- •Contents
- •Preface
- •1.1 Smart Antenna Architecture
- •1.2 Overview of This Book
- •1.3 Notations
- •2.1 Single Transmit Antenna
- •2.1.1 Directivity and Gain
- •2.1.2 Radiation Pattern
- •2.1.3 Equivalent Resonant Circuits and Bandwidth
- •2.2 Single Receive Antenna
- •2.3 Antenna Array
- •2.4 Conclusion
- •Reference
- •3.1 Introduction
- •3.2 Data Model
- •3.2.1 Uniform Linear Array (ULA)
- •3.3 Centro-Symmetric Sensor Arrays
- •3.3.1 Uniform Linear Array
- •3.3.2 Uniform Rectangular Array (URA)
- •3.3.3 Covariance Matrices
- •3.4 Beamforming Techniques
- •3.4.1 Conventional Beamformer
- •3.4.2 Capon’s Beamformer
- •3.4.3 Linear Prediction
- •3.5 Maximum Likelihood Techniques
- •3.6 Subspace-Based Techniques
- •3.6.1 Concept of Subspaces
- •3.6.2 MUSIC
- •3.6.3 Minimum Norm
- •3.6.4 ESPRIT
- •3.7 Conclusion
- •References
- •4.1 Introduction
- •4.2 Preprocessing Schemes
- •4.2.2 Spatial Smoothing
- •4.3 Model Order Estimators
- •4.3.1 Classical Technique
- •4.3.2 Minimum Descriptive Length Criterion
- •4.3.3 Akaike Information Theoretic Criterion
- •4.4 Conclusion
- •References
- •5.1 Introduction
- •5.2 Basic Principle
- •5.2.1 Signal and Data Model
- •5.2.2 Signal Subspace Estimation
- •5.2.3 Estimation of the Subspace Rotating Operator
- •5.3 Standard ESPRIT
- •5.3.1 Signal Subspace Estimation
- •5.3.2 Solution of Invariance Equation
- •5.3.3 Spatial Frequency and DOA Estimation
- •5.4 Real-Valued Transformation
- •5.5 Unitary ESPRIT in Element Space
- •5.6 Beamspace Transformation
- •5.6.1 DFT Beamspace Invariance Structure
- •5.6.2 DFT Beamspace in a Reduced Dimension
- •5.7 Unitary ESPRIT in DFT Beamspace
- •5.8 Conclusion
- •References
- •6.1 Introduction
- •6.2 Performance Analysis
- •6.2.1 Standard ESPRIT
- •6.3 Comparative Analysis
- •6.4 Discussions
- •6.5 Conclusion
- •References
- •7.1 Summary
- •7.2 Advanced Topics on DOA Estimations
- •References
- •Appendix
- •A.1 Kronecker Product
- •A.2 Special Vectors and Matrix Notations
- •A.3 FLOPS
- •List of Abbreviations
- •About the Authors
- •Index
30 |
Introduction to Direction-of-Arrival Estimation |
transmitting or receiving electromagnetic waves or radio signals. It can convert voltages/currents to electromagnetic waves and vice versa. Due to the fact that an antenna radiates its energy nonuniformly in space, parameters such as directivity, gain, and radiation pattern are often used to quantify performances of an antenna. Since an antenna is also fre- quency-selective, an equivalent circuit can be introduced to describe an antenna in terms of its terminal voltage and current. Because of the reciprocity of transmit and receive operations of an antenna, the performances of an antenna are often investigated for its transmit properties; the results can be directly used for an assessment of its receive performance.
There is a huge body of published literature on various topics of antennas. Such a large amount of available information usually gets a nonantenna specialist lost or confused in selecting a good text as a starting point. In order to avoid the similar confusion, we list only a single reference in this chapter. This reference is the excellent textbook by C. A. Balanis [1]; it presents an introduction to various topics of antenna technologies including the basic concepts of antennas and arrays; the contents of the book are very much sufficient for the potential readers of this book.
Reference
[1]Balanis, C. A., Antenna Theory: Analysis and Design, 3rd ed., New York: John Wiley & Sons, 2005.
3
Overview of Basic DOA Estimation
Algorithms
3.1 Introduction
This chapter presents an overview of some of the popular algorithms for DOA estimation. In general, the direction-of-arrival (DOA) estimation techniques can be broadly classified into conventional beamforming techniques, subspace-based techniques, and maximum likelihood techniques. This chapter is organized as follows. In Section 3.1, the signal and data model used in this book is described. A uniform linear array is used to explain this model. In Section 3.2, the concept of centro-symmetric sensor arrays, which are demanded by many DOA algorithms, is discussed. Two such arrays, uniform linear array (ULA) and uniform rectangular array (URA), are described. Later, the basic principles of a few basic algorithms belonging to each DOA class are briefly discussed.
An excellent doctoral dissertation on array signal processing for DOA estimations by M. Haardt was published by Shaker Verlag [1]. It presents a comprehensive review and study on one of the DOA techniques, the ESPRIT technique. This book uses it as one of the major references. In order to facilitate a reader in checking on this major reference without much confusion, this book employs the same mathematical symbols and technical terms as those in [1]; these symbols and terms have also been used in other related literature.
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