Carrier Frequency Offset Recovery For ZERO-IF OFDM Receivers

brief description

PERMISSION TO USE
In presenting this thesis in partial fulfillment of the requirements for a Postgraduate
degree from the University of Saskatchewan, it is agreed that the Libraries of this
University may make it freely available for inspection. Permission for copying of this
thesis in any manner, in whole or in part, for scholarly purposes may be granted by
the professors who supervised this thesis work or, in their absence, by the Head of the
Department of Electrical Engineering or the Dean of the College of Graduate Studies
and Research at the University of Saskatchewan. Any copying, publication, or use
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to the University of Saskatchewan in any scholarly use which may be made of any
material in this thesis.
Request for permission to copy or to make any other use of material in this thesis
in whole or in part should be addressed to:
Head of the Department of Electrical Engineering
57 Campus Drive
University of Saskatchewan
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S7N 5A9
i
ABSTRACT
As trends in broadband wireless communications applications demand faster de-
velopment cycles, smaller sizes, lower costs, and ever increasing data rates, engineers
continually seek new ways to harness evolving technology. The zero intermediate
frequency receiver architecture has now become popular as it has both economic and
size advantages over the traditional superheterodyne architecture.
Orthogonal Frequency Division Multiplexing (OFDM) is a popular multi-carrier
modulation technique with the ability to provide high data rates over echo ladened
channels. It has excellent robustness to impairments caused by multipath, which
includes frequency selective fading. Unfortunately, OFDM is very sensitive to the
carrier frequency offset (CFO) that is introduced by the downconversion process. The
objective of this thesis is to develop and to analyze an algorithm for blind CFO re-
covery suitable for use with a practical zero-Intermediate Frequency (zero-IF) OFDM
telecommunications system.
A blind CFO recovery algorithm based upon characteristics of the received signal’s
power spectrum is proposed. The algorithm’s error performance is mathematically
analyzed, and the theoretical results are verified with simulations. Simulation shows
that the performance of the proposed algorithm agrees with the mathematical anal-
ysis.
A number of other CFO recovery techniques are compared to the proposed algo-
rithm. The proposed algorithm performs well in comparison and does not suffer from
many of the disadvantages of existing blind CFO recovery techniques. Most notably,
its performance is not significantly degraded by noisy, frequency selective channels.
ii
ACKNOWLEDGMENTS
I would like to express my sincere gratitude and appreciation to my supervisor,
Dr. J. Eric Salt for his guidance, his teaching, and his continued patience and en-
couragement throughout the course of Graduate Studies.
I would also like to extend my thanks to the management and staff of TRLabs
(Saskatoon) for their technical support, for the excellent facilities that they made
available to me during the course of my research work, and for their financial assis-
tance in cooperation with The National Science and Engineering Research Council
(NSERC).
Finally, I would like to extend special thanks to my mother and my family, for
their continued love and endless encouragement. For without them, none of this
would have been possible.
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Table of Contents
PERMISSION TO USE i
ABSTRACT ii
ACKNOWLEDGMENTS iii
TABLE OF CONTENTS iv
LIST OF FIGURES viii
LIST OF TABLES xi
LIST OF ABBREVIATIONS xii
1 INTRODUCTION 1
1.1 Radio Frequency Receiver Design . . . . . . . . . . . . . . . . . . . . 1
1.2 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . . . 2
1.3 Carrier Frequency Offset Recovery . . . . . . . . . . . . . . . . . . . . 4
1.4 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 BACKGROUND INFORMATION 7
2.1 Receiver Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Superheterodyne Receiver . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Zero-IF Receiver . . . . . . . . . . . . . . . . . . . . . . . . . 9
iv
2.2 Broadband Wireless Access . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Wireless Channels . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . . . 11
