Synchronization Algorithms and VLSI
Implementation for DC-OFDM based
UWB System
By
Jun Zhou
Supervisor: Prof. Junyan Ren
Examiner:
Thesis Period: Aug 2009 — Mar 2010
Department of Microelectronics,
School of Information Science and Technology
Fudan University, Shanghai, China
Royoal Institute of Technology (KTH), Stockholm, Sweden
Acknowledgments
First I would like to express my heartfelt appreciation to my advisor, Professor
Junyan Ren, who has been an excellent teacher and an inspiring advisor. His
constant encouragement and valuable advices have guided me throughout this
research work. His enthusiasm and devotion have always inspired me during my
hard times. What I have learned from him is an invaluable asset for my future.
I would like to thank Dr. Fan Ye for serving my academic committee. I also
acknowledge Professors Lirong Zheng, Shili Zhang, Hannu Tenhunen, Axel Jantsch,
Ahmed Hemani, C. M. Zetterling, Mats Brorsson, Mohammed Ismail and Shaofang
Gong for traveling hundreds and thousands of miles to China to teach me the most
valuable courses that I have taken at Fudan-KTH Joint Master Program.
I would like to thank Liang Liu for his stimulating discussions and generosity in
sharing his knowledge. I will always remember the colleagues from the digital group.
These people include Xuejing Wang, Jingfeng Li, Zhigui Liu, Cheng Zhang, Gan
Ouyang, Wenyan Su, Xu Shen, Chenxi Li, Wei Liang, Kai Li, Yu Nie and Yunqi
Zeng. I have learned a lot from their presentations and discussions. I cherish the
friendship and teamwork we have made during the past three years.
I would like to thank my girlfriend Yi Mao. I never feel lonely with her support,
patience, understanding and sacrifices. I also gratefully acknowledge my friends
Yuanwen Li, Xin Tian, Xiangxin Liu and Haixiang Bu, who create a pleasant
environment for living and studying.
Most of all, I would like to thank my parents sincerely for their unconditional
support, care and love throughout years. Without them, I would not have ventured so
far. I am honored to dedicate this thesis to them.
2
For my parents
I
Contents
Contents ........................................................................................................................ 2
List of Figures ............................................................................................................. III
List of Tables ................................................................................................................. V
List of Abbreviations .................................................................................................. VI
摘要 ............................................................................................................................... 1
Abstract ......................................................................................................................... 3
Chapter 1. ...................................................................................................................... 4
1.1 Background of UWB Communication ............................................................. 5
1.2 OFDM based UWB System ............................................................................. 7
1.3 Contributions of Thesis .................................................................................... 9
1.4 Organization of Thesis ................................................................................... 10
Chapter 2. ..................................................................................................................... 11
2.1 System Description ........................................................................................ 12
2.1.1. Receiver Architectures ........................................................................ 12
2.1.2. System Architecture ............................................................................ 14
2.1.3. UWB Channel ..................................................................................... 15
2.2 Signal Structure .............................................................................................. 17
2.2.1. Frame Structure ................................................................................... 17
2.2.2. Symbol Structure................................................................................. 18
2.2.3. System Parameters .............................................................................. 18
2.3 Conclusion ..................................................................................................... 21
Chapter 3. .................................................................................................................... 21
3.1 Synchronization Errors .................................................................................. 22
3.2 Symbol Timing Algorithm ............................................................................. 25
3.2.1. Packet Detection ................................................................................. 26
3.2.2. Coarse Timing ..................................................................................... 30
3.2.3. TFC Detection ..................................................................................... 34
3.2.4. Fine Timing ......................................................................................... 36
3.3 VLSI Implementation for Symbol Timing ..................................................... 40
3.3.1. Auto-correlation Algorithm ................................................................. 42
3.3.2. Cross-correlation Algorithm ............................................................... 43
II
3.3.3. Real-number Divider .......................................................................... 44
3.4 Conclusion ..................................................................................................... 45
Chapter 4. .................................................................................................................... 45
4.1 Analog Front-end Imperfections .................................................................... 46
4.1.1. Carrier Offset ...................................................................................... 46
4.1.2. Sampling Offset .................................................................................. 50
4.1.3. I/Q Imbalance ...................................................................................... 51
4.2 Performance Degradation .............................................................................. 54
4.2.1. Mathematics Model ............................................................................ 54
4.2.2. EVM Analysis ..................................................................................... 57
4.2.3. Simulation Results .............................................................................. 58
4.3 Algorithms ...................................................................................................... 60
4.3.1. I/Q Imbalance Estimation and Compensation .................................... 61
4.3.2. Joint Estimation and Compensation .................................................... 70
4.4 VLSI Implementation for CFO Cancellation ................................................. 79
4.5 Conclusion ..................................................................................................... 82
Chapter 5. .................................................................................................................... 82
5.1 Conclusion of Current Work .......................................................................... 83
5.2 Prospective Research Area ............................................................................. 84
5.2.1. Phase Noise ......................................................................................... 85
5.2.2. Non-linear Power Amplification ......................................................... 85
5.2.3. DC Offset ............................................................................................ 86
5.2.4. ADCs Mismatch .................................................................................. 86
Reference .................................................................................................................... 88
Acknowledgments ....................................................................................................... 92
III
List of Figures
Figure 1.1: FCC spectrum mask of UWB emission level. ............................................. 6
Figure 1.2: UWB applications ....................................................................................... 6
Figure 2.1: Superheterodyne receiver architecture ...................................................... 13
Figure 2.2: Direct conversion receiver architecture ..................................................... 14
Figure 2.3: Band group allocation in DC-OFDM based UWB system. ...................... 14
Figure 2.4: Block diagram for DC-OFDM base UWB system .................................... 15
Figure 2.5: PHY frame structure for DC-OFDM based UWB system ........................ 17
Figure 2.6: Symbol structure for DC-OFDM based UWB system .............................. 18
Figure 2.7: Frame structure for DC-OFDM base UWB system .................................. 19
Figure 2.8: Frequency hopping in DC-OFDM based UWB, TFC 9 ............................ 20
Figure 3.1: OFDM symbol structure (di denotes synchronization error) ..................... 23
Figure 3.2: Influence to constellation chart due to time synchronization error ........... 24
Figure 3.3: Channel estimation: ZP-OFDM system and CP-OFDM system............... 25
Figure 3.4: Power detection method, SNR=0dB, data rate 480Mbps, CM1. .............. 28
Figure 3.5: Auto-correlation method, SNR=0dB, 480Mbps, CM1. ............................. 29
Figure 3.6: Packet detection, SNR=5dB, 480Mbps, CM1. .......................................... 29
Figure 3.7: Packet detection, SNR=3dB, 200Mbps, CM2. .......................................... 30
Figure 3.8: Packet detection, SNR=3dB, 53.3Mbps, CM3. ......................................... 30
Figure 3.9: Timing sequence of packet detection and coarse timing ........................... 31
Figure 3.10: Process flow diagram of dynamic searching ........................................... 32
Figure 3.11: Coarse timing, SNR=5dB, 480Mbps, CM1............................................. 33
Figure 3.12: Coarse timing, SNR=3dB, 200Mbps, CM2. ........................................... 33
Figure 3.13: Coarse timing, SNR=3dB, 53.3Mbps, CM3. .......................................... 33
Figure 3.14: TFC searching chart for DC-OFDM UWB ............................................. 35
Figure 3.15: Standard Preamble 3 for TFC 3 or 9. ...................................................... 37
Figure 3.16: Cell structure in standard Preamble 3. ..................................................... 38
Figure 3.17: Fine timing, SNR=5dB, 480Mbps, CM1. ............................................... 39
Figure 3.18: Fine timing, SNR=3dB, 200Mbps, CM2. ............................................... 39
Figure 3.19: Fine timing, SNR=3dB, 53.3Mbps, CM3. .............................................. 40
Figure 3.20: Timing sequence for symbol timing module ........................................... 41
Figure 3.21: Signal processing flow for auto-correlation ............................................ 42
Figure 3.22: Hardware structure of cross-correlation cell ........................................... 43
IV
Figure 3.23: Hardware structure of cross-correlation. ................................................. 44
Figure 3.24: Signal processing flow for dual-bit division ........................................... 45
Figure 4.1: OFDM symbol spectrum with 3 sub-carriers. ........................................... 47
Figure 4.2: I/Q imbalance model in DCR. ................................................................... 52
Figure 4.3: Error vector magnitude definition ............................................................. 55
Figure 4.4: Simulated and analytical EVM versus SNR, 16-QAM. ............................ 59
Figure 4.5: Simulated and analytical EVM versus IRR, SNR=20dB. ......................... 60
Figure 4.6: Power spectral arrangement in OFDMsymbol .......................................... 62
Figure 4.7: Frequency domain illustration of the effect of I/Q imbalance .................. 63
Figure 4.8: Training scheme for both I/Q imbalance and channel estimation. ............ 64
