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6385 results in Communications and signal processing

Page 112 of 320

  • 8 - Final Notes and Future Directions

  • Thomas L. Marzetta, Erik G. Larsson, Linköpings Universitet, Sweden, Hong Yang, Hien Quoc Ngo, Queen's University Belfast
  • Book:
    Fundamentals of Massive MIMO
    Published online:
    03 November 2016
    Print publication:
    17 November 2016, pp 157-162

  • Summary

    This chapter summarizes some open questions that demand further research, and briefly discusses selected topics that we have been unable to cover in the book but on which substantial investigations have taken place, or are taking place at the time of this writing.

    Alternative Approaches to Performance Analysis

    Our capacity analyses use techniques first developed in [48] for the uplink, and [49] for the downlink. This approach has several advantages: the resulting capacity bounds are rigorous and do not involve approximations, and the resulting expressions are in closed form and easy to interpret intuitively.

    Alternative approaches to the capacity analysis of Massive MIMO exist. Most notably, the sequence of papers [50–52] used asymptotic random-matrix theoretic results in order to obtain “deterministic equivalent” capacity expressions. An advantage of that approach is that MMSE and regularized zero-forcing processing can be analyzed, whereas the theory developed in this book is only applicable to zero-forcing and maximum-ratio processing. While our capacity analyses assume independent small-scale fading, [50–52] accounted for spatial correlation; however, they were unable to obtain exact closed-form performance expressions.

    Multiple-Antenna Terminals

    Massive MIMO, in contrast to Point-to-Point MIMO, works extremely well with only single-antenna terminals. Nothing in our discussion, however, precludes the use ofmultipleantenna terminals. A multiple-antenna terminal, for example, could enjoy throughput in proportion to the number of antennas that it possesses without requiring exponentially growing SINRs. The simplest mode of operation would treat the multiple-antenna terminal as a multiplicity of single-antenna terminals. Alternatively, a terminal could use multiple antennas for out-of-system interference suppression, facilitated by adding a “quiet interval” in each coherence interval, during which none of the base stations or terminals transmits. The terminals (and incidentally the base station) could each identify the subspace in which the interference is contained, and then operate in the orthogonal interference-free subspace.

    Pilot Contamination and Pilot Assignment

    We saw in Chapter 6 that pilot contamination can be a significant impairment in a multi-cell system and that it may be mitigated by adopting a pilot reuse factor greater than one. However, the greater overhead of high reuse factors limits the number of mobile terminals that can simultaneously be served.

  • 2 - Models and Preliminaries

  • Thomas L. Marzetta, Erik G. Larsson, Linköpings Universitet, Sweden, Hong Yang, Hien Quoc Ngo, Queen's University Belfast
  • Book:
    Fundamentals of Massive MIMO
    Published online:
    03 November 2016
    Print publication:
    17 November 2016, pp 19-44

  • Summary

    This chapter introduces the basic signal and channel models to be used throughout the book. We use standard complex baseband representations of all signals and noise, with the implicit assumption that all signals are eventually modulated onto a carrier with frequency fc and wavelength λ = c/fc, where c is the speed of light. Also, unless stated explicitly, all Gaussian random variables are complex-valued and circularly symmetric; see Appendix A for a treatment of such variables.

    Single-Antenna Transmitter and Single-Antenna Receiver

    The wireless channel takes an input signal x(t), emitted by a transmit antenna, and yields an output signal y(t), observed at a receive antenna. The relation between x(t) and y(t) is linear, owing to the linearity of Maxwell's equations. However, this relation generally is timevarying, since the transmitter, receiver, and other objects in the propagation environment may move relative to one another.

    Coherence Time

    The time during which the channel can be reasonably well viewed as time-invariant is called the coherence time and denoted by Tc (measured in seconds). To relate Tc to the characteristics of the physical propagation environment, we consider a simple two-path propagation model where a transmit antenna emits a signal x(t) that reaches the receiver both directly via a LoS path, and via a single specular reflection; see Figure 2.1(a). If both paths have unit strength, and the bandwidth of x(t) is small enough that time-delays can be

    approximated as phase shifts, then by the superposition principle the received signal is

    where d1 and d2 are the propagation path lengths defined in Figure 2.1(a).

