Xiong, Hao (2013) Antenna array geometries and algorithms for direction of arrival estimation ...

115 Pages·2017·2.45 MB·English

by  Christine Middleton

THE UNIVERSITY OF NOTTINGHAM
DEPARTMENT OF ELECTRICAL AND ELECTRONIC
ENGINEERING

Antenna Array Geometries and
Algorithms for Direction
of Arrival Estimation

by Hao Xiong, BEng.
Supervised by Dr. Kristof Cools

Thesis submitted to the University of Nottingham for the degree of Master
of Science (by Research) in Electromagnetics Design
SEPTEMBER 2012
Abstract
Direction of arrival (DOA) estimation with the antenna array was a forever
topic of scientist. In this dissertation, a detailed comparison of the direction of
arrival (DOA) estimation algorithms, including three classic algorithms as
MUSIC, Root-MUSIC and ESPRIT, was performed and an analysis of various
array geometries’ (configurations) properties in DOA estimation was
demonstrated. Cramer-Rao Bound (CRB) was used for theoretic analysis and
Root Mean Square Error (RMSE), which determined the best performance for
a given geometry, regardless the specific estimation algorithm used, was
implemented in simulation comparison.
In the first part, MUSIC, Root-MUSIC and ESPRIT were illustrated, where
theoretic underlying of the algorithms were expressed by revisited, paseudo
code algorithms, and compared in the aspects of accuracy and computational
efficiency. Consequently, ESPRIT was found more efficient than the other two
algorithms in computation. However, the accuracy of MUSIC was better than
ESPRIT.
In the second part, four particular array geometries, including Uniform Circular
Array (UCA), L Shaped Array (LSA), Double L Shaped Array (DLSA) and
Double Uniform Circular Array (DUCA), were analyzed in the area of
directivity, accuracy and resolving ability. A simulation comparison of DOA
estimation with these four array geometries by MUSIC algorithm in two
dimensions was made then, since MUSIC had the best accuracy in these three
algorithms. According to the analysis and comparison, it was found that L
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Shaped Array (LSA) and Double L Shaped Array (DLSA) were more accurate
than others, considering both azimuth and elevation estimation. Also, in the
case of two dimensional DOA estimation, the Double L Shaped Array (DLSA)
was shown a theoretically relative isotropy to other array geometries. From the
simulation, the detection ability of Double L Shaped Array (DLSA) was
proved the best in the array geometries discussed in this dissertation.
These findings had significant implications for the further study of the array
geometry in DOA estimation.
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Acknowledgement
It is a pleasure to thank all of those who made this thesis possible. Firstly, I
would like to thank my supervisors, Dr. Kristof Cools and Dr. Ana Vukovic,
for their excellent guidance, support and encouragement. I have been greatly
inspired by their insightful knowledge and expertise. Special thanks are owed
to Professor Trevor Benson and Dr. Steven Greedy for their assistance and
suggestions. It has been a great pleasure working with the people in GGIEMR.
This thesis would not have been possible without the input from all of them.
The moral support from my friends and family has greatly motivated me and I
would like to show my gratitude to them for their wonderful love and support. I
sincerely thank my parents, Aiping Wu and Muchun Xiong, who have given
me the chance to research.
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List of Acronyms
1D One dimensional
2D Two dimensional
3D Three dimensional
BER Bit Error Rate
CRB Cramer-Rao Bound
CRLB Cramer-Rao Lower Bound
DLSA Double L Shaped Array
DOA Direction of Arrival
DUCA Double Uniform Circular Array
ESPRIT Estimation of Signal Parameters via Rotational Invariance
Techniques

L Shaped Array
LSA
Maximum-likelihood
ML
Maximum-likelihood Method
MLM
Multiple Signal classification
MUSIC
Minimum Variance Distortionless Response
MVDR
Quality of Service
QoS
Rectangular Array
RA
Root Mean Square Error
RMSE
Signal to Noise Ratio
SNR
Time Division-Synchronous Code Division Multiple Access
TD-SCDMA
Uniform Linear Array
ULA
Uniform Circular Array
UCA
Weighted Subspace Fitting
WSF
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YSA Y Shaped Array

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List of Symbols
A Magnitude of the wave function
Peak magnitude of the oscillation

A Relation among array elements matrix
⃗( ) Steering vector

⃗⃗ Magnetic field
Configuration matrix
B
Speed of light
c
Number of resources
D
d Ordinary Euclidean distance
Expectation operator
E[ ]
Eigenvector matrix
E
Noise subspace matrix

Electric field
⃗⃗
Null-space matrix
F
Incident signals matrix
Fi
Identity matrix
I
Fisher information function
Inf
Wave vector
⃗⃗⃗
Number of wave
k
Location of elements vector
⃗

Number of array elements
M
Noise signal
n
Probability density function
p
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R Covariance matrix
⃗ Radius vector
T Efficiency of CRB
T Transition matrix
U Incident angle matrix
V A random vector
⃗⃗ ( ) Unit vector pointing towards the dth source

W White random vector
X Received data complex vector
Permeability
Permittivity
Wavelength of the wave
Eigenvalue

Wave’s angular frequency
Wave phase shift with the units of radians
An unknown deterministic parameter
Inter element spacing
Subarray location matrix
( ) Propagation delay of source signal

Variance
Mean
Varying amplitude function
S Power spectral density function
Impulse function
Function of variance

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( ) Incident angle

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Contents
Abstract ................................................................................................................ i
Acknowledgement ............................................................................................. iii
List of Acronyms ............................................................................................... iv
List of Symbols .................................................................................................. vi
Contents ............................................................................................................. ix
Chapter 1 Introduction ........................................................................................ 1
1.1 The development of Smart Antenna ............................................................. 1
1.2 Smart Antenna in present age ....................................................................... 3
1.2.1 Smart Antenna and Antenna Array........................................................ 4
1.2.2 Types of Antenna Array ........................................................................ 4
1.2.3 Advantages and disadvantages of Antenna array .................................. 5
1.3 Comparison of Antenna Array and Ordinary Antennas ............................... 5
1.3.1 Efficiency and Power in space ............................................................... 6
1.3.2 Efficiency and power in Frequency ....................................................... 6
1.3.3 Estimation Time..................................................................................... 6
1.3.4 Capacity and Quality of Service (QoS) ................................................. 7
1.3.5 Conclusion ............................................................................................. 7
1.4 Outline of this dissertation ............................................................................ 7
1.5 Reference ...................................................................................................... 8
Chapter2 Problem Statement .............................................................................. 9
2.1 Direction of Arrival (DOA) estimation ........................................................ 9
2.2 Performance of eigendecomposition algorithms ........................................ 10
2.3 Property of array geometry ......................................................................... 10
2.4 Reference .................................................................................................... 11
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