Figure 4.9: QPSK modulation constellation. ............................................................... 64
Figure 4.10: SNR enhancement versus additional phase rotation. .............................. 66
Figure 4.11: MSE versus Eb/No for I/Q imbalance estimation, 480 Mbps. ................ 69
Figure 4.12: PER versus Eb/No, 16-QAM, 480 Mbps. ............................................... 70
Figure 4.13: MSE of CFO estimation versus SNR, 480 Mbps, CM1 .......................... 77
Figure 4.14: MSE of SFO estimation versus SNR, 480 Mbps, CM1 .......................... 78
Figure 4.15: PER versus SNR in DC-OFDM based UWB system. ............................. 78
Figure 4.16: Timing sequence for CFO estimation module ......................................... 80
Figure 5.1: 60-GHz wireless applications .................................................................... 84
V
List of Tables
Table 2.1: UWB channel model characteristics .......................................................... 16
Table 2.2: DC-OFDM UWB system parameters ........................................................ 19
Table 2.3: Cover sequence for standard preamble ...................................................... 19
Table 2.4: Time-frequency hoping code for DC-OFDM based UWB system ............ 21
Table 3.1: Synthesis result for symbol timing module ............................................... 41
Table 4.1: Peak-to-mean magnitude ratio for M-QAM scheme ................................. 56
Table 4.2: I/Q imbalance profiles ................................................................................ 59
Table 4.3: System parameters I ................................................................................... 69
Table 4.4: System parameters II .................................................................................. 76
Table 4.5: Front-end imperfection parameters at Carrier 1 for TFC 9 ........................ 76
Table 4.6: Synthesis result of CORDIC unit ............................................................... 81
Table 4.7: Synthesis result of CFO cancellation ......................................................... 81
VI
List of Abbreviations
ADC Analog to Digital Converter
AGC Auto Gain Control
AWGN Additive White Gaussian Noise
BPF Band-Pass Filter
CFO Carrier Frequency Offset
CIR Channel Impulse Response
CMOS Complementary Metal-Oxide Semiconductor
CP Cyclic Prefix
CPO Carrier Phase Offset
DAC Digital to Analog Converter
DCR Direct Conversion Radio
DFT Discrete Fourier Transform
DSP Digital Signal Processing
DSSS Direct Sequence Spread Spectrum
ECMA European Computer Manufactures Association
FIFO First in First out
EIRP Effective Isotropic Radiated Power
EVM Error Vector Magnitude
FCC Federal Communications Commission
FCS Frame Check Sequence
FFT Fast Fourier Transform
HCS Header Check Sequence
IBO Input Power Backoff
ICI Inter-Carrier Interference
IDFT Inverse Discrete Fourier Transform
I/Q In-phase and Quadrature-phase
IRR Image Rejection Ratio
ISI Inter-Symbol Interference
ITRS International Technology Roadmap for Semiconductors
LNA Low-Noise Amplifier
LO Local Oscillator
LOS Light of Sight
VII
LPF Low-Pass Filters
OFDM Orthogonal Frequency Division Multiplexing
PA Power Amplifier
PAPR Peak to Average Power Ratio
PLCP Physical Layer Convergence Protocol
SFO Sampling Frequency Offset
SINR Signal to Interference and Noise Ratio
SNR Signal to Noise Ratio
SoC System on Chip
SPO Sampling Phase Offset
TFC Time Frequency Code
UWB Ultra-wideband
VLSI Very Large Scale Integrated Circuit
ZP Zero Padding
1
摘要
超宽带(Ultra Wide Band,UWB)是一种适用于短距离、高速、无线数据
传输的技术。它能够在 2 米的室内多径环境中,提供最高 480Mbps 的传输速率。
超宽带技术在下一代无线个域网、无线家庭互联等领域拥有广泛的应用前景。
目前,WiMedia 联盟倡导的基于正交频分多路复用(MB-OFDM)技术的超宽
带架构被国际标准组织(ISO)采纳为超宽带国际标准。在中国,一种基于双载
波正交频分复用(DC-OFDM)技术的超宽带技术被采纳为中国超宽带标准草案。
这种双载波正交频分复用超宽带系统具有更多的频谱资源、较低的硬件要求等
优点,同时它兼容了 MB-OFDM 传输标准,具有较高的灵活性。
同步(Synchronization)处于接收机数字基带最前端,是任何无线通信系统
中不可或缺的过程。它的性能好坏直接决定了接收机能否正确接收射频信号,
基带模块能否有效完成数字信号处理功能。在基于 OFDM 技术的无线通信系统
中,同步过程大致分为两个部分:符号同步和频率同步。符号同步完成对经过
多径信道衰落影响的 OFDM 符号起始位置的判断。频率同步完成对模拟前端诸
多非理想因素干扰的估计和补偿。
本文围绕 DC-OFDM 超宽带系统中同步问题展开系统研究,首次分析了适
用于 DC-OFDM 超宽带系统的同步算法与硬件实现方法,并给出了同步模块的
VLSI 设计结果。论文整体分为符号同步和频率同步两个部分。
在符号同步方面,我们分析了多种同步误差对 OFDM 系统造成的性能影
响。然后,我们将整个符号同步过程按照功能划分为包检测、粗同步、时频码
检测和精细同步四个部分,并通过系统仿真确认每一部分的参数设置。算法设
计方面,我们采用了相关检测和能量检测相结合的方法来满足超宽带系统对于
室内多径环境下的要求,实现了较好的鲁棒性。硬件实现方面,我们重点介绍
了符号同步模块中重要的信号处理单元的结构和 VLSI 实现结果,如自相关器、
互相关器、实数除法器等。
在频率同步方面,我们首先分析了 OFDM 系统中多种模拟前端非理想因素
的影响,如载波频偏,采样频偏和 I/Q 失配,并给出了他们在 DC-OFDM 超宽
带系统中的数学模型。然后,我们采纳误差矢量幅度(Error Vector Magnitude,
EVM)作为参考,分析讨论了这些非理想因素对于 OFDM 系统性能的损失。射
频工程师可以通过本文的理论分析在失配参数与性能损失之间建立关联,从而
指导工程师在硬件设计的早期完成系统规划。算法设计方面,本文分析了 I/Q
失配引入镜像频率干扰的特点,继而设计了一种基于相位旋转的训练序列并给
出了相应的失配估计算法。仿真结果表明,新的训练序列能够获得 I/Q 失配过
2
程中引入的分集信息,从而使系统在解调过程中得到额外的分集增益。然后,
我们针对多种模拟前端非理想因素共存的复杂情形提出了一种联合估计和补偿
算法。硬件实现方面,我们给出了适合于 DC-OFDM 超宽带系统中载波频偏估
计和补偿模块的设计方法,并着重介绍了负责三角函数运算的 CORDIC 单元。
VLSI 实现结果表明,本文所设计的频率同步模块满足 DC-OFDM 超宽带系统的
时序和资源要求。
论文最后给出了未来的工作计划。在 60GHz 无线应用中将包括更多非理想
因素的影响,如相位噪声、非线性功率放大、直流偏移、ADC 偏差等。对于这
些非理想因素的联合估计和补偿将更具挑战性。
关键字:超宽带,正交频分复用,同步,VLSI 实现
中图分类号:TN492;TN919.72;TN919.3
3
Abstract
UWB is a promising technology for short-range high-rate wireless applications.
It is able to provide maximal 480Mbps data-rate at a distance of 2 meters in realistic
indoor multi-path environments. UWB technology is widely applied to the next
generation WPAN as well as the wireless access of consumer electronics at home.
Recently, Multi-Band OFDM based UWB technology proposed by WiMedia has
been selected as the international standard by ISO. In China, a new transmission
architecture based on Dual-Carrier OFDM technology is adopted as UWB standard
draft. Comparing to MB-OFDM based UWB system, DC-OFDM based UWB
system has multiple advantages, like more spectrum resource, lower requirements on
devices, etc. Besides, it is compatible with existing MB-OFDM based UWB
technology. Therefore, DC-OFDM based UWB is more flexible.
Synchronization is the first step at the receiver digital baseband, which is of
tremendous importance in any wireless communication systems. The performance of
synchronization directly determines whether the receiver can pick up radio signals
correctly or not, whether the baseband modules can fulfill the digital signal
processing effectively or not. The synchronization process in OFDM system can be
briefly divided into two parts: symbol timing and frequency synchronization.
Symbol timing serves to judge the starting position of OFDM symbols after
considering the impact of multi-path fading channel. While the frequency
synchronization estimates the multiple imperfections in analog front-end signal
processing and make proper compensation.
This thesis puts the emphasis on synchronization issues in DC-OFDM based
UWB systems. We are the first to analyze the synchronization algorithm as well as
the hardware implementation method tailored for DC-OFDM based UWB system.
We also present the VLSI implementation result for synchronization module. The
thesis consists of symbol timing and frequency synchronization.
Regarding on the symbol timing, we analyze the impact of several
synchronization errors in OFDM system. After that, we divide the synchronization
process into four modules by functionality: packet detection, coarse timing, TFC
detection and fine timing. The internal parameters in each module are determined by
system simulations. In the aspect of algorithm development, we adopt the joint
auto-correlation and cross-correlation method to meet the requirements of UWB
4
system in different indoor multi-path environments, and therefore achieve the
robustness. In the aspect of hardware implementation, we put the attention on the
structure of some key modules in symbol timing and their VLSI implementation
result, such as auto-correlator, cross-correlator, real-number divider, etc.
Regarding on the frequency synchronization, we first investigate the multiple
analog front-end imperfections in OFDM system, like CFO, SFO and I/Q imbalance,
and present their mathematics models respectively in DC-OFDM based UWB
system. After that, we analyze the performance degradation in OFDM system due to
these non-ideal effects by the metric of EVM. RF designer can build the connection
between mismatching parameters and performance degradation by referring to the
analysis. Hence, the RF designer is able to trace out the outline of system design. In
the aspect of algorithm development, we explore the intrinsic character of I/Q
imbalance which causes the image interference. Then, we design a set of new
training sequences based on phase rotation and give the corresponding estimation
algorithm. The simulation result shows that the new training sequence is able to
obtain the diversity message introduced by I/Q imbalance and therefore achieve the
diversity gain during demodulation process. In order to deal with the challenging
situation where multiple analog front-end imperfections co-exist, we propose a joint
estimation and compensation scheme. In the aspect of hardware implementation, we
present the hardware structure of CFO estimation and compensation module catered
for DC-OFDM based UWB system, with the emphasis on CORDIC unit that is
responsible for triangle calculations. The VLSI implementation result shows that the
proposed CFO estimation and compensation module satisfies the timing and
resource requirements in DC-OFDM based UWB system.
In the last, we present the prospective research area in 60-GHz applications. It
includes multiple non-ideal impairments, like phase noise, non-linear power
amplification, DC offset, ADCs mismatch, etc. It is even more challenging to
develop joint estimation and compensation scheme for these non-ideal effects.
Key words: UWB, OFDM, synchronization, VLSI implementation
CLC Number: TN492; TN919.72; TN919.3
Chapter 1
5
Chapter 1.
1.1 Background of UWB Communication
Ultra-wideband (UWB) is a promising radio technology owing to its potential
for very high data rate transmission at low power and with low implementation
complexity. Originated as a baseband, carrier free technology, UWB has mainly been
used in the intercept and detection for military and government communication
systems for the past two decades. In February 2002, the Federal Communications
Commission (FCC) allocated the frequency spectrum from 3.1 GHz to 10.6 GHz for
high-data-rate short-range UWB wireless communications [1]. It defines a signal to
be a UWB signal if its fractional bandwidth is greater than 20%, or its bandwidth is
greater than 500 MHz. The fractional bandwidth is calculated as
/ 2
H Lc
H L
f ff
f f
(1. 1)
where, Hf and Lf are the upper and lower -10 dB corner frequencies,
respectively. Figure 1.1 shows the FCC spectrum mask of UWB emission level for
indoor and outdoor handheld devices [1]. The Effective Isotropic Radiated Power
(EIRP) is limited to -41.3 dBm/MHz. All of the UWB devices must be confined
within this spectrum mask for legal operation. Moreover, at a low transmit power
level, the UWB signal will attenuate rapidly below the noise level in air when the
communication distance increases to longer than 10 meters. From the viewpoint of
narrowband system, such a low-power signal would appear as noise, which increases
the capacity of UWB system to co-exist with other narrowband systems.
Even at a low transmit power spectral density, the UWB system can afford a
high data rate up to 480 Mbps. This high data rate capability can be explained by
Shannon’s theorem, as shown below
2log (1 )C B SNR (1. 2)
where, C is the channel capacity of the communication link in bits per second,
B is the channel bandwidth, and SNR is the Signal to Noise Ratio at the detector
input. The channel capacity is linearly proportional to the channel bandwidth and
follows a logarithmic relation with SNR Therefore, when a very large bandwidth is
provided, only a small transmission power is required to achieve the high data rate.
Chapter 1
6
Figure 1.1: FCC spectrum mask of UWB emission level.
The large bandwidth, high data rate and low complexity advantages of the UWB
system have made it a promising candidate in industrial and commercial applications
such as medical imaging, ranging, construction applications and high-speed home or
office networking. Moreover, as shown in Figure 1.2, consumers can wirelessly and
rapidly share photos, music, video and voice data among their networked PCs,
mobile phones and consumer electronics such as DVD player and personal video
recorder, enabling the possible removal of all the wires to the printer, scanner,
mass-storage devices in the home office [2].