    Suppose, for the sake of argument, that when the receiver is located as shown in Figure 2.1(a), d1/λ and d2/λ are integers. Then the two paths add up constructively and y(t) = 2x(t). Next, if the receiver is displaced d meters to the right, so that we have the situation in Figure 2.1(b), the received signal will instead be

    The two paths add up destructively if the cosine in (2.2) is equal to zero. As shown in Figure 2.2(a), this occurs periodically for displacements d that are spaced λ/2 meters apart. The channel may be considered time-invariant as long as the receiver does not move farther than this distance, λ/2.

  • Preface

  • Thomas L. Marzetta, Erik G. Larsson, Linköpings Universitet, Sweden, Hong Yang, Hien Quoc Ngo, Queen's University Belfast
  • Book:
    Fundamentals of Massive MIMO
    Published online:
    03 November 2016
    Print publication:
    17 November 2016, pp 1-4
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  • Summary

    Simplification ofmodes of proof is notmerely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for further progress.

    – W. Thomson [1st Baron Kelvin] and P. G. Tait, Elements of Natural Philosophy, 1873

    There are three timeless truths in the field of wireless communications:

  • • Demand for wireless throughput, both mobile and fixed, will always increase.

  • • The quantity of available electromagnetic spectrum will never increase, and the most desirable frequency bands that can propagate into buildings and around obstacles and that are unaffected by weather constitute only a small fraction of the entire spectrum.

  • • Communication theorists and engineers will always be pressured to invent or to discover breakthrough technologies that provide higher spectral efficiency.

    • Given the history of more than a century of wireless innovation, we must look to the physical layer for breakthrough technologies. The central assertion of this book is that Massive MIMO constitutes a breakthrough technology. It is a scalable technology whereby large numbers of terminals simultaneously communicate through the entire allocated frequency spectrum. What enables this aggressive multiplexing is, first, an excess number of service antennas compared with terminals, and, second, performing the multiplexing and de-multiplexing based on measured propagation characteristics rather than on assumed propagation characteristics. A disproportionate number of service antennas compared with active terminals makes it likely that the propagation channels are conducive to successful multiplexing, and basing the multiplexing on direct channel measurements makes the antenna array tolerances independent of the number of antennas. The activity of growing the number of antennas relative to the number of active terminals renders the simplest types of multiplexing and de-multiplexing signal processing exceedingly effective, and it permits the same quality of service with reduced radiated power. Low radiated power is conducive to frequency reuse. The combined action ofmany antennas eliminates frequency-dependent fading and simplifies power control. By virtue of the time-division duplexing operation, the propagation channel characteristics aremeasured on the uplink and used both for uplink data detection and downlink beamforming. This facilitates operation in high-mobility scenarios. Also, by performing appropriate power control, Massive MIMO yields uniformly good service to all terminals, as measured in terms of 95%-likely throughputs on both the uplink and downlink.

Fundamentals of Massive MIMO
  • Thomas L. Marzetta, Erik G. Larsson, Hong Yang, Hien Quoc Ngo
  • Published online:
    03 November 2016
    Print publication:
    17 November 2016
  • Written by pioneers of the concept, this is the first complete guide to the physical and engineering principles of Massive MIMO. Assuming only a basic background in communications and statistical signal processing, it will guide readers through key topics in multi-cell systems such as propagation modeling, multiplexing and de-multiplexing, channel estimation, power control, and performance evaluation. The authors' unique capacity-bounding approach will enable readers to carry out effective system performance analyses and develop advanced Massive MIMO techniques and algorithms. Numerous case studies, as well as problem sets and solutions accompanying the book online, will help readers put knowledge into practice and acquire the skill set needed to design and analyze complex wireless communication systems. Whether you are a graduate student, researcher, or industry professional working in the field of wireless communications, this will be an indispensable guide for years to come.

