Introduction to Direction-of-Arrival Estimation by Zhizhang Chen

00583b962625038-261x361.jpeg Author Zhizhang Chen
Isbn 9781596930896
File size 2.4MB
Year 2010
Pages 193
Language English
File format PDF
Category engineering and technology


Introduction to Direction-of-Arrival Estimation For a listing of related titles in the Artech House Signal Processing Library turn to the back of this book. Introduction to Direction-of-Arrival Estimation Zhizhang Chen Gopal Gokeda Yiqiang Yu Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Cover design by Vicki Kane ISBN 13: 978-1-59693-089-6 © 2010 ARTECH HOUSE 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. 10 9 8 7 6 5 4 3 2 1 Contents Preface 9 1 Introduction 11 1.1 Smart Antenna Architecture 12 1.2 Overview of This Book 17 1.3 Notations 18 References 19 2 Antennas and Array Receiving System 21 2.1 2.1.1 2.1.2 Single Transmit Antenna Directivity and Gain Radiation Pattern 23 23 24 2.1.3 Equivalent Resonant Circuits and Bandwidth 25 2.2 Single Receive Antenna 26 2.3 Antenna Array 27 5 6 Introduction to Direction-of-Arrival Estimation 2.4 Conclusion 29 Reference 30 3 Overview of Basic DOA Estimation Algorithms 31 3.1 Introduction 31 3.2 Data Model 32 3.2.1 Uniform Linear Array (ULA) 33 3.3 3.3.1 3.3.2 3.3.3 Centro-Symmetric Sensor Arrays Uniform Linear Array Uniform Rectangular Array (URA) Covariance Matrices 38 40 41 45 3.4 3.4.1 3.4.2 Beamforming Techniques Conventional Beamformer Capon’s Beamformer 46 47 49 3.4.3 Linear Prediction 51 3.5 Maximum Likelihood Techniques 52 3.6 Subspace-Based Techniques 54 3.6.1 3.6.2 3.6.3 3.6.4 Concept of Subspaces MUSIC Minimum Norm ESPRIT 54 57 61 62 3.7 Conclusion References 63 63 4 Preprocessing Schemes and Model Order Estimation 65 4.1 Introduction 65 4.2 4.2.1 4.2.2 Preprocessing Schemes Forward-Backward Averaging Spatial Smoothing 66 67 69 4.3 4.3.1 4.3.2 Model Order Estimators Classical Technique Minimum Descriptive Length Criterion 74 75 75 Contents 7 4.3.3 Akaike Information Theoretic Criterion 77 4.4 Conclusion References 78 79 5 DOA Estimations with ESPRIT Algorithms 81 5.1 Introduction 81 5.2 Basic Principle 82 5.2.1 5.2.2 5.2.3 Signal and Data Model Signal Subspace Estimation Estimation of the Subspace Rotating Operator 83 84 85 5.3 5.3.1 Standard ESPRIT Signal Subspace Estimation 86 88 5.3.2 5.3.3 Solution of Invariance Equation Spatial Frequency and DOA Estimation 91 91 5.4 Real-Valued Transformation 92 5.5 5.5.1 5.5.2 Unitary ESPRIT in Element Space One-Dimensional Unitary ESPRIT in Element Space Two-Dimensional Unitary ESPRIT in Element Space 94 94 98 5.6 5.6.1 Beamspace Transformation DFT Beamspace Invariance Structure 105 107 5.6.2 DFT Beamspace in a Reduced Dimension 112 5.7 5.7.1 Unitary ESPRIT in DFT Beamspace One-Dimensional Unitary ESPRIT in DFT Beamspace 113 5.7.2 Two-Dimensional Unitary ESPRIT in DFT Beamspace 116 5.8 Conclusion References 120 122 6 Analysis of ESPRIT-Based DOA Estimation Algorithms 123 6.1 Introduction 123 6.2 Performance Analysis 126 113 8 Introduction to Direction-of-Arrival Estimation 6.2.1 Standard ESPRIT 126 6.2.2 6.2.3 The One-Dimensional Unitary ESPRIT The Two-Dimensional Unitary ESPRIT 138 148 6.3 Comparative Analysis 158 6.4 Discussions 167 6.5 Conclusion 173 References 174 7 Discussions and Conclusion 175 7.1 Summary 175 7.2 Advanced Topics on DOA Estimations References 176 177 Appendix 179 A.1 Kronecker Product 179 A.2 Special Vectors and Matrix Notations 180 A.3 FLOPS 180 List of Abbreviations 183 About the Authors 185 Index 187 Preface Direction-of-arrival (DOA) estimation (or direction finding) essentially concerns the estimation of direction-of-arrival of signals, either in the form of electromagnetic (i.e., radio) or acoustic waves, impinging on a sensor or antenna array. The requirement for DOA estimation arises from the needs of locating and tracking signal sources in both civilian and military applications, such as search and rescue, law enforcement, sonar, seismology, and wireless 911 emergency call locating. Various theories and techniques have been developed for array signal processing related to DOA estimations. A large body of literature has also existed on the subject. However, during our course of research and development for real-world implementations, we have found that relevant publications have been quite scattered, making it hard for the beginners or students who want to enter the area in a relatively short time. In other words, few review books are available that systematically describe the principles and basic techniques of DOA estimation under one roof. This book is intended