Figure 1.2: UWB applications
Chapter 1
7
1.2 OFDM based UWB System
Solutions targeting at addressing the physical layer design challenges in UWB
systems have been presented in many research literature and standardization
documents. In particular, two data transmission and detection schemes have been
proposed to the IEEE 802.15.3a Working Group as the potential physical layer
solution, i.e., the single carrier UWB using Direct Sequence Spread Spectrum (DSSS)
technology introduced by XtremeSpectrum [3] and the Orthogonal Frequency
Division Multiplexing (OFDM) technology supported by WiMedia [4].
In 2005, Multi-Band OFDM (MB-OFDM) based UWB PHY were adopted in
European Computer Manufactures Association (ECMA) standard [5]. It was also
accepted by ISO subsequently as international standard in 2007 [6]. Recently, the
MB-OFDM based UWB technology has been selected as the physical layer standard
of high data rate wireless specifications, such as Wireless Universal Serial Bus
(W-USB), Bluetooth 3.0 and Wireless High Definition Media Interface (W-HDMI)
[7]. In China, Dual-Carrier OFDM (DC-OFDM) based UWB technology is proposed
[8]. DC-OFDM based UWB PHY is similar with that of MB-OFDM based UWB
system, except that the former one occupies two carriers while the later one uses one
carrier when transmitting data. More bands are available to DC-OFDM based UWB
system comparing to MB-ODFM based UWB system. It means that DC-OFDM
based UWB system is more efficient in bandwidth utilization. Moreover, the
dual-carrier architecture decreases the sampling frequency at baseband from
528MHz to 264MHz. It relieves the timing requirements on high-frequency devices.
Besides these advantages, DC-OFDM based UWB technology is compatible with
existing MB-OFDM based UWB technology. Based on these reasons, the focus is
placed on the DC-OFDM based UWB systems in this thesis, especially on
synchronization issues. However, the mathematical models, theoretical analysis and
algorithms presented in this thesis can be extended to MB-OFDM based UWB
system directly.
After employing the OFDM modulation scheme, the DC-OFDM based UWB
systems should inhere the advantages of the OFDM technology. The unique merits
of the OFDM systems can be characterized as follows:
(1) Higher. The OFDM employs multi-carriers in order to transmit information
in parallel over the channel and sub-carriers are overlapped but orthogonal
Chapter 1
8
to one another. Therefore, data rate and bandwidth efficiency are
comparatively higher than the traditional single carrier transmission [9].
(2) Faster. The Discrete Fourier Transform (DFT) was applied to the
modulation and demodulation process [10]. Therefore, the processing
complexity of the OFDM can be alleviated by using Fast Fourier Transform
(FFT).
(3) Stronger. The OFDM uses zero prefix to eliminate the Inter-Symbol
Interference (ISI), so a reliable reception can be achieved. Furthermore, the
multi-carrier structure splits the available frequency spectrum into a
number of narrowband channels, which are known as sub-carriers. By
employing FFT technique to each of these sub-carriers, the OFDM is robust
against frequency selective fading channels [11].
Though a number of merits, there are several challenges in the DC-OFDM based
system. To begin with, DC-OFDM based UWB system provides only four preambles
for synchronization purpose, including symbol timing and frequency
synchronization. The tight timing sequence is a challenge in DC-OFDM based UWB
system design. Therefore, we need a robust and efficient synchronization scheme.
Moreover, DC-OFDM based UWB system is sensitive to multiple non-ideal effects
in analog front-end processing, such as Carrier Frequency Offset (CFO), Sampling
Frequency Offset (SFO) and In-phase and Quadrature-phase (I/Q) imbalance [12],
[13]. Being a multi-carrier system, a major disadvantage of OFDM is its sensitivity
to frequency offsets. CFO is usually caused by frequency error between the Local
Oscillators (LO) at the transmitter and receiver and/or by Doppler shift. SFO is
caused by sampling frequency error between the Analog to Digital Converter (ADC)
in the transmitter and the Digital to Analog Converter (DAC) in the receiver.
Frequency offsets cause the loss of orthogonality among sub-carriers and result in a
number of impairments, including amplitude attenuation of the desired signal and
Inter-Carrier Interference (ICI) [14]. Meanwhile, the Direct Conversion Radio (DCR)
architecture [15] is currently seen as one of the most promising candidates for
low-cost, low-power, and small-size System on Chip integration [15], [16]. Owning
multiple advantages, DCR architecture is favored by UWB system. Unfortunately,
DCR architecture suffers from analog front-end component mismatch, such as I/Q
imbalance [13]. For the wideband system, the I/Q imbalance can be categorized into
two types with different frequency characteristics. The imbalance from LO, known
Chapter 1
9
as imperfect 90 degree phase shift and unequal amplitudes, which is constant over
signal bandwidth thus frequency independent. Another type is named as frequency
dependent imbalance, caused by In-phase and Quadrature-phase branch components
with mismatched frequency response. The estimation and compensation to CFO and
SFO with the presence of frequency dependent I/Q imbalance poses another
challenge in DC-OFDM based UWB system.
In the DC-OFDM based UWB system, the carrier frequency can reach ten
gigahertz. Achieving two orthogonal signals for LO at such a high frequency should
be a challenging task for silicon implementation. Integrated circuit technologies such
as low-cost Complementary Metal-Oxide Semiconductor (CMOS) technology have
considerable mismatches between components due to fabrication process variations
including doping concentration, oxide thickness, mobility, and geometrical sizes over
the chip [17]. Generally, different LOs are used at transmitter and receiver sides,
which results in CFO and SFO. Besides, analog circuits are sensitive to the
component variations, there will be unavoidable errors in analog front-end signal
processing due to process mismatches and temperature variations. As stated in the
2008 edition of International Technology Roadmap for Semiconductors (ITRS-2008)
[18], a number of challenges lie in yield enhancement. For near-term with 32-nm
technology node and above, the process stability versus absolute contamination level
including the correlation to yield is critical in actual implementation. The maximum
process variation needs to be well controlled. Besides, test structures, methods and
data are needed for correlating defects caused by wafer environment and handling
with yield. For long-term with 22-nm technology node and beyond, we will encounter
non-visual defects and more severe process variations. The defects and process
variations require new approaches in methodologies, diagnostics and control. The
irregularity of features in logic areas makes them very sensitive to systematic yield
loss mechanism. Therefore, an efficient digital-assistant algorithm to compensate the
process variation as well as inherent bias of individual devices is essential and exigent
for hardware implementation of the DC-OFDM based UWB system.
1.3 Contributions of Thesis
In this thesis, the focus is placed on the synchronization problems in the
DC-OFDM based UWB system, including symbol timing and frequency
synchronization. The main contributions of this thesis are listed as follows:
Chapter 1
10
(1) Development of symbol timing algorithm and hardware implementation for
DC-OFDM based UWB system. The algorithm meets the tight timing
requirements in DC-OFDM based UWB system. Simulation shows that the
proposed symbol timing scheme owns very good robustness in different
UWB channel environments. Besides, hardware reuse between different
modules dramatically decreases the implementation complexity and chip
area.
(2) Construction of a mathematical models for analog front-end imperfections
(CFO, SFO and I/Q imbalance) in DC-OFDM based UWB system. Based
on these models, we establish analysis for performance degradation due to
these three analog front-end imperfections. Theoretical analysis is derived
to evaluate the distortion by the metric of Error Vector Magnitude (EVM).
As the design constraint, RF designers can straightforwardly figure out the
tolerant distortion by referring to these equations.
(3) Development of a set of algorithms for CFO, SFO and I/Q imbalance in
DC-OFDM based UWB system. Firstly, we investigate the I/Q imbalance
in OFDM system and design a new training sequence which is able to
obtain the diversity message introduced by I/Q imbalance. Then we present
a joint estimation and compensation scheme for CFO and SFO with the
presence of I/Q imbalance. Preambles are used for imperfections estimation.
After that, the spread information within packet header is used to track the
phase distortion caused by residual CFO and SFO. The hardware
implementation of CFO estimation is presented. The synthesis result by
Design Compiler shows the design meets the timing requirement.
1.4 Organization of Thesis
As stated above, the thesis places the attention on the synchronization problems
in DC-OFDM based UWB system, including symbol timing and frequency
synchronization. In Chapter 2, we present the fundamental architecture of
DC-OFDM based UWB system, with the emphasis on OFDM signal structure. In
Chapter 3, we propose a symbol timing scheme tailored for the limited training
sequence in DC-OFDM based UWB system. Both of the algorithms and hardware
implementation are presented. In Chapter 4, we investigate multiple analog front-end
imperfections in DC-OFDM based UWB system. For systematic study, this chapter
Chapter 1
11
is divided into three parts. Firstly, we construct the mathematics model for CFO,
SFO and I/Q imbalance effects in the wideband OFDM system. Secondly, we
analyze the performance degradation due to these analog front-end imperfections by
the metric of EVM. Thirdly, we design a set of algorithms to estimate and
compensate the multiple non-ideal effects. In Chapter 5, we give the conclusion and
some prospective research areas in the future 60-GHz applications.
Chapter 2
12
Chapter 2.
In this chapter, we present the system architecture for DC-OFDM based UWB
applications. Firstly, we describe the system block diagram in UWB physical layer,
including receiver architectures, system components and wireless channels. This
section shows a brief picture on the area we are interested in. Secondly, we introduce
the signal structure of DC-OFDM based UWB system. Thirdly, we introduce some
important parameters focused on synchronization issues. Without special notation,
these parameters represent the same throughout the thesis. As we can see, the very
limited synchronization resource calls for very efficient synchronization scheme,
which serves as the motivation of Chapter 3. Thirdly, we analyze the characteristics
of UWB channel.
2.1 System Description
2.1.1. Receiver Architectures
Generally, digital communications receivers are divided into analog portion and
digital portion. The main duty of analog portion is to down-convert the Radio
Frequency (RF) signal to a frequency that can be sampled by a commercially
available Analog to Digital Converter (ADC). Because of the powerful Digital Signal
Processing (DSP) algorithms, virtually all of the signal processing is done in the
digital domain. However, the analog down conversion stage introduces several
non-ideal effects and determines the nature of the input data as well as its impairments
introduced by non-ideal effects. In this section we compare the classical
superheterodyne receiver architecture with that of a Direct Conversion Receiver
(DCR). This enables an appreciation of the advantages of the DCR architecture which
is adopted in DC-OFDM based UWB system. Furthermore, it allows for a better
understanding of the analog front-end imperfections that the thesis focuses on.
2.1.1.1 Superheterodyne Receiver
Figure 2.1 shows the architecture of a typical superheterodyne receiver. The main
components in superheterodyne receiver are Band-Pass Filter (BPF), Low-Noise
Chapter 2
13
Amplifier (LNA), mixer and ADC. As is illustrated in the figure, the received signal
first passes through a band-pass Radio Frequency (RF) filter. This is a broadband
filter with the purpose to reduce the power of out-of-band signals which would
otherwise cause the LNA to saturate.
Figure 2.1: Superheterodyne receiver architecture
When the received signal is down-converted by mixer at the receiver side, both of
the desired Intermediate Frequency (IF) signal and an undesirable image response are,
| |IF c LOf f f (2. 1)
2 ;
2 ;
c IF LO
image
c IF LO
f f f ff
f f f f
(2. 2)
The selected intermediate frequency and the IF band-pass filter must satisfy the
following requirements [19]:
(1) The IF filter should provide steep attenuation outside the bandwidth of the IF
signals. This requires a relatively low IF, because such a filter is easier to be
realized with practical components.