  • 6 - Radiative Transfer and Atmospheric Compensation

  • Dimitris G. Manolakis, Ronald B. Lockwood, Thomas W. Cooley
  • Book:
    Hyperspectral Imaging Remote Sensing
    Published online:
    10 November 2016
    Print publication:
    20 October 2016, pp 295-359

  • Summary

    The next processing step for calibrated imaging spectrometer data is the conversion from the at-aperture radiance to a surface reflectance signature, for the VNIR/SWIR spectral range, or to a surface emissivity signature and temperature, for the LWIR spectral range. This requires that the transmission and emission of the atmosphere be quantified from the aggregated information that is present in the at-aperture radiance. In the solar reflective range this includes estimates of the amount of water in the scene, which is highly variable, and of the aerosol loading in order to calculate both the diffuse radiance and the contribution from light that is scattered and reflected from the directly viewed pixel and the surrounding area. Similarly, for a sensor operating in the emissive regime, the water and the atmospheric thermal emission is quantified in order to retrieve the ground-leaving radiance that is used to estimate the temperature and emissivity of the surface.

    In this chapter, the physics of radiative transfer will be developed first, in order to establish a basis for the discussion of the particular techniques that are applied in the reflective and emissive regimes. The modeling tools that are used to quantitatively describe the processes of absorption, transmission, and emission in a forward sense, i.e. in the direction of light propagation, are introduced prior to delving into the problem of retrieving the surface properties of interest. The reflectance retrieval is treated in detail and includes the derivation of the inverse radiative transfer model, the estimation of the quantities that are required to apply the inverse model, and the algorithms that are utilized, using both physics-based modeling and empirical techniques. The final sections address the problem of atmospheric compensation in the longwave infrared.

    Radiative Transfer

    The propagation of radiation through the atmosphere is described by the theory of radiative transfer. A complete description of radiative transfer is beyond our scope; however, the critical concepts required to understand the processes of atmospheric compensation are introduced within the limitations of a book devoted to remote sensing using an imaging spectrometer. Radiative transfer as a discipline was established by Arthur Schuster's paper in 1905, where he recognized the importance of multiple scattering (Schuster, 1905).

Hyperspectral Imaging Remote Sensing
  • Physics, Sensors, and Algorithms
  • Dimitris G. Manolakis, Ronald B. Lockwood, Thomas W. Cooley
  • Published online:
    10 November 2016
    Print publication:
    20 October 2016
  • A practical and self-contained guide to the principles, techniques, models and tools of imaging spectroscopy. Bringing together material from essential physics and digital signal processing, it covers key topics such as sensor design and calibration, atmospheric inversion and model techniques, and processing and exploitation algorithms. Readers will learn how to apply the main algorithms to practical problems, how to choose the best algorithm for a particular application, and how to process and interpret hyperspectral imaging data. A wealth of additional materials accompany the book online, including example projects and data for students, and problem solutions and viewgraphs for instructors. This is an essential text for senior undergraduate and graduate students looking to learn the fundamentals of imaging spectroscopy, and an invaluable reference for scientists and engineers working in the field.

  • 11 - Hyperspectral Data Exploitation

  • Dimitris G. Manolakis, Ronald B. Lockwood, Thomas W. Cooley
  • Book:
    Hyperspectral Imaging Remote Sensing
    Published online:
    10 November 2016
    Print publication:
    20 October 2016, pp 551-620

  • Summary

    The main objective of hyperspectral imaging remote sensing is the identification of materials or phenomena from their reflectance or emissivity spectra to serve the needs of different applications. In this chapter, building on the understanding of the phenomenology of spectral remote sensing and the introduced signal processing methods, we develop algorithms for some unique hyperspectral imaging applications: detection of hard targets, gas detection, change detection, and image classification. The emphasis is on algorithms developed based on phenomenologically sound signal models, realistic application-driven requirements, and rigorous signal processing procedures, rather than ad hoc algorithms or trendy theoretical algorithms based on unrealistic assumptions.

