pioneering work by Foschini and Telatar predicting remarkable capacity growth for wireless systems with multiple antennas when the channel exhibits rich scattering and its variations can be accurately tracked. This promise of exceptional spectral efficiency almost “for free,” also studied in earlier work by Winters, resulted in an explosion of research and commercial activity to characterize the theoretical and practical issues associated with MIMO systems. However, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. This chapter provides a comprehensive summary of MIMO Shannon capacity for both single- and multi-user systems with and without fading under different assumptions about what is known at the transmitter(s) and receiver(s).

Introduction

The preceding chapter considered the design of receivers for MIMO systems operating as single-user systems. Increasingly however, as noted in Chapters 2 and 4, wireless communication networks operate as shared-access systems in which multiple transmitters share the same radio resources. This is due largely to the ability of shared-access systems to support flexible admission protocols, to take advantage of statistical multiplexing, and to support transmission in unlicensed spectrum. In this chapter we will extend the treatment of Chapter 5 to consider receiver structures for multi-user, and specifically, multiple-access MIMO systems. We will also generalize the channel model considered to include more general situations than the flat-fading channels considered in Chapter 5. To treat these problems, we will first describe a general model for multi-user MIMO signaling, and then discuss the structure of optimal receivers for this signal model. This model will generally include several sources of interference arising in MIMO wireless systems, including multiple-access interference caused by the sharing of radio resources noted above, inter-symbol interference caused by dispersive channels, and inter-antenna interference caused by the use of multiple transmit antennas. Algorithms for the mitigation of all of these types of interference can be derived in this common framework, leading to a general receiver structure for multi-user MIMO communications over frequency-selective channels. As we shall see, these basic algorithms will echo similar algorithms that have been described in Chapters 3 and 5. Since optimal receivers in this situation are often prohibitively complex, the bulk of the chapter will focus on useful lower complexity sub-optimal iterative and adaptive receiver structures that can achieve excellent performance in mitigating interference in such systems. This discussion is organized as follows.

Introduction

This chapter is devoted to MIMO receivers, with special focus on single-user systems and frequency-flat channels (multi-user systems and more general channels will be the subject of the next chapter). We start with a brief discussion of uncoded MIMO systems, describing their optimum (maximum-likelihood, ML) receivers. Since these may exhibit a complexity that makes them unpractical, it is important to seek receivers that achieve a close-to-optimum performance while keeping a moderate complexity: these would remove the practical restriction to small signal constellations or few antennas. Linear receivers and receivers based on the sphere-detection algorithm are examined as possible solutions to the complexity problem. Next, we study iterative processing of received signals. We introduce here the idea of factor graphs. Their use offers a versatile tool, allowing one to categorize in a simple way the approximations on which MIMO receivers and their algorithms are based. In addition, they yield a “natural” way for the description of iterative (turbo) algorithms, and of their convergence properties through the use of EXIT-charts. Using factor graphs, we describe iterative algorithms for the reception of MIMO signals, along with some noniterative schemes that can be easily developed by using the factor-graph machinery.

A basic assumption in this chapter is that channel state information (i.e., the values taken on by all path gains) is available at the receiver, while the transmitter knows the channel distribution (i.e., the joint probability density function of the channel gains). In addition, the channel is quasi-static (i.e., it remains constant throughout the transmission of a whole data frame or codeword), and the transmitted signals are two-dimensional.

Wireless is one of the most rapidly developing technologies in our time, with dazzling new products and services emerging on an almost daily basis. These developments present enormous challenges for communications engineers, as the demand for increased wireless capacity grows explosively. Indeed, the discipline of wireless communications presents many challenges to designers that arise as a result of the demanding nature of the physical medium and the complexities in the dynamics of the underlying network. The dominant technical issue in wireless communications is that of multipath-induced fading, namely the random fluctuations in the channel gain that arise due to scattering of transmitted signals from intervening objects between the transmitter and the receiver. Multipath scattering is therefore commonly seen as an impairment to wireless communication. However, it can now also be seen as providing an opportunity to significantly improve the capacity and reliability of such systems. By using multiple antennas at the transmitter and receiver in a wireless system, the rich scattering channel can be exploited to create a multiplicity of parallel links over the same radio band, and thereby to either increase the rate of data transmission through multiplexing or to improve system reliability through the increased antenna diversity. Moreover, we need not choose between multiplexing and diversity, but rather we can have both subject to a fundamental tradeoff between the two.

This book addresses multiple-input/multiple-output (MIMO) wireless systems in which transmitters and receivers may have multiple antennas. Since the emergence of several key ideas in this field in the mid-1990s, MIMO systems have been one of the most active areas of research and development in the broad field of wireless communications.

Introduction

The essential feature of wireless transmission is the randomness of the communication channel which leads to random fluctuations in the received signal commonly known as fading. This randomness can be exploited to enhance performance through diversity. We broadly define diversity as the method of conveying information through multiple independent instantiations of these random fades. There are several forms of diversity; our focus in this chapter will be on spatial diversity through multiple independent transmit/receive antennas. Information theory has been used to show that multiple antennas have the potential to dramatically increase achievable bit rates, thus converting wireless channels from narrow to wide data pipes.

The earliest form of spatial transmit diversity is the delay diversity scheme proposed in where a signal is transmitted from one antenna, then delayed one time slot, and transmitted from the other antenna. Signal processing is used at the receiver to decode the superposition of the original and time-delayed signals. By viewing multiple antenna diversity as independent information streams, more sophisticates transmission (coding) scheme can be designed to get closer to theoretical performance limits. Using this approach, we focus on space-time coding (STC) schemes defined by Tarokh et al. and Alamouti, which introduce temporal and spatial correlation into the signals transmitted from different antennas without increasing the total transmitted power or the transmission bandwidth. Therefore is, in fact, a diversity gain that results from multiple paths between the base-station and the user terminal, and a coding gain that results from how symbols are correlated across transmit antennas.

Although we have seen that most of the MC signals have peaks of value about √n ln n, there are plenty of signals with maxima of order √n. This chapter is devoted to methods of constructing such signals. I begin with relating the maxima in signals to the distribution of their a periodic correlations (Theorem 7.2). Then I describe in Section 7.2 the Rudin–Shapiro sequences over {−1, 1}, guaranteeing a PMEPR of at most 2 for n being powers of 2. They appear in pairs, where each one of the sequences possesses the claimed property. The Rudin–Shapiro sequences are representatives of a much broader class of complementary sequences discussed in Section 7.3. The signals defined by these sequences also have a PMEPR not exceeding 2, while existing for a wider spectrum of lengths. In Section 7.4, I introduce complementary sets of sequences. The number of sequences in the sets can be more than two, and the corresponding sequences have a PMEPR not exceeding the number of sequences in the set. In Section 7.5, I generalize the earlier derived results to the polyphase case, and describe a general construction of complementary pairs and sets stemming from cosets of the first-order Reed–Muller codes within the second-order Reed–Muller codes. Another idea in constructing sequences with low PMEPR is to use vectors defined by evaluating the trace of a function over finite fields or rings. This topic is explored in Section 7.6 using estimates for exponential sums. Finally, in Sections 7.7 and 7.8, I study two classes of sequences, M-sequences and Legendre sequences, guaranteeing PMEPR of order at most (ln n)2.