(2) The IF filter should reject the image response as well as the other spurious
responses caused by mixer. This requires a relatively high IF, which causes
the two image frequencies are far enough apart.
(3) A stable and economical high-gain IF amplifier should be taken into account
when choosing the proper intermediate frequency.
We note that, as carrier frequency increases, many systems adopt multiple IF
stages in cascade in order to sufficiently satisfy the above considerations. Therefore,
superheterodyne receiver usually costs high.
2.1.1.2 Direct Conversion Receiver
The Direct Conversion Receiver (DCR), which is also known as homedyne or
Chapter 2
14
zero-IF receiver, is a special case of the superheterodyne receiver when LO has the
same frequency as the carrier. DCR generates both In-Phase and Quadrature-Phase
(I/Q) signals to differentiate between signal components above and below the LO
frequency. If the radio frequency signal is translated directly to baseband, the IF filters
are not required. Instead, Low-Pass Filters (LPF) can be used. The LPF in DCR has
lower power consumption, smaller size, higher reliability, easier for integration, and
high system flexibility than IF filters used in the superheterodyne architecture. Figure
2.2 shows the basic architecture for DCR.
Figure 2.2: Direct conversion receiver architecture
DCR owns the simplified RF front end, which makes it very attractive in UWB
applications. However, there are several challenges for system design. Care must be
taken to I/Q imbalance caused by the mismatches of front-end components.
Fortunately, a number of digital algorithms can be used to reduce or to eliminate the
imperfection.
2.1.2. System Architecture
Figure 2.3 shows the band group allocation in DC-OFDM based UWB system.
According to [8], the operating bandwidth consists of two parts: 4.2GHz~4.8GHz
and 6.0GHz~9.0GHz. Each part includes several 264MHz subbands. The first two
subbands form the band group 1, while the rest ten subbands form the band group 2.
Figure 2.3: Band group allocation in DC-OFDM based UWB system.
DC-OFDM based UWB system has many similarities with the traditional
Chapter 2
15
OFDM system. It adopts Time Frequency Code (TFC) as the frequency hopping
indicator. The OFDM symbols are allocated to different carriers for transmission at
different time according to specific TFC. In any time, DC-OFDM based UWB
system occupies two subbands for transmission. However, the whole bandwidth for
signal transmission in one carrier is 264MHz.
DC-OFDM based UWB system supports multiple data rates for practical
applications: 53.3Mbps, 80Mbps, 106.7Mbps, 160Mbps, 200Mbps, 320Mbps,
400Mbps and 480Mbps.
The fundamental architecture of DC-OFDM based UWB system is illustrated in
Figure 2.4. For simplicity, only one carrier is presented. As shown, the system is
briefly divided into three sections: digital baseband, AD/DA converters and
radio-frequency components. The digital baseband components at the transmitter
side are made up of scrambler, convolution encoder, interleaver, mapping, IFFT,
Insert ZP, generate preamble, etc. The modules at the receiver side are similar, but
with function reversed. The AD/DA converters work as the connection between
analog and digital domain. The radio-frequency components include band filter,
mixer, amplifier, etc. Typical DCR is adopted in UWB transceiver for low-cost
implementation.
Figure 2.4: Block diagram for DC-OFDM base UWB system
2.1.3. UWB Channel
The physical transmission medium in wireless applications, which is also known
Chapter 2
16
as the channel, is the air through which electromagnetic signals are broadcast. The
channel is divided into generalized electromagnetic frequency bands.
In this section, we will explore the characteristics of UWB channel. As well
acknowledged, channel is an indispensable part of wireless communication system,
and its time-frequency characteristics have an influence on system components and
the performance directly. UWB channel is a relatively new in literatures, catering for
short-range indoor environment. How to build a proper and efficient channel model
is very important to system design. Currently, there are several UWB channel
models available, such as multi-path model proposed by Intel [20], Scholtz model
[21] and AT&T model [22]. IEEE P802.15 Working Group summarizes the work of
channel modeling and provides the final recommendation for UWB channel [23]. In
order to keep concise and comparable, we only introduce the channel model
proposed by IEEE 802.15.3a Working Group. The simulations and analysis are all
based on this channel model, if without special note.
UWB channel is characterized as the clustering of multi-path arrivals and
log-normal amplitude distribution [20]. [24] describes the UWB channel model,
denoted as channel model one to channel model four (CM1~ CM4) for different
channel environments, Light of Sight (LOS) or Non-Light of Sight (NLOS). Table
2.1 summarizes the typical characteristics of UWB channel models.
Table 2.1: UWB channel model characteristics
Channel Model Characteristics
CM1 LOS, 0-4m
CM2 NLOS, 0-4m
CM3 NLOS, 4-10m
CM4 Extreme, NLOS multipath
The IEEE 802.15.3a UWB RF channel model is given by
, ,
0 0
( ) ( )hL K
RF k l l k l
l k
h t X t T
(2. 3)
where lT , ,k l and X are random variables representing the delay of the thl
cluster, the delay of the thk multi-path component of the thl cluster, and the
log-normal shadowing respectively. The channel coefficients are defined as a
product of small-scale and large-scale fading coefficients, i.e. , , ,k l k l l k lp . The
Chapter 2
17
small-scale coefficient is ,k lp , which takes on equiprobable 1 to account for
signal inversion due to reflections. The large-scale coefficient is ,l k l , which is
log-normal distributed path gains.
In this thesis, we consider a low-pass equivalent system that absorbs the carrier
frequency hopping into the Channel Impulse Response (CIR). The sample-spaced
low-pass equivalent CIR for the thq band is given by
,2 ( )
, , 0
0 0
( ) ( )h
q l k l
L Kj f T
q k l s l k l
l k
h n X e p nT T t
(2. 4)
where the effect of the combined transmit and receive filter with the impulse
response ( )p t whose span is 0 0[ , ]t t has been included in the CIR, and the delay
0t is inserted for the causality. Details of the channel models are referred to [25] and
references therein.
2.2 Signal Structure
2.2.1. Frame Structure
Figure 2.5 shows the structure of a PHY frame [8]. Generally, one frame
consists of Preamble, Physical Layer Convergence Protocol (PLCP) Header, Frame
Payload, Frame Check Sequence (FCS), Tail Bits and Pad Bits. There are two types
of preamble: Standard and Burst. In this thesis, we explore the characteristics of
standard preamble. The PLCP header is protected by a Header Check Sequence
(HCS). FCS follows its Frame Payload.
Figure 2.5: PHY frame structure for DC-OFDM based UWB system
Data transmission is based on frame from the source device to the destination
device in identical bit order. The start of a frame refer to the leading edge of the first
symbol and the end of a frame refers to the tailing edge of the last symbol.
Chapter 2
18
2.2.2. Symbol Structure
OFDM symbol is the basic cell of frame. The DC-OFDM based UWB system
adopts standard multi-band OFDM modulation, and the modulation length is 128. In
time domain, each symbol consists of 128 data bits. In frequency domain, it means
each subband consists of 128 sub-carriers. As each subband is 264MHz, inter-carrier
spacing subf equals 2.062MHz.
1 1sub
s
fNT T
(2. 5)
where T is the sampling period, N is the number of sub-carriers and sT is
the symbol period. The structure of discrete OFDM symbol is shown in Figure 2.6.
ix n denotes the thn sample in thi OFDM symbol, 0 1n N .
0 1 1i i i ix x x x N (2. 6)
Traditionally, cyclic prefix is added before data symbol to form a complete
OFDM symbol. The cyclic prefix for thi OFDM symbol ip is made up of the
latest gN samples in ix
g g 1 1i i i ip x N N x N N x N
(2. 7)
Therefore, the whole length for an OFDM symbol is gN N .
Figure 2.6: Symbol structure for DC-OFDM based UWB system
2.2.3. System Parameters
In this section, we will introduce some important system parameters and several
important parameters for synchronization issues, such as preamble structure, TFC.
Table 2.2 shows some system parameters in DC-OFDM based UWB system.
Packet-based transmission is adopted in DC-OFDM based UWB system. From
the purpose of synchronization, the frame structure for DC-OFDM based UWB
system is illustrated in Figure 2.7.
Chapter 2
19
Table 2.2: DC-OFDM UWB system parameters
Parameters Value
N :Sub-carrier Number 128
B :Sub-band Bandwidth 264MHz
F :Sub-carrier Spacing 2.0625MHz(= B N )
FFTT :IFFT/FFT Period 484.8ns(=1 F )
ZPT :Zero Padding Length 121.2ns(= 32 B )
GIT :Guard Interval Length 18.94ns(= 5 B )
SYMT :Symbol Interval 625ns(=FFT ZP GIT T T )
Figure 2.7: Frame structure for DC-OFDM base UWB system
In each packet, a group of 20 OFDM preamble symbols is added before data
symbols. Of the 20 preambles, the first 16 identical preamble symbols are assigned
for packet detection, time synchronization, frequency synchronization and Auto Gain
Control (AGC). The next 4 preamble symbols are assigned for channel estimation.
The data symbols including frame header and frame payload are transmitted after the
preamble group.
In preamble group, all preambles are identical with the same absolute value, but
the sign of samples may be exactly opposite due to cover sequence. Table 2.3 shows
the cover sequence for standard preambles.
Table 2.3: Cover sequence for standard preamble
m Scover[m], TFC=1,2,8,9 Scover[m], TFC=3,4,10,11 Scover[m], TFC=5,6,7,12,13
0 1 1 -1
1 1 1 -1
2 1 1 -1
3 1 1 -1
4 1 1 1
5 1 1 -1
Chapter 2
20
6 1 1 1
7 1 1 -1
8 1 1 1
9 1 1 -1
10 1 1 1
11 1 1 -1
12 1 1 -1
13 1 -1 1
14 -1 1 -1
15 -1 -1 1
Before sending the UWB signal to transmission antenna, the baseband signal
should be up-converted to the carrier frequency. In the proposed DC-OFDM based
UWB system, the whole frequency band are divided into twelve subbands for data
transmission. Each subband has a central carrier frequency cf . In the every moment
of data transmission, two subbands are picked out and occupied according to a
defined set of time-frequency hopping code (TFC). After that, each OFDM symbol
is transmitted subsequently in different subbands. Generally, TFC describes the
transmission subband selected by transmitter and its order for occupation. The
DC-OFDM based UWB system adopts a transmission scheme with four-step
hopping. It means that of the total twenty preambles, there are only four preambles
in each selected subband available for synchronization purpose, and only one
preamble for channel estimation purpose.
Table 2.4 describes the TFC defined by DC-OFDM based UWB system [8].
Figure 2.8: Frequency hopping in DC-OFDM based UWB, TFC 9
Chapter 2
21
Table 2.4: Time-frequency hoping code for DC-OFDM based UWB system
DC-TFC Index Preamble Index DC-TFC Subband Index
1 1 (1,2) (1,2) (1,2) (1,2)
2 2 (3,5) (4,6) (7,9) (8,10)
3 3 (3,5) (4,6) (8,10) (7,9)
4 4 (3,5) (7,9) (4,6) (8,10)
5 5 (3,5) (7,9) (8,10) (4,6)
6 6 (3,5) (8,10) (4,6) (7,9)
7 7 (3,5) (8,10) (7,9) (4,6)
8 2 (3,7) (4,8) (5,9) (6,10)
9 3 (3,7) (4,8) (6,10) (5,9)
10 4 (3,7) (5,9) (4,8) (6,10)
11 5 (3,7) (5,9) (6,10) (4,8)
12 6 (3,7) (6,10) (4,8) (6,10)
13 7 (3,7) (6,10) (6,10) (4,8)
14 1 (11,12) (11,12) (11,12) (11,12)
Figure 2.8 shows the transmission of OFDM symbols corresponding to TFC=9
for Band Group 2 in [8]. As one part of time synchronization, TFC should be
detected correctly in order to guarantee the receiver works properly. In Chapter IV,
we introduce the details of the proposed TFC detection mechanism.