to cover the issue by providing an overview and performance analysis of the basic DOA algorithms and comparisons among themselves. In particular, systematic descriptions, performance analysis, and comparisons of various DOA algorithms are presented with a final focus on the family of ESPRIT (estimation of signal parameters via rotational invariance techniques). This book is aimed at beginners such as graduate students or engineers or government regulators who need to gain insight into the fundamentals of DOA estimations in a relatively quick manner. It is also 9 10 Introduction to Direction-of-Arrival Estimation suitable for those who specialize in the area but would like to refresh their knowledge of the basics of DOA estimations. It is our hope that this book can present sufficient information on theoretical foundations of DOA estimation techniques to a reader so that he or she can understand DOA basics and move on to advanced DOA topics if he or she wishes. 1 Introduction Wireless technology applications have spread into many areas, such as environmental monitoring, sensor networks, public security, and search and rescues. In light of these developments, many technological policies have been established to accommodate the needs of various demands. For instance, a mandatory rule was passed by the FCC [1] that requires 125-m location accuracy on wireless emergency calls. As well, search and rescue always require the location of electromagnetic beacon sources. All these applications perhaps can be counted as the main reason for the recent increased interest in determining the direction of arrival (DOA) of radio signals in wireless systems. In fact, estimating the direction of arrival of several radio signals impinging on an array of sensors is required in a variety of other applications as well, including radar, sonar, and seismology. Another technology that has become equally glamorous is smart antenna technology [2, 3]. In smart antenna technology, a DOA estimation algorithm is usually incorporated to develop systems that provide accurate location information for wireless services [4]. A smart antenna, for this book discussion, is a system that combines multiple antenna elements with a signal processing capability to optimize its radiation and/or reception pattern automatically in response to the system’s signal environment. This technology is particularly found useful in mobile communications in lieu of an increasing number of mobile subscribers and limited resources. Smart antennas can be used to enhance the coverage through range extension and to increase system capacity [2, 3]. Smart antennas can also be used to spatially separate signals, allowing 11 12 Introduction to Direction-of-Arrival Estimation different subscribers to share the same spectral resources, provided that they are spatially separable at the base station. This spatial division multiple access (SDMA) method allows multiple users to operate in the same cell and on the same frequency/time slot provided by utilizing the adaptive beamforming techniques of the smart antennas. Since this approach allows more users to be supported within a limited spectrum allocation, compared with conventional antennas, SDMA can lead to improved capacity. The smart antenna technology can be divided into three major categories depending on their choice in transmit strategy: • Switched lobe (SL): This is the simplest technique and comprises only a basic switching function between predefined beams of an array. When a signal is received, the setting that gives the best performance, usually in terms of received power, is chosen for the system to operate with. • Dynamically with phased array (PA): This technique allows contin- uous tracking of signal sources by including a direction-of-arrival (DOA) finding algorithm in the system; as a result, the transmission from the array can be controlled intelligently based on the DOA information of the array. The PA technique can be viewed as a generalization of the switched lobe concept. • Adaptive array (AA): In this case, a DOA algorithm for determin- ing the directions of interference sources (e.g., other users) is also incorporated in addition to finding the DOA of the desired source. The beam pattern can then be adjusted to null out the interferers while maximizing the transmit power at the desired source. The importance of DOA estimation for smart antenna can be understood by studying the architecture of smart antenna as described in the following section. 