    Target Detection in the Reflective Infrared

    The objective of hyperspectral target detection is to find objects of interest (called “hard targets” or simply “targets”) within a hyperspectral image and to discriminate between various target types on the basis of their spectral characteristics. The advantages are automated signal processing and lower spatial resolution requirements for the sensor. In this section we discuss the defining features of the target detection problem, we explain how to choose target detection algorithms, we investigate the consequences of practical limitations, and we evaluate performance using field data. Predicting detection performance using theoretical models is discussed in Section 11.2.

    Definition of the Target Detection Problem

    Hyperspectral target detection algorithms search for targets by exploiting the spectral characteristics of the target's surface material by looking at the spectrum of each pixel. Depending on the spatial resolution of the sensor, targets of interest may not be clearly resolved, and hence may appear in only a few pixels or even as part of a single pixel (subpixel target). Thus, the first key attribute of the hyperspectral target detection problem is that a “target present” versus “target absent” decision must be made individually for every pixel of a hyperspectral image. In most applications each target is characterized by its spectral signature and detection algorithms make decisions using the target signature and the data cube of the imaged scene.

    Typical “search-and-detection” applications include the detection of man-made materials in natural backgrounds for the purpose of search and rescue, and the detection of military vehicles for purposes of defense and intelligence.

  • 1 - Introduction

  • Dimitris G. Manolakis, Ronald B. Lockwood, Thomas W. Cooley
  • Book:
    Hyperspectral Imaging Remote Sensing
    Published online:
    10 November 2016
    Print publication:
    20 October 2016, pp 1-35

  • Summary

    This chapter provides an introduction to the basic principles of hyperspectral remote sensing. The main objective is to explain how information about the earth's surface is conveyed to a remote hyperspectral imaging sensor, which are the key factors determining the nature and quality of the acquired data, and how the data should be processed to extract meaningful information for practical applications. By definition, hyperspectral imaging systems collect co-aligned images in many relatively narrow bands throughout the ultraviolet, visible, and infrared regions of the electromagnetic spectrum.

    Introduction

    The term “remote sensing” has several valid definitions. In the broadest sense, according to Webster's dictionary, remote sensing is “the acquisition of information about a distant object without coming into physical contact with it.” For our purposes, remote sensing deals with the acquisition, processing, and interpretation of images, and related data, obtained from aircraft and satellites that record the interaction between matter and electromagnetic radiation.

    The detection of electromagnetic radiation via remote sensing has four broad components: a source of radiation, interaction with the atmosphere, interaction with the earth's surface, and a sensor (see Figure 1.1). The link between the components of the system is electromagnetic energy transferred by means of radiation.

    Source The source of electromagnetic radiation may be natural, like the sun's reflected light or the earth's emitted heat, or man-made, like microwave radar. This leads to a classification of remote sensing systems into active and passive types. Active systems emit radiation and analyze the returned signal. Passive systems detect naturally occurring radiation either emitted by the sun or thermal radiation emitted by all objects with temperatures above absolute zero. With active systems, like microwave radar, it is possible to determine the distance of a target from the sensor (range); passive systems cannot provide range information.

    Atmospheric interaction The characteristics of the electromagnetic radiation propagating through the atmosphere are modified by various processes, including absorption and scattering. This distortion is undesirable and requires correction if we wish to study the earth's surface, or desirable if we wish to study the atmosphere itself.