2.3.1 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 OFDM Transmitter Model and Symbol Construction . . . . . 16
2.4 Carrier Frequency Offset . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 ALGORITHM AND ANALYSIS 22
3.1 Power Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.1 Generalized Length Power Spectrum Analysis . . . . . . . . . 27
3.2 Algorithm Description . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Overview and Block Diagram . . . . . . . . . . . . . . . . . . 30
3.2.2 Power Spectrum Estimator . . . . . . . . . . . . . . . . . . . . 31
3.2.3 Information Band Isolator . . . . . . . . . . . . . . . . . . . . 35
3.2.4 Carrier Frequency Offset Estimator . . . . . . . . . . . . . . . 38
3.3 Variance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 Variance Analysis of the Power Spectral Estimate . . . . . . . 39
3.3.2 Variance Analysis of the Carrier Frequency Offset Estimator . 43
4 ANALYSIS VERIFICATION VIA SIMULATION 51
4.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
v
4.1.1 OFDM Signal Characteristics . . . . . . . . . . . . . . . . . . 51
4.1.2 Channel Characteristics . . . . . . . . . . . . . . . . . . . . . 52
4.1.3 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Verification of Power Spectrum Estimator Characteristics . . . . . . . 54
4.2.1 Power Spectrum Estimator Mean . . . . . . . . . . . . . . . . 54
4.2.2 Power Spectrum Estimator Variance . . . . . . . . . . . . . . 56
4.2.3 Power Spectrum Estimator Pattern-Dependent Noise Distribu-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 System Parameter Effects on CFO Estimator Variance . . . . . . . . 57
4.3.1 Effects of the Cyclic Prefix Length . . . . . . . . . . . . . . . 59
4.3.2 Effects of the Number of Symbols Used in the Estimator . . . 60
4.3.3 Effects of Additive White Gaussian Channel Noise . . . . . . . 61
4.3.4 Effects of the Modulation Type . . . . . . . . . . . . . . . . . 62
4.3.5 Effects of the Carrier Frequency Offset Value . . . . . . . . . . 63
5 RESULTS 64
5.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1.1 Channel Characteristics . . . . . . . . . . . . . . . . . . . . . 65
5.2 Algorithm Performance Comparisons . . . . . . . . . . . . . . . . . . 70
5.2.1 CFO Estimation Based on Cyclic Prefix Correlation . . . . . . 70
5.2.2 CFO Estimation Based on Subspace Structure . . . . . . . . . 72
vi
5.2.3 CFO Estimation based on Power Spectral Estimation . . . . . 74
5.3 Performance Requirements for Practical Applications . . . . . . . . . 76
6 CONCLUSIONS AND FUTURE WORK 79
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
A MATLAB SOURCE CODE 86
vii
List of Figures
2.1 Superheterodyne receiver architecture . . . . . . . . . . . . . . . . . . 8
2.2 Zero-IF receiver architecture . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Sample IFFT output time sequences . . . . . . . . . . . . . . . . . . 13
2.4 DFT results for an sinusoid that is orthogonal over the interval shown 14
2.5 DFT results for an sinusoid with delayed samples from a previous symbol 15
2.6 DFT results for an sinusoid that is not orthogonal over the interval
shown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7 OFDM transmitter block diagram . . . . . . . . . . . . . . . . . . . . 17
2.8 Gray mapped QPSK and rectangular 16-QAM constellations . . . . . 18
2.9 OFDM message symbol spectral arrangement . . . . . . . . . . . . . 20
3.1 Illustration of the simplification of a double sum . . . . . . . . . . . . 25
3.2 Theoretical power spectrum with varied cyclic prefix length . . . . . . 28
3.3 Theoretical power spectrum with varied cyclic prefix length and CFO 28
3.4 Theoretical power spectrum with DFT length  varied . . . . . . . . 30
3.5 Overall block diagram of proposed CFO estimator . . . . . . . . . . . 31
3.6 Power spectrum partitioning . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 Block diagram of power spectrum estimator . . . . . . . . . . . . . . 32
viii
3.8 Illustration of data segmentation . . . . . . . . . . . . . . . . . . . . 33
3.9 Illustration of power spectrum sampling . . . . . . . . . . . . . . . . 34
3.10 Averaging effects of the DFT length . . . . . . . . . . . . . . . . . . . 36
3.11 Power spectrum partitioning with transition bands shown . . . . . . . 37
3.12 Diagram of CFO estimator block . . . . . . . . . . . . . . . . . . . . 38
4.1 OFDM symbol spectral arrangement . . . . . . . . . . . . . . . . . . 52
4.2 Comparison of simulated and theoretical power spectrum means in the