1.1 Smart Antenna Architecture Typical smart antenna architectures for a base station can be divided into following functional blocks, as shown in Figures 1.1 and 1.2: Introduction 13 Beamforming Unit Radio Unit W1 W2 To Receiving Base Station W3 W4 Adaptive Antenna Processor Figure 1.1 Smart antenna receiver. • Radio unit: This unit mainly consists of: (1) antenna arrays that intercept radio frequency (RF) signals from the air, (2) downconversion chains that remove the carrier(s) of the RF signals received by the antenna array, and (3) analog-to-digital converters that convert the no-carrier signals to the corresponding digital signals for further processing. Antenna arrays can be one-, two-, or even three-dimensional, depending on the dimension of the space one wants to access. The radiation pattern of the array depends on the element type, the relative positions, and the excitation (amplitude and phase) to each element [5]. • Beamforming unit: The beamforming unit is responsible for forming and steering the beam in the desired direction. In it, the weighting of the received (or transmitted) signals is applied. Basically, the data signals xk, k = 0, …, M − 1 received by an M-element array are directly multiplied by a set of weights to form a beam at a desired angle. In other words, by multiplying the data signals with appropriate sets of weights, it is possible to form a set of beams with pointing angles directed at the desired angles, resulting in a signal peak at the output of a beamformer. Mathematically it can be expressed as: 14 Introduction to Direction-of-Arrival Estimation Input Data Model Order Estimator MDL AIC DOA Estimator ESPRIT PAST Spatial Filter MOORE PENROSE User Identification DDF SDF User Tracking CSD CD Weight Generation LMS SMI Uplink and Downlink Weights Figure 1.2 Adaptive antenna processor. y ( θi ) = M −1 ∑w k =0 i k xk (1.1) where y(θi) is the output of a beamformer, xk is the data sample from the kth array element and w ki is the weight for forming a beam or null at angle θi. More descriptions on (1.1) are given in Chapters 2 and 3. By selecting the appropriate values for the set of the weights i w k k = 0 ,,K, M =1 , one can implement beam steering, adaptive nulling, Introduction 15 and beamshaping. These weights that determine the radiation pattern are generated by the adaptive processor unit. • Adaptive antenna processor: The function of the adaptive proces- sor unit is to determine the complex weights for the beamforming unit. The weights can be optimized from two main types of criteria: maximization of the data signal from the desired source (e.g., switched lobe or phased array) or maximization of the signal-to-interference ratio (SIR) by suppressing the signal from the interference sources (adaptive array). In theory with M antenna elements, one can “null out” M − 1 interference sources, but due to multipath propagation, this number will be normally lower. The method for calculating the weights will differ depending on the types of optimization criteria. When a switched lobe is used, the receiver will test all the predefined weights and choose the one that gives the strongest received data signal. However, if the phased array or adaptive array approach is used, which consists of directing a maximum gain towards the strongest signal component, the directions of arrival (DOAs) of the signals are first estimated and the weights are then calculated in accordance with the desired steering angle. In general, as shown in Figure 1.2, the adaptive antenna processor consists of several computation processes: • Model order estimator: From the input data xk, k = 0, …, M − 1 received by the antenna elements, the number of wavefronts impinging on the array is estimated using model order estimation algorithms, such as AIC or MDL, which will be described in Chapter 4. The knowledge of number of the signals impinging on the array is crucial to DOA estimation algorithms; hence, these algorithms are run prior to DOA estimation algorithms. • DOA estimator: This forms the vital stage of the adaptive antenna processor where algorithms like MUSIC or ESPRIT are used for estimating the direction of arrival of all the signals impinging on the array. This stage gives DOAs of all the relevant signals of the user sources and other interference sources. To make the process faster, instead of estimating the signal space every time, subspace tracking algorithms like dPAST and PAST (Projection 16 Introduction to Direction-of-Arrival Estimation Approximation Subspace Tracking) are used to recursively track the signal subspace. Usually, the signal subspace is only slowly time-varying. It is therefore more efficient to track those changes than to perform full subspace estimation. The DOAs can then be estimated faster from these signal subspaces. Detailed descriptions of these DOA algorithms are presented in Chapter 3, 4, and 5. • Spatial filter: After the DOAs of all the signals impinging on the array are obtained, the signals are filtered by reconstructing the signals for each of the DOAs estimated. Estimating the signals from the estimated DOAs is usually called signal reconstruction or signal copy. With the knowledge of DOAs, the corresponding steering vectors a and eventually the estimated steering matrix A are constructed. The signal is then reconstructed from S = WX where S is the matrix of impinging signals extracted from the noise corrupted signals (or data signals) received by an array X and the weighting matrix W is chosen to be the Moore-Penrose pseudo inverse of the estimated array steering matrix A. More details are given in Chapter 3. • User identification: Once the signals are separated with respect to their distinct DOAs, the desired user corresponding to these DOAs needs to be identified. By comparing the received mid-ambles (training sequences) with the desired user mid-amble, the number of bit errors within the training sequence can be calculated. A spatially resolved wavefront and thus the corresponding DOA are attributed to a user, when the number of bit errors is smaller than a threshold. In this way not only a single user path but also all paths that correspond to the intended user can be identified. The DOA of the user path with the strongest instantaneous power is then detected. As a training sequence detector, standard sequence estimators like delayed decision feedback (DDF) and soft decision feedback (SDF) are applied [6]. • User tracking: A fast reactive adaptive estimator is needed for tracking changes of signal parameters. The tracker does not only prevent far-off estimates from disturbing the beamforming, but also prevents the DOA estimates from changing too much Introduction 17 between two consecutive signal bursts. This is reasonable, since a mobile user in real time does not move far during one frame of observation. Hence, the variation in DOA is gradual. The approach to user tracking is based on recursive formulation for tracking DOAs where small changes in the difference of correlation matrix estimates result in small changes in difference of steering matrices through which the DOAs are extracted. One of the problems that these algorithms pose is the data association problem, that is, association of DOA estimates established at the previous time instant with that of current time instant. To overcome this problem, algorithms like constrained steepest descent (CSD), steepest descent (SD), and conjugate gradient (CD) are developed and employed [7, 8]. • Weight generation: The tracked DOA with the strongest instanta- neous power is selected and thus weights for the beamforming unit to adaptively focus the beams at a desired source can be generated. Adaptive antenna algorithms like least mean square (LMS) or sample matrix inversion (SMI) [9] are used to generate these weights. The choice of the adaptive algorithm for deriving the adaptive weights is highly important in that it determines both the speed of convergence and hardware complexity required to implement the algorithm. 1.2 Overview of This Book DOA estimation algorithms form the heart of smart antenna systems. Across the board, there are a variety of DOA estimation algorithms for use in smart antenna systems targeted at position-location applications [10], and more are emerging [3, 11]. The challenge for a designer, however, is to choose the right DOA estimation algorithm because the most advanced smart antenna implementations involve simultaneously maximizing the useful signal and nulling out the interference sources. Even with the powerful signal processing units available today, it is a challenging task to perform this in real time. Consequently, efficiency and effectiveness of an algorithm become critical in selecting a DOA estimation algorithm. In other words, a thorough understanding of a DOA estimation algorithm is needed for a designer who will use the smart antenna technique. 18 Introduction to Direction-of-Arrival Estimation This book is intended to provide an introduction to the basic concepts of DOA estimations with an overview of basic techniques. In addition, the algorithms that belong to the family of ESPRIT (estimation of signal parameters via rotational invariance techniques) will be elaborated in more detail. This is because of ESPRIT’s simplicity and high-resolution capability as a signal subspace-based DOA estimation algorithm; based on it, many state-of-the-art techniques have been developed. Currently, few books are available commercially that systematically describe the principles and basic techniques of DOA estimations. This book is intended to add to that knowledge base by providing an overview and a performance analysis of the basic DOA algorithms and comparisons among themselves. In particular, systematic study, performance analysis, and comparisons of the DOA algorithms belonging to the family of ESPRIT are provided. In short, this book lays out the theoretical foundations of DOA estimation techniques for a reader to understand DOA basics and to continue on to advanced DOA topics if he or she wishes [10, 11]. The book is aimed at beginners such as graduate students or engineers or government regulators who need to gain rapid insight into the fundamentals of DOA estimations. It is also suitable for those who specialize in the area but would like to refresh their knowledge of the basics of DOA estimations. 1.3 Notations In this work, vectors and matrices are denoted in bold letters, either lowercase or uppercase. The superscripts (⋅)H and (⋅)T denote complex conjugate transposition and transposition without complex conjugation, respectively. The overbar () denotes complex conjugate. E{⋅} denotes expectation operator. Rm×n refers to a real number matrix of m rows and n m×n columns. C refers to a complex number matrix of m rows and n columns. ∈ means belong to. Frequently used exchange matrix Πp and diagonal matrix are briefly explained in the appendix. Also, a definition of Kronecker products is provided in the appendix. Introduction 19 References [1] Federal Communications Commission, [2] Liberti, Jr., J. C., and T. S. Rappaport, Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications, Upper Saddle River, NJ: Prentice-Hall, 1999. [3] Sarkar, T. K. Smart Antennas, New York: IEEE Press/Wiley-Interscience, 2003. [4] Kuchar, A., et al., “A Robust DOA-Based Smart Antenna Processor for GSM Base Stations,” Proc. IEEE Intl. Conf. on Communications, Vol. 1, June 6–10, 1999, pp. 11–16. [5] Balanis, C. A., Antenna Theory: Analysis and Design, 3rd ed., New York: Wiley, 2005. [6] Hallen, A. D., and C. Heegard, “Delayed Decision Feedback Sequence Estimation,” IEEE Trans. on Communications, Vol. 37, No. 5, May 1989, pp. 428–436. [7] Griffiths, L. J., and C. W. Jim, “An Alternative Approach to Linearly Constrained Beamforming,” IEEE Trans. on Antennas and Propagation, Vol. AP-30, No. 1, January 1982, pp. 27–34. [8] Karttunen, P., and R. Baghaie, “Conjugate Gradient Based Signal Subspace Mobile User Tracking,” Proc. IEEE Vehicular Technology Conference, Vol. 2, May 16–20, 1999, pp. 1172–1176. [9] Compton, Jr., R. T., Adaptive Antennas, Englewood Cliffs, NJ: Prentice-Hall, 1988. [10] Krim, H., and M. Viberg, “Two Decades of Array Signal Processing Research,” IEEE Signal Processing Magazine, Vol. 13, No. 4, July 1996, pp. 67–94. [11] Van Tree, H. L., Optimum Array Processing, New York: John Wiley & Sons.

Author Zhizhang Chen Isbn 9781596930896 File size 2.4MB Year 2010 Pages 193 Language English File format PDF Category Engineering and Technology Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare Direction-of-Arrival (DOA) estimation concerns the estimation of direction finding signals in the form of electromagnetic or acoustic waves, impinging on a sensor or antenna array. DOA estimation is used for location and tracking signal sources in both civilian and military applications. This authoritative volume provides an overview and performance analysis of the basic DOA algorithms, including comparisons between the various types. The book offers a detailed understanding of the arrays pertinent to DOA finding, and presents a detailed illustration of the ESPRIT-based DOA algorithms complete with their performance assessments. From antennas and array receiving systems, to advanced topics on DOA estimation, this book serves as a one-stop resource for professionals and students. It is suitable for electrical engineers whose work involves either civilian or military DOA estimation applications, as well as for graduate electrical engineering students in related courses.     Download (2.4MB) Sound Propagation through the Stochastic Ocean Harmonic Balance Finite Element Method Flexoelectricity In Solids: From Theory To Applications Sensor Array Signal Processing Analytical Modeling in Applied Electromagnetics Load more posts

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