2.3 Conclusion
In this chapter, we introduce the fundamental information of DC-OFDM based
UWB system. Block diagram of DC-OFDM based UWB PHY layer is presented. We
put the emphasis on the system structure and parameters that cast impact on the
synchronization. The UWB channel models are also introduced to evaluate the
system performance. Without special notes, all analysis and simulations in this thesis
are carried out in typical DC-OFDM based UWB system presented in this chapter.
Chapter 3
22
Chapter 3.
In communication system, signals are passed on from one terminal to another,
which are generally separated in a certain distance. Synchronization is a fundamental
function that guarantees the system performance. No matter the terminals are
connected by wireline or wireless, one special mechanism is required to compensate
the time delay, phase shift, frequency offset and to guarantee the proper
synchronization. From the OFDM system perspective, the whole process of
synchronization can be briefly divided into two parts: symbol timing and frequency
synchronization. As the first module in receiver baseband, symbol timing serves to
judge when receiver should wake up to accept the signals, when an OFDM symbol
begins, and when it ends after considering the impact of multi-path channel. In this
chapter, we focus on symbol timing issues, which is also known as time
synchronization. The frequency synchronization is presented in the Chapter 4.
This chapter is organized as follows. Firstly, we investigate the symbol timing
errors, and show that synchronization error may introduce Inter-Symbol Interference
(ISI). Secondly, we explore the algorithms in symbol timing, which are presented in
the sequence of signal processing in receiver baseband. Algorithms are proposed for
symbol timing in DC-OFDM based UWB system, which caters for the limited
system resource. Thirdly, we give Very Large Scale Integrated Circuit (VLSI)
implementation of the symbol timing modules. Synthesis result shows the hardware
design satisfies the system requirements.
3.1 Synchronization Errors
In OFDM system, symbol timing process is also known as time synchronization.
OFDM symbol is the basic processing unit in OFDM system. The symbol structure
has been introduced in Chapter 2. Nearly all modules in digital baseband need the
exact position of the leading edge and tailing edge of a symbol. Although OFDM is
well known for its ability to mitigate the impact of ISI introduced by multi-path
channels [11], incorrect positioning of the FFT window within an OFDM symbol
reintroduces ISI during data demodulation, causing serious performance degradation
[26], [27]. In this part, we will explore the ISI influence due to time synchronization
error.
Chapter 3
23
Figure 3.1 describes the structure of discreet OFDM symbol after sampling.
Recall the expression of OFDM signal in time domain in (2.6), 0 1n N .
0 1 1i i i iy y y y N (3. 1)
The cyclic prefix for thi OFDM symbol ip is made up of the latest gN
samples in iy
g g 1 1i i i ip y N N y N N y N
(3. 2)
Therefore, the whole length for an OFDM symbol is gN N .
Figure 3.1: OFDM symbol structure (di denotes synchronization error)
Then we analyze the synchronization error in the following two cases.
A. Synchronization position falls in cyclic prefix.
In this case, FFT input window acquires id points in thi cyclic prefix and the
other iN d points in thi data symbol. Here, we define id N
, 1 , , 1 , 0 , 1 , , 1i i i i i i i i i iw y N d y N d y N y y y N d (3. 3)
According to the cyclic characteristic of FFT, the signal after FFT processing
can be denoted as
2 /ij kd N
i iY k Y k e
(3. 4)
where iY k is the FFT output when perfect synchronization is obtained. In
(3.4), a phase rotation of 2 /ikd N is added to the signal of thk subcarrier. This
phase rotation can be compensated during channel equalization in frequency domain.
Suppose the frequency response of practical channel is H k , and the
estimated result is H k
2 /ij kd Ni
i
Y kH k H k e
X k
(3. 5)
Chapter 3
24
After channel equalization, the baseband signal is
iY k
X k X kH k
(3. 6)
From (3.6), we can see the receiver can demodulate the OFDM signal correctly.
In other word, if the synchronization position falls in the cyclic prefix, and satisfies
the constraint g iN d L ( L denotes the length of channel response),
synchronization error does not affect system performance.
B. Synchronization position falls out of cyclic prefix.
In this situation, synchronization position falls in the data symbol, and part of
the next symbol data is forwarded to FFT module. The FFT input signals is
1 1 1, 1 , , , , 1 , , 1i i i i i i i g i g i g iw y d y d y N y N N y N N y N N d
(3. 7)
After FFT processing,
2 /ij kd N
i i iY k Y k ISI k e
(3. 8)
1
2 /
1
0
idj km N
i i g i
m
ISI k y m N N y m e
(3. 9)
Therefore, phase rotation as well as ISI will be added simultaneously to thk
subcarrier of thi symbol. It is the ISI that causes sever performance degradation in
OFDM system.
Synchronization position (a) falls within cyclic prefix (b) falls out of cyclic prefix
Figure 3.2: Influence to constellation chart due to time synchronization error
(subcarrier number N=2048, cyclic prefix length L=128, 64-QAM, normalized error 36)
Chapter 3
25
Figure 3.2 describes the changes on constellation chart due to time
synchronization error. In (a), synchronization position falls within the Cyclic Prefix
(CP). Based on the above discussion, only phase rotation is added to the received
symbol, which will not cause ISI. Therefore, the constellation chart displays several
circles; In (b), synchronization position falls out of the cyclic prefix. We can find
that the constellation chart is completely blurred due to ISI.
To conclude, the correct symbol timing returns the symbol start position within
its cyclic prefix, while the incorrect positioning falls out of it.
Special note should be given that some OFDM based communication system,
like DC-OFDM based UWB system, use Zero Padding (ZP) rather than CP based on
the consideration of power spectrum. However, it does not affect the conclusion
above. Regarding ZP system, one more processing should be carried out before
channel estimation: the first gN samples in thi data symbol should add the ZP
samples in ( 1)thi OFDM symbol. The processed OFDM symbol owns the same
characteristics as CP-OFDM symbol. Figure 3.3 shows the detailed processing.
Figure 3.3: Channel estimation: ZP-OFDM system and CP-OFDM system
3.2 Symbol Timing Algorithm
In digital receivers, symbol timing can be carried out either in a feedforward or
feedback mode. Although feedback schemes archive good tracking performance,
they normally require a relatively long acquisition time. In DC-OFDM based UWB
system, very limited training symbols are provided for each subband synchronization.
Therefore, feedforward synchronization schemes are more suitable.
In literature, there are a number of methods have been proposed for OFDM
symbol timing. Methods that exploit the periodic structure of cyclic prefixes in
Chapter 3
26
OFDM symbols have been proposed in [27], [28]. Utilizing the repeated preambles,
the authors of [29], [30] propose the data-aided algorithms. Although the techniques
of [27]-[30] may be applied to DC-OFDM based UWB system, a higher
synchronization scheme is required for high-speed low-power transmission.
In this section, we introduce the proposed time synchronization scheme catered
for DC-OFDM based UWB system. Time synchronization can be briefly divided
into several parts: packet detection, coarse timing, TFC detection, and fine timing.
Note that in frequency hopping system, all the above parts should be carried out in
each subband respectively.
3.2.1. Packet Detection
As stated in Chapter 2, DC-OFDM based UWB system adopts packet-based
transmission mode. In most packet-based transmission system, packet is formed by
several frames, and there are intervals between the consecutive frames. Receiver is
responsible for signal detection and demodulation. Although the synchronizer is very
important in data reception, it does not necessarily mean that every components in
receiver baseband should be ready to process signals whenever power is on. On the
contrary, we can assign the packet detection module to work, while shut off all the
other baseband modules. The packet detection module serves to judge when a new
data packet arrives. We assume the packet detection module is able to detect signal
from noise. Therefore, the packet detection module will not wake up the receiver
baseband until a new data packet arrives. When a new packet comes, the packet
detection module will be informed and the message is passed on to other baseband
modules. Then the whole receiver baseband gets to work. Similarly when a packet
ends, all the other baseband modules will be shut off again except the packet
detection module. By this way, a great deal of power is saved during intervals.
Obviously, this arrangement meets the low power characteristic of UWB system.
The above is the basic idea of packet detection. How to make correct judgment
is essential in the whole procedure. Normally, we can set a threshold for this
judgment. For example, if certain indicator exceeds the threshold, we assume a new
packet begins, and vice versa.
Several data-aided algorithms have been proposed for packet detection in
literature. Generally, they can be divided into two groups: power detection method
and auto-correlation method. For the former method, the input signal power is
Chapter 3
27
calculated in (3.10).
1
( ) ( ) ( )N
n
P n y n y n
(3. 10)
where N equals the FFT length. For simplicity, we assume the wireless signal
is corrupted by Additive White Gaussian Noise (AWGN) only. It means that
( ) ( ) ( )y n x n w n . Then,
1
2 2
1
( ) [ ( ) ( )] [ ( ) ( )]
( ) ( ) ( ) ( ) ( ) ( )
N
n
N
n
P n x n w n x n w n
x n x n w n x n w n w n
(3. 11)
In order to make correct decision, the signal power should be larger than the
noise, that is SNR is larger than 1. However, when SNR equals or bellows 1, this
method can hardly pick out the signal from noise, as the power of signal is
completed buried in noise.
The second method uses auto-correlation algorithm. As DC-OFDM based UWB
system provides a group of preambles in the head of every frame, we can use the
data-aid method, like correlation scheme. If channel noise is independent, identically
distributed (i.d.d.) zero-mean Gaussian noise, then
1
1
( ) [ ( ) ( )] [ ( ) ( )]
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
N
auto
n
N
n
C n x n m w n m x n w n
x n m x n x n m w n x n w n m w n m w n
(3. 12)
where m is the distance between two consecutive OFDM symbols for
auto-correlation. Since noise samples on different time index are independent, the
last term in (3.12) equals zero. Therefore, the auto-correlation algorithm is robust to
noise comparing to the power detection method.
In order to get a general indicator for different channel environments, we use the
normalized auto-correlation coefficient.
1
1
( ) ( )
( )
( ) ( )
N
n
N
n
y n m y n
n
y n y n
(3. 13)
Both of two methods require a complex number multiplier and an accumulator.
Auto-correlation method also requires a divider to calculate the normalized
Chapter 3
28
auto-correlation coefficient. However, due to the strict power spectrum mask
published by FCC [1], the practical UWB system usually works in the area with low
SNR.
We set the simulation environment as follows. For each cases, we choose
TFC=9 at the transmitter side, while the two carrier frequencies at the receiver side
1cf and 2cf are set to Subband 3 and Subband 5 respectively. 500 discrete noise
samples are added before data frame. Packet detection is carried on both two carriers
simultaneously. According to Table 2.4, data packet shall be detected on carrier 1 at
the first OFDM symbol, while carrier 2 will miss the first OFDM symbol. It is
because the first symbol on carrier 2 is transmitted on Subband 7 rather than
Subband 5.