information band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 Comparison of simulated and theoretical power spectrum means in the
transition band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 Comparison of Simulated and Theoretical Power Spectrum Estimator
Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 PDF of one output point from the power spectrum estimator . . . . . 58
4.6 Effect of varying the cyclic prefix length for a symbol of 256 samples . 59
4.7 Effect of varying the number of symbols used in the CFO estimator . 60
4.8 Effect of varying the SNR . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1 Sample Frequency response for SUI-1 low delay channel model (hilly
terrain with high tree density) . . . . . . . . . . . . . . . . . . . . . . 66
5.2 Sample Frequency response for SUI-4 moderate delay channel model
(intermediate path-loss condition) . . . . . . . . . . . . . . . . . . . . 67
ix
5.3 Sample Frequency response for SUI-5 high delay channel model (flat
terrain with light tree density) . . . . . . . . . . . . . . . . . . . . . . 67
5.4 (a) Fourier series of the raised sinusoidal power spectrum; (b) Fourier
series of a multipath channel’s frequency response; (c) Fourier series of
the received power spectrum for a multipath channel . . . . . . . . . 68
5.5 Effects of multipath on simulated CFO estimator performance . . . . 69
5.6 Performance of cyclic prefix correlation based CFO estimator . . . . . 71
5.7 Performance of subspace structure based CFO estimator . . . . . . . 73
5.8 Proposed CFO estimator performance (SUI-4 channel) . . . . . . . . 75
5.9 Proposed CFO estimator performance (SUI-1 and SUI-5 channels) . . 75
5.10 Proposed algorithm performance for practical pequirements . . . . . . 78
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List of Tables
4.1 Simulation Reference Parameters . . . . . . . . . . . . . . . . . . . . 53
5.1 Multipath Channel Model Parameters . . . . . . . . . . . . . . . . . . 66
5.2 Tuning Parameters for Practical Performance Levels . . . . . . . . . . 77
xi
List of Abbreviations
A/D Analog to Digital
ASIC Application Specific Integrated Circuit
CFO Carrier Frequency Offset
D/A Digital to Analog
DFT Discrete Fourier Transform
DSP Digital Signal Processing
IQ In-Phase and Quadrature
ICI Inter-Carrier Interference
IDFT Inverse Discrete Time Fourier Transform
IEEE Institute of Electrical and Electronic Engineers
IF Intermediate Frequency
IFFT Inverse Fast Fourier Transform
ISI Inter-Symbol Interference
FDM Frequency Division Multiplexing
FFT Fast Fourier Transform
FPGA Field Programmable Gate Array
LAN Local Area Network
LO Local Oscillator
LOS Line of Sight
LNA Low Noise Amplifier
MAN Metropolitan Area Network
MSE Mean Squared Error
OFDM Orthogonal Frequency Division Multiplexing
xii
PSD Power Spectral Density
PSK Phase Shift Keying
QPSK Quadrature Phase Shift Keying
QAM Quadrature Amplitude Modulation
RF Radio Frequency
RFIC Radio Frequency Integrated Circuit
SAW Surface Acoustic Wave (Filter)
SNR Signal to Noise Ratio
SUI Standford University Interim (Channel Model)
xiii
1. INTRODUCTION
Technological advances over the past two decades have led to the rapid evolution
of the telecommunications industry. No longer limited to narrow-band voice signals,
modern communications integrate voice, images, data, and video on a level that was
once considered to be impossible. As applications demand faster development cycles,
smaller sizes, and ever increasing data rates, engineers continually seek new ways to
harness evolving technology.

bibliography

6.2 Future Work
Compared to other blind CFO recovery algorithms in the literature, the proposed
estimator is shown to perform very well in frequency selective channels. That said,
improvements to the proposed algorithm’s performance and mathematical charac-
terization could be investigated as a source of future work. In order to enhance
performance, alternate methods of spectral estimation could be examined. One ex-
ample would be to use overlapping and possibly windowed data segments as is done
in Welch’s method of spectral estimation [32]. It would also be beneficial to analyze
the variance of the estimator in greater detail given that overlapping and windowed
segments would introduce significantly more complex correlation between segments.
Similarly, the effects of multipath channels could be included throughout the entire
mathematical analysis.
82
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