  • Appendix Introduction to Gaussian Optics

  • Dimitris G. Manolakis, Ronald B. Lockwood, Thomas W. Cooley
  • Book:
    Hyperspectral Imaging Remote Sensing
    Published online:
    10 November 2016
    Print publication:
    20 October 2016, pp 621-653

  • Summary

    To understand both the spectral discrimination and the image production from an imaging spectrometer requires both Gaussian, or geometrical, and physical optics that govern the processes of diffraction and interference. This appendix provides the barest introduction to Gaussian optics and a qualitative description of aberration theory. Physical optics is introduced in Chapter 4 when it is required, as in, for example, the action of a grating. The analysis presented is for centered or axially symmetric systems about an axis that passes through the centers of the sequential optical elements known as the optical axis. The concept of paraxial ray tracing, where the rays travel infinitesimally close to the optical axis, is also introduced, providing the location and size of the image. The brightness of an image is developed through the definition and placement of pupils and stops. Finally the quality of an image is determined through aberration theory.

    The Optical Path

    In Chapter 2 we introduced the concept of a wavefront as the surface of constant phase for an electromagnetic wave. This surface is perpendicular to the wave vector k, which is in the direction of propagation of the wave. A ray of light is defined to be parallel to the wave vector and is in the direction of energy propagation as described by the Poynting vector. The ray, an infinitely narrow beam of light, is the construct used in geometrical optics but has no precise physical meaning. For example, if we attempt to create a narrow beam of light by illuminating a pinhole we are defeated by diffraction effects that spread the beam out, with the effect becoming larger as the pinhole diameter is reduced. Nevertheless the ray is an extremely useful and practical concept that is universally used in Gaussian optics and ray tracing. The wavefront, on the other hand, has a precise physical meaning and, for the isotropic materials used in imaging spectrometers, the direction of energy propagation is always along the wavefront normal.

    In Gaussian optics, light is assumed to propagate rectilinearly along the rays with their directions changed only by the processes of reflection and refraction. The optical systems considered here are composed of a series of surfaces that can be either refracting or reflecting and have a common axis of rotational symmetry known as the optical axis.

  • 9 - Spectral Mixture Analysis

  • Dimitris G. Manolakis, Ronald B. Lockwood, Thomas W. Cooley
  • Book:
    Hyperspectral Imaging Remote Sensing
    Published online:
    10 November 2016
    Print publication:
    20 October 2016, pp 443-493

  • Summary

    Analysis of spectral mixtures is important in remote sensing imaging spectroscopy, because essentially the spectrum of any pixel of a natural scene is a mixture. The analysis of mixed spectra, known as Spectral Mixture Analysis (SMA), is the subject of this chapter. SMA attempts to answer two questions: (a) What are the spectra of the individual materials? (b) What are the proportions of the individual materials? We focus on linear mixing because of its relative analytical and computational simplicity and because it works satisfactorily in many practical applications.We discuss the physical aspects of the linear mixing model, geometrical interpretations and algorithms, and statistical analysis using the theory of least squares estimation. The main applications of SMA are in the areas of hyperspectral image interpretation and subpixel target detection.

    Spectral Mixing

    When a ground resolution element contains several materials, all these materials contribute to the individual pixel spectrum measured by the sensor. The result is a composite or mixed spectrum, and the “pure” spectra that contribute to the mixture are called endmember spectra. Spectral mixtures can be macroscopic or intimate depending on what scale the mixing is taking place (see Figure 9.1).

    In a macroscopic mixture the materials in the field of view are optically separated in patches so there is no multiple scattering between components (each reflected photon interacts with only one surface material). Such mixtures are linear: that is, the combined spectrum is simply the sum of the fractional area times the spectrum of each component. Linear mixing is possible as long as the radiation from component patches remains separate until it reaches the sensor.

    In an intimate mixture, such as the microscopic mixture of mineral grains in a soil or rock, a single photon interacts with more than one material. In this case, mixing occurs when radiation from several surfaces combines before it reaches the sensor. These types of mixtures are nonlinear in nature and therefore more difficult to analyze and use.

    To illustrate some of the issues involved in SMA, we discuss some examples of mixed spectra provided by Adams and Gillespie (2006). Figure 9.2(a) shows spectra for mixtures of a material having a featureless spectrum (quartz) with a material having a spectrum with diagnostic absorption bands (alunite).

Page 112 of 320