Figure 3.4 and Figure 3.5 compare the performance of the two packet detection
methods with the same channel environment, and shows that the auto-correlation is
superior to power detection method in low SNR applications (SNR=0 dB). In Figure
3.4, the signal power sampled from signal band has the same level with that of noise.
Therefore, we can hardly pick out the UWB signals from the noise. In Figure 3.5, we
can find an obvious hop on the connection of noise and signal, which can be detected
and used as an indicator for a new data packet. Since the UWB applications are
usually working at low SNR environment, we need an algorithm robust to noise.
Based on these considerations, we choose the auto-correlation method for packet
detection.
0 200 400 600 800 1000 12000
0.5
1
1.5
2
2.5
3x 10
4
Discrete samples index at time domain
Po
we
r
Power detection method at Carrier 1
0 200 400 600 800 1000 12000
0.5
1
1.5
2
2.5
3x 10
4
Discrete samples index at time domain
Po
we
r
Power detection method at Carrier 2
Figure 3.4: Power detection method, SNR=0dB, data rate 480Mbps, CM1.
Chapter 3
29
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
tAuto-correlation method at Carrier 1
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Auto-correlation method at Carrier 2
Figure 3.5: Auto-correlation method, SNR=0dB, 480Mbps, CM1.
Figure 3.6, Figure 3.7 and Figure 3.8 show the simulation results of
auto-correlation algorithm on different channel environments with typical data rate.
As we can see from the simulation results, the auto-correlation algorithm owns very
good robustness in different channel environments. Based on these simulations, we
choose 0.5 as the threshold for packet detection because this threshold satisfies most
of channel environments. The normalized auto-correlation coefficient reaches peak
at the time index 600 around.
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Auto-correlation method at Carrier 1
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Auto-correlation method at Carrier 2
Figure 3.6: Packet detection, SNR=5dB, 480Mbps, CM1.
Chapter 3
30
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
tAuto-correlation method at Carrier 1
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Auto-correlation method at Carrier 2
Figure 3.7: Packet detection, SNR=3dB, 200Mbps, CM2.
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Auto-correlation method at Carrier 1
0 200 400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
Discrete samples index at time domain
No
rma
liza
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Auto-correlation method at Carrier 2
Figure 3.8: Packet detection, SNR=3dB, 53.3Mbps, CM3.
3.2.2. Coarse Timing
In OFDM system, time synchronization is also known as symbol timing. The
final result of time synchronization should provide the exact start position of an
OFDM symbol for FFT window. The symbol timing process should take the impact
of multi-path channel into account. Note that in frequency hopping system, start
position in each subband is different from each other and therefore shall be detected
respectively. This result is achieved by three steps in our proposed synchronization
scheme: coarse timing, TFC detection and fine timing. As the first step, the coarse
Chapter 3
31
timing gives coarse estimation of the end position of an OFDM symbol, which can
be used to estimate a start position for the next OFDM symbol. Basically, the
estimated position should fall into the zero padding area, several samples ahead the
next OFDM symbol. This margin is left for TFC detection and the shift window of
fine timing.
We can also use the auto-correlation algorithm to obtain the coarse timing
position. Unlike packet detection presented in previous section, we choose
auto-correlation coefficient rather than the normalized result. It is because the
division in (3.13) shall introduce additional time consumption as well as inevitable
quantization error after VLSI implementation, which will decrease the precision and
cause incorrect judgment. It is confirmed by the simulation results. Then the problem
turns to the peak detection of auto-correlation coefficient. Because of the identical
training sequence in preamble group, the peak of auto-correlation coefficient will
appear at the end of data symbol. Figure 3.9 illustrates the proposed position for
packet detection and coarse timing.
Figure 3.9: Timing sequence of packet detection and coarse timing
In order to detect the peak, we can refer to the following two methods, which are
both simple for VLSI implementation.
A. Find the maximum value in a fixed range.
This method is straight-forward, but a precise search window is needed to find
the maximum value. Due to the impact of multi-path fading channel, the position of
packet detection will vary in different environments. Thus, it is difficult to obtain a
relatively precise search range. If the search range does not cover the tailing edge of
the data symbol, coarse timing fails.
B. Dynamic searching.
Any time when a new coefficient generated, we compare this value with the
Chapter 3
32
existing maximum one. If the new value is bigger than the old one, we set the new
value to the current maximum value, and reset the status count to zero. If not, we
maintain the current maximum value and the status counter adds 1. This operation is
carried out whenever a new frame is detected until the status counter reaches a
certain value dS defined beforehand. Figure 3.10 shows the detailed flow process
diagram of dynamic searching.
In practical system, received signals are corrupted by fading channel and noise,
which causes fluctuation in auto-correlation coefficient. Though the threshold value
can be obtained by simulation, fluctuations in severe channel environment may
result in wrong judgment. In order to smooth the fluctuation, we can refer to typical
low-pass filter. However, it will cause extra hardware cost.
Figure 3.10: Process flow diagram of dynamic searching
Figure 3.11, Figure 3.12 and Figure 3.13 compare the coarse timing results in
DC-OFDM based UWB system by using auto-correlation result and normalized
auto-correlation coefficient. The value “0” at time index represents the instant of
packet detection. As we can see, both of the two methods return a peak-like curve. It
is because the auto-correlation coefficient expects to get the maximal value when the
two consecutive OFDM symbols are fully correlated. However, with the presence of
noise, fluctuations exist in the curve, which may cause incorrect judgment in
searching the peak value. Besides, the division in normalized process renders the
peak even more indistinct. It is because the noise component in numerator and
denominator results in more uncertainty to division result.
Chapter 3
33
0 20 40 60 802000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
Discrete samples index at time domain
Au
to-c
orr
ela
tio
n c
oe
ffic
ien
t
0 20 40 60 800.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
Discrete samples index at time domain
No
rma
lize
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Figure 3.11: Coarse timing, SNR=5dB, 480Mbps, CM1.
0 50 100 1500.5
1
1.5
2
2.5
3x 10
4
Discrete samples index at time domain
Au
to-c
orr
ela
tio
n c
oe
ffic
ien
t
0 50 100 1500.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Discrete samples index at time domain
No
rma
lize
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Figure 3.12: Coarse timing, SNR=3dB, 200Mbps, CM2.
0 20 40 60 80 100 1202
3
4
5
6
7
8x 10
4
Discrete samples index at time domain
Au
to-c
orr
ela
tio
n c
oe
ffic
ien
t
0 20 40 60 80 100 1200.45
0.5
0.55
0.6
0.65
0.7
Discrete samples index at time domain
No
rma
lize
d a
uto
-co
rre
latio
n c
oe
ffic
ien
t
Figure 3.13: Coarse timing, SNR=3dB, 53.3Mbps, CM3.
Chapter 3
34
3.2.3. TFC Detection
DC-OFDM based UWB system adopts frequency hopping mechanism to
mitigate the impact of multi-path channel. However, without knowing the specific
value of TFC, receiver can not know which subbands have been used for
transmission and their corresponding sequence. Therefore, when a new coarse timing
is fulfilled, the next step is to determine the hopping sequence, which is also known
as TFC detection.
Since the receiver itself does not know the TFC at the very beginning of a new
frame, we design a searching chart to decide TFC. Refer to Figure 2.8, we can see
that two subbands are selected to transmit data at every moment due to the two
carriers architecture. We can set the two carrier frequencies to a certain combination,
and check whether UWB signal is on corresponding carrier subband by referring to
the method of packet detection. If there are signals on a certain subband, the
normalized auto-correlation coefficient should exceed the threshold of packet
detection, and vice versa. By this way, we can narrow the searching range of TFC
value. In the following discussion, we will present the details of TFC searching
chart.
According to Table 2.4, TFC for DC-OFDM based UWB system is briefly
divided into two groups. One is the non-hopping group. The system fixes on certain
subband when TFC equals 1 or 14. This mode is useful for debug. The other group
adopts frequency hopping mechanism. As we can see when TFC equals to 2~13,
different combination of subbands are occupied for data transmission with different
sequence. However, there is certain relationship between different TFCs. At the first
hopping stage, only two combination can be selected, that is (3, 5) or (3, 7). It means
Subband #3 is occupied no matter which TFC is chosen as a frequency hopping
indicator. Therefore, we can set the first carrier of UWB receiver to the central
frequency of Subband #3, and set the second one to the central frequency of Subband
#5. Obviously, the normalized auto-correlation coefficient of the first carrier will
exceed the threshold when a new data packet arrives, while there is signal on second
carrier or not depends on the TFC selected by transmitter. By this way, we decrease
half of the searching range at the first hopping stage. The following processes are
similar if we choose the proper combination for TFC detection. The detailed
searching chart proposed for TFC detection in DC-OFDM based UWB system is
Chapter 3
35
illustrated in Figure 3.14.
In Figure 3.14, the whole process for TFC detection is divided into four stages.
The first three stages are named as searching stage, during which we narrow the
searching range step by step according to the search result of previous stage. The
search results are presented on arrows from one stage to the next one. Generally,
there are three possible searching results in this searching chart, named as “1”, “2”,
“3” respectively. “1” denotes that UWB signal is detected on the first carrier subband.
“2” denotes that UWB signals is detected on the second carrier subband. “3” denotes
that UWB signals are neither on the first carrier subband nor on the second carrier
subband. The fourth stage is named as TFC check. As illustrated in Figure 2.3,
DC-OFDM based UWB system selects four subbands for each carrier when adopting
frequency hopping mode. According to our TFC searching chart, TFC in each frame
can be determined in Stage 3. Thus, we utilize Stage 4 to check the detected TFC. If
UWB signals can be detected on both of the carrier subbands, then we are sure TFC
detection in current frame is correct. Checking TFC is very important, because
without the correct TFC, receiver can never achieve correct data reception. If TFC
detection is fulfilled correctly, we allow the following modules get to work;
otherwise, the current frame shall be discarded.
Figure 3.14: TFC searching chart for DC-OFDM UWB
Chapter 3
36
Note that in Figure 3.14, it does not contain the situation when TFC equals to 1
and 14. These two TFCs represent that UWB systems occupy fixed subbands for
data transmission. In this situation, we need an external signal to indicator which
TFC is selected in our hardware design.
3.2.4. Fine Timing
At the transmitter side, there are 37 zero samples between every two consecutive
OFDM data symbols. On frequency hopping mode, the two consecutive OFDM
symbols are transmitted on different subbands. These 37 zero samples are designed
as guard period, during which multiple functions shall be carried out, such as fine
timing, carrier frequency switch , etc. If we assume AWGN channel and moderate
sampling frequency offset, the 37-sample interval remains unchanged at the receiver
side. However, multi-path channel in practical applications result in the change of
guard period on time domain. When frequency hopping mechanism is applied, the
guard periods may vary from each other. Nevertheless, the interval between two
OFDM symbols on the same subband fixes at 660. It equals to four times of OFDM
symbol length. This phenomenon is due to the static channel characteristics in every
subband.
In order to know the exact start position of an OFDM symbol to FFT input, fine
timing process is needed on each subband selected for transmission. Fine timing
module returns the exact index at which an OFDM symbol begins after involving the
impact of multi-path channel. Based on above discussion, fine timing process shall
be carried out four times in each subband. The results of fine timing may vary due to
the influence of different channels.
As shown in simulation results, power detection algorithm and auto-correlation
algorithm can only obtain a coarse estimation of start position. Therefore, we need a
more precise algorithm to fulfill fine timing.
There are seven types of preamble available for data transmission in DC-OFDM
based UWB system, named as Preamble 1~7. According to Table 2.4, only one
preamble is selected with a specific TFC. Note that, we can determine the preamble
information after TFC detection. After exploring the standard preambles, we find
that each type of preamble has a cell-based structure. Without losing generality, we
take Preamble 3 as an example, which is applied to TFC=3 or 9. Time domain
samples of standard Preamble 3 is shown in Figure 3.15.
Chapter 3
37
Figure 3.15: Standard Preamble 3 for TFC 3 or 9.
If we denote the first sample in Preamble 3 as 0S and the last one as 127S , the
whole preamble can be divided into 16 cells 0A ~ 15A , with 8 samples in each cell, as
illustrated in Figure 3.16. The sequence of signal sign in the first cell 0C is {+, +, -,
+, +, -, -, -}. If we set the sign of the first cell as positive, then the subsequent cells
take the exactly same or opposite sign as that of the first cell, which is denoted as {+,
+, -, -, -, +, -, -, -, +, -, -, +, -, +, +} in Figure 3.16. Therefore, the sign sequence for
whole samples on time domain is 0 1 14 15{ , , , , }C C C C C . In order to get the exact
start position of OFDM symbol, we calculate the amplitude accumulation of 128
samples. This operation can be fulfilled by cross-correlation between received signal
and the known preamble sequence. For simplicity, we use the sign of preamble
sequence C instead of specific value.
Chapter 3
38
Figure 3.16: Cell structure in standard Preamble 3.
, 1
( ) ( )N
cross
k n
C k y k n C
(3. 14)
If the cross-correlation window covers the preamble exactly, the amplitudes of
preamble samples shall be added coherently. Otherwise, the amplitudes of some
samples will cancel the other ones, resulting in a lower accumulation value.
Therefore, a peak in amplitude accumulation can be detected when cross-correlation
window covers the preamble exactly. We use the cross-correlation algorithm to
fulfill fine timing.
Figure 3.17, Figure 3.18, Figure 3.19 show the fine timing results in different
channel environments. Based on the consideration of hardware complexity, we build
up 20 sets of cross-correlation calculator, each shifts one time-domain sample. The
value “0” at time index represents the start position of cross-correlation window.
Therefore, the fine timing process is equivalent to the peak value detection of
Chapter 3
39
amplitude accumulation. From the simulation results, an obvious peak can be found
within the search range in good channel environments (CM1 and CM2). Even in the
bad channel (CM3), the accumulation method is still able to survive. Though the
estimated position may deviate from the ideal position with one sample in Figure
3.19, this effect can be compensated during channel equalization due to the cyclic
characteristics of FFT.
0 5 10 15 20-1000
-800
-600
-400
-200
0
200
400
Discrete samples index at time domain
Accum
ula
ted
am
plitu
de
Figure 3.17: Fine timing, SNR=5dB, 480Mbps, CM1.
0 5 10 15 20-800
-600
-400
-200
0
200
400
600
Discrete samples index at time domain
Accu
mu
late
d a
mp
litu
de
Figure 3.18: Fine timing, SNR=3dB, 200Mbps, CM2.
Chapter 3
40
0 5 10 15 20-1000
-800
-600
-400
-200
0
200
400
600
800
1000
Discrete samples index at time domain
Accu
mu
late
d a
mp
litu
de
Figure 3.19: Fine timing, SNR=3dB, 53.3Mbps, CM3.
3.3 VLSI Implementation for Symbol Timing
In previous section, we introduce the symbol timing algorithms for each key
modules, like packet detection, coarse timing, TFC detection and fine timing. These
algorithms are modified to cater for the requirements of DC-OFDM based UWB
system. In practical system design, we should consider the system performance
(clock frequency, data rate, quantization error, packet error rate, etc) and hardware
complexity (chip area, power consumption, etc).
The sampling frequency of A/D converter at receiver baseband is 264MHz, and
the throughput rate of the whole symbol timing module should archive 264MS/s. We
adopt 2 paths in parallel, each with 132MHz sampling frequency. We adopt an
additional signal to indicate the first signal path and the second one.
DC-OFDM based UWB system provides 16 identical preambles for
synchronization, including the function of symbol timing and frequency
synchronization. The detailed timing sequence for symbol timing module on one
carrier is shown in Figure 3.20. The preamble set is formed by four consecutive
preambles from each subband. We see that the proposed symbol timing scheme
requires 3 preamble sets: the first 2 preamble sets are used for packet detection,
coarse timing and TFC detection, Preamble set 3 is used for fine timing. The
Chapter 3
41
numbers in Figure 3.20 indicate a time interval with a certain time-domain samples.
The rising edge of “FH_pulse” indicates the frequency hopping position, at which
the mixer switches the carrier frequency to the next subband. During the Preamble
set 2, the distance between hopping pulses is equal to an OFDM symbol length 165.
Before we start fine timing in the first subband, we need to adjust the fine timing
window. It is because we can only calculate and store 20 cross-correlation result due
to hardware complexity. We must guarantee the ideal fine timing position in each
subband falls in the 20-depth window. In Figure 3.20, we delay it by 22 samples,
which is decided by simulations. Note that, when we get the fine timing result, we
can simply obtain the subsequent pulses by delaying the previous one 660
sample-distance.
Figure 3.20: Timing sequence for symbol timing module
In the proposed symbol timing scheme, some algorithms are adopted in multiple
modules, which provides the possibility of hardware reuse. For example, we adopt
auto-correlation method in packet detection module and coarse timing module, the
cross-correlation method in fine timing module. In the following section, we
describe the hardware design for auto-correlation, cross-correlation and real-number
division. We adopt SMIC 0.13um technology library. The synthesis result of symbol
timing module from Design Compiler is presented in Table 3.1.
Table 3.1: Synthesis result for symbol timing module
Combinational area 694449.514821
Noncombinational area 731528.492498
Net Interconnect area 10931446.299591
Dynamic Power 144.4965 mW
Chapter 3
42
Cell Leakage Power 487.8115 uW
Critical Path 4.58ns
3.3.1. Auto-correlation Algorithm
Auto-correlation is the cross-correlation of a signal with itself. It is the similarity
between signal observations as a function of the time separation between them. In
DC-OFDM based UWB system, the time separation for auto-correlation is 2.5ms
which equals to four times of OFDM symbol interval. In other word, there are 660
discrete samples between the two consecutive OFDM symbols on the same subband.
Figure 3.21 shows the signal processing flow for normalized auto-correlation
( )n . ( )x n is the input signal. -DZ means delay unit, where D=660, N=128.
1
0
1 12
0 0
( ) ( ) ( )
( ) ( ) ( ) | ( ) |
N
k
N N
k k
C n x n k x n k D
P n x n k D x n k D x n k D
(3. 15)
Figure 3.21: Signal processing flow for auto-correlation
In order to calculate ( )n , we need two set of First in First out (FIFO) with 660
depth, a complex-number multiplier, a real-number divider. On FIFO is assigned to
( )C n and the other to ( )P n . The amplitude of discrete time-domain sample in the
DC-OFDM based UWB system is from -32 to 31. Therefore, we use 6-bits to
describe a discrete sample, 1-bit for sign and 5-bits for value. ( )C n and ( )P n are
characterized by 18-bits.
From (3.15) we can see that ( )C n and ( )P n need to calculate summation of
128 consecutive samples. Whenever a new sample comes, we update ( )C n and
( )P n by abstracting the oddest and adding the new sample. It can be denoted as,
2 2( 1) ( ) | ( 127) | | ( 1) |C n C n x n x n (3. 16)
Chapter 3
43
2 2( 1) ( ) | ( 127) | | ( 1) |P n P n x n x n (3. 17)
3.3.2. Cross-correlation Algorithm
Cross-correlation is used in fine timing process. It need two signal inputs: one is
received signal ( )y n , the other is the preamble sequence used at transmitter side.
Suppose receiver baseband knows the complete information of preamble sequence.
Thus whenever a new input comes, we can calculate its correlation result with
preamble. For simplicity, we use the sign of preamble sequence C for correlation.
Figure 3.22 shows the hardware structure of cross-correlation cell. We assume
TFC=9 and the receiver makes correct TFC detection. The whole cross-correlation
process can be divided into two stages. In the first stage, we shift the values in
register set 1 and calculate the cross-correlation result with the sign 0C and store it
in register set 2 in every cycle. Assume we store the first cross-correlation result in
reg0. After eight cycle, the register set 1 changes its value by receiving new samples
of ( )y n . Then the result is stored in reg8. By this method, we calculate the
cross-correlation of 128 samples ( )y n and C . Note that, this cross-correlation
result is divided into 16 parts, from reg0 to reg120 as illustrated in Figure 3.22.
Figure 3.22: Hardware structure of cross-correlation cell
At the second stage, we adjust the value sign in reg0, reg8, …, reg120 according
to the sign of 16 cells 0A ~ 15A , and get the summation, which is the final
cross-correlation result. Note that the hardware for cross-correlation can not be
reused, we need to copy the cross-correlation cell 20 times if we need a shift window
with 20 depth. Figure 3.23 shows the complete hardware structure of
Chapter 3
44
cross-correlation in DC-OFDM based UWB system.
Figure 3.23: Hardware structure of cross-correlation.
3.3.3. Real-number Divider
We need a real-number divider to calculate the normalized auto-correlation
coefficient in (3.13). Since the input ( )C n and ( )P n are 18-bits words, the time
consumption for division is very high. In order to guarantee the divider works at the
frequency of 132MHz or above, we adopt the full pipeline structure. Besides, the
traditional “shift-abstract” structure in divider can calculate only one bit during each
cycle. For 18-bits input, we need 18 cycles to get the final division result, which is
obviously very inefficient. To improve its performance, we propose a dual-bit
division algorithm. It shortens the calculation time to 9 cycles.
Figure 3.24 shows the signal processing flow of the proposed dual-bit division
algorithm. The divider proceeds two bits in every cycle. It reduces the time for
division by half with very little hardware cost.
Chapter 3
45
Figure 3.24: Signal processing flow for dual-bit division
3.4 Conclusion
In this chapter, we present symbol timing problem in DC-OFDM based UWB
system. In the first part, we analyze the synchronization errors in symbol timing
processing. As discussed, the synchronization position outside the CP or ZP period
will result in ISI and degrade the performance. In order to successfully fulfill symbol
timing, we propose a data-aided synchronization scheme catered for DC-OFDM
based UWB system in second part. The scheme divides the whole symbol timing
processing into four parts: packet detection, coarse timing, TFC detection and fine
timing. We adopts multiple algorithms, such as auto-correlation in packet detection,
power detection in coarse timing and cross-correlation in fine timing. Simulation
shows that the proposed scheme achieves good robustness in practical indoor
applications. Lastly, we present the hardware implementation of this symbol timing
scheme. We give the timing sequence arrangement and resource allocation in
DC-OFDM based UWB system. We also present the hardware structure of some key
modules as well as the VLSI implementation results, which show the design meets
the requirements in DC-OFDM based UWB system.
Chapter 4
46
Chapter 4.
Orthogonal Frequency Division Multiplexing (OFDM) is an attractive
multi-carrier modulation technique for high data rate applications. It provides strong
spectral efficiency in the face of multi-path distortion. However, all these advantages
are based on orthogonality of the sub-carriers, which makes it very sensitive to
Carrier Frequency Offset (CFO), Sampling Frequency Offset (SFO). Moreover, I/Q
imbalance is usually inevitable in practical Direct Conversion Receive (DCR). In
DC-OFDM based UWB system, frequency dependent I/Q imbalance shall be
considered due to large bandwidth. All these three non-ideal effects are known as
analog front-end imperfections in this thesis. They cause Inter-Carrier Interference
(ICI) in and result in performance degradation. Therefore, a robust estimation and
compensation algorithm is needed for system design. In this chapter, we focus our
attention on frequency synchronization problems and propose a systematic study on
front-end imperfections.
This chapter is organized as follows. Firstly, we explore the cause and effect of
carrier offset, sampling offset, I/Q imbalance. Mathematics model is constructed for
theoretic analysis. Secondly, theoretical analysis is derived to evaluate the
performance degradation by metric of Error Vector Magnitude (EVM). RF designers
can figure out the distortion magnitude by referring to these equations. Thirdly, we
present the estimation and compensation algorithm for these analog front-end
imperfections. Targeting the diversity message during I/Q imbalance, we develop a
set of training sequence and algorithms for estimation and compensation of analog
front-end imperfections. Simulation results show that the proposed algorithms
achieve better performance comparing to existing methods. Then, we propose a joint
estimation and compensation scheme for CFO, SFO and I/Q imbalance. Lastly,
hardware implementation is presented for CFO cancellation. Synthesis result shows
the VLSI implementation satisfies the system requirement.
4.1 Analog Front-end Imperfections
4.1.1. Carrier Offset
In OFDM system, carrier offset consists of CFO and Carrier Phase Offset
Chapter 4
47
(CPO). Normally, these non-ideal effects are caused by mismatch of local oscillators
between transmitter and receiver.
4.1.1.1 Carrier Frequency Offset
CFO can be viewed as carrier frequency mismatch during up-conversion and
down-conversion processing at transceiver side. For simplicity, we assume the
receiver achieves perfect time synchronization and the same sampling frequency
between transmitter and receiver. If there is no CFO between transmitter and receiver,
frequency response of band-pass filter is illustrated in Figure 4.1 (a). Maximal
amplitude can be obtained when sub-carrier is sampled at frequency nf . Besides,
there is no ICI between sub-carriers and therefore the signal can be demodulated
correctly. However, if there is an offset between carrier frequencies 'c c cf f f ,
then sampling point will deviate from the best position, resulting reduction in signal
magnitude and ICI. This phenomenon is shown in Figure 4.1 (b).
(a) No carrier frequency offset (b) carrier frequency offset cf
Figure 4.1: OFDM symbol spectrum with 3 sub-carriers.
In the following part, we investigate the effects of CFO in OFDM systems. To
simplify the discussion, we assume the system has the following characteristics. The
filters at the transmitter and receiver side are ideal low-pass filters with bandwidth
1/ 2T . Additive White Gaussian Noise (AWGN) channel is adopted as wireless
channel. The real part and image part of complex noise samples are mutually
independent, with 0 / 2N power spectrum density.
Let us introduce the normalized CFO coefficient CFO as the ratio of the actual
carrier frequency offset cf to the inter-carrier spacing subf
cCFO
sub
f
f
(4. 1)
Chapter 4
48
Generally, the normalized CFO coefficient can be divided into two parts:
CFO cz (4. 2)
where z is an integer, which indicates a “coarse” carrier frequency offset, i.e.
the integral multiple of sub-carrier spacing. c denotes “fine” carrier frequency
offset, which is no bigger than half of sub-carrier space, 0.5 0.5c . Note that,
z can be viewed as sub-carrier shift, which does not affect the system performance.
The effect of z can be estimated by irregularity in preamble. Therefore, we
consider “fine” carrier frequency offset 0c in the following discussion.
Then after FFT processing, the received signal on thk sub-carrier of thi
symbol can be denoted as,
( )1 1 2
•
0 0
1( ) ( ) ( )
cl kN N j nN
i i
l n
Y k X l e W kN
(4. 3)
where ( )W k presents the sample of Gaussian noise. In (4.3), we can find that if
0c , we have i iY k X k W k . Rewrite (4.3) as,
1
0,
( ) ( ) ( ) ( ) 0,1, , 1N
k l
i i ik kl l k
Y k X k I X l I W k k N
(4. 4)
in which l
kI
is the ICI coefficient between the two sub-carriers l and k .
sin( ( )) 1exp ( )
sin( ( ) / )
l
k
l k NI j l k
N l k N N
(4. 5)
In equation (4.4), the first term is the expected signal. If there is no CFO
( 0c ), the ICI coefficient l
kI
achieve the maximal value 1. The second term is
ICI part. As c increasing, the magnitude of desired signal decrease, while ICI
coefficient l
kI
increases.
Thus, the Signal to Interference and Noise Ratio (SINR) is
2
1 2
0
0,
/
k
k
Nl
sk
i j k
E I
SINR
N E I
(4. 6)
where sE denotes the power of an OFDM symbol, 0N denotes the noise
power. Comparing (4.6) with the equation without CFO 0sSNR E N , we can get
the degradation on system SNR as
Chapter 4
49
12 2
0 0,
10log log 10log 1N
sk l
k kl l k
SINR EDc E I E I
SNR N
(4. 7)
In (4.7), the first term presents the effect of signal amplitude reduction, the
second term presents the inter-carrier interference due to destruction of orthogonality
between sub-carriers. The equation (4.7) can be simplified as
2
0
10 11
ln10 3
sc
ED
N
(4. 8)
The data rate for transmission is /R N T for OFDM system. While for single
carrier system, the data rate is 1/R T . Since the CFO can be rewritten as
/c cc subf f f T , we have,
2
0
2
0
10 11 , OFDM system
ln10 3
10 11 single carrier system
ln10 3
sc
c
sc
f EN
R ND
f E
R N
,
(4. 9)
From equation (4.9), we can find that the performance degradation in OFDM
system and single carrier system are both directly proportion to CFO c . However,
the performance degradation is also directly square proportion to the sub-carrier
number in OFDM system. Hence, the OFDM system is very sensitive to the carrier
frequency offset.
4.1.1.2 Carrier Phase Offset
If we assume the phase offset between carrier frequency signals is , the
discrete signals at receiver side can be written as,
jy n y n e (4. 10)
After FFT processing, the signal is transferred to frequency domain,
* jY k FFT y n Y k e (4. 11)
From equation (4.11), we can find that the carrier phase offset introduce a
constant phase offset to the received signals, which can be compensated during
channel equalization.
Chapter 4
50
4.1.2. Sampling Offset
At the receiver side, A/D converter samples the continuous signals. If the signal
is sampled at different frequency or phase, sampling offset will be introduced.
Sampling offset consists of two parts: SFO and Sampling Phase Offset (SPO).
4.1.2.1 Sampling Frequency Offset
SFO is caused by sampling frequency error between D/A in transmitter and A/D
in receiver. We assume the sampling frequency of ADC at receiver side is
' 1s s sf f , and the first same at receiver side is coincide with the first one at
transmitter side, then the signal of thk samples in thm OFDM symbol on time
domain is,
'1 2
0
11 12 2
0 0
s
s
s s
kf mN nN j
N f
m m
k
k mN n kn k mNN Nj jN N
m m
k k
y n X k e
X k e X k e
(4. 12)
After FFT processing, (4.12) can be written as,
1 12
2
0 0
1s
ikN Nj km k iN
m m m k m k m
i ii k
Y k y i e e X k I X k I W kN
(4. 13)
where i
kI denotes the ICI coefficient,
sin 1 1
exp 11
sin
si
k s
s
k i NI j k i
Nk iN
N
(4. 14)
Generally, s is smaller than 100ppm. For example, when 100ppms ,
1 127k , we have 0.9997k
kI , and arg 0.01k
kI
. The ICI component
1
0,
Ni
m k
i i k
X k I
is so small that we can neglect the effect of it. Therefore, the
impact of SFO can be viewed as the 2 skm phase rotation on received signals,
Chapter 4
51
2j km
m mY k X k e (4. 15)
From (4.15), we can find that the phase rotation is relative to the symbol index
m and sub-carrier index k . This phase rotation will accumulate when symbol
index goes large, and cause incorrect demodulation.
4.1.2.2 Sampling Phase Offset
We assume the normalized sampling phase offset is 0 , then the received signal
is denoted as,
0
0 0
1 2
0
1 12 2 2
0 0
s
s
kf mN nN j
N f
m m
k
k mN n kknN Nj j jN N N
m m
k k
y n X k e
X k e X k e e
(4. 16)
After FFT processing, the received signal on frequency domain is
02
kj
Nm mY k X k e
(4. 17)
From equation (4.17), we can see that the phase rotation is only relative to
sub-carrier index k and phase offset 0 . Therefore, the impact of sampling phase
offset can be compensated during channel equalization.
4.1.3. I/Q Imbalance
In OFDM system, the complex number is transmitted by two independent paths.
Of the two paths, one is responsible for real part, and the other for image part. In
Chapter 2, we have discussed the mismatches on I- and Q- branch are inevitable due
to fabrication variation in direct conversion receiver. These mismatches are named
as I/Q imbalance [31]. For wideband system, the I/Q imbalance can be categorized
into two types with different frequency characteristics. The imbalance from Local
Oscillator (LO), known as imperfect 90°phase shift and unequal amplitudes, is
constant over signal bandwidth thus frequency independent. Another type is named
as frequency dependent imbalance, caused by I- and Q- branch components with
mismatched frequency response. Motivated by these reasons, the model of Figure
4.2 is used.
Chapter 4
52
y t , cos 2LO I Cx t f t
, sin 2LO Q Cx t g f t
NOMH f
NOMH f
IH f
QH f
Iy t
Qy t
Figure 4.2: I/Q imbalance model in DCR.
4.1.3.1 Frequency Independent Mismatch
The frequency independent I/Q imbalance is caused by the mismatch in
quadrature demodulator. The local oscillator signal ( )LOx t of an imbalanced
quadrature demodulator is here modeled as
2 2
1 2( ) cos(2 ) sin(2 ) c cj f t j f t
LO c cx t f t jg f t K e K e
(4. 18)
where parameter g and characterizes the magnitude and phase imbalance
between the two local oscillator signals, ,LO Ix and
,LO Qx in Figure 4.2. The
mismatch coefficients are given by 1 (1 ) / 2jK ge ,
2 (1 ) / 2jK ge .
4.1.3.2 Frequency Dependent Mismatch
Frequency dependent I/Q imbalance is caused by the mismatch between branch
components. The branch component mismatches can be easily modeled as
imbalanced Low-Pass Filters (LPF)
,
,
I NOM I LPF
Q NOM Q LPF
H f H f H f
H f H f H f
(4. 19)
where ( )NOMH f is the nominal LPF response rejecting the high-frequency
components, , ( )I LPFH f and
, ( )Q LPFH f represent the actual mismatch effects due
to branch filters, AGCs, A/Ds