Author | Zhizhang Chen | |

Isbn | 9781596930896 | |

File size | 2.4MB | |

Year | 2010 | |

Pages | 193 | |

Language | English | |

File format | ||

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
artechhouse.com
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, http://www.fcc.gov/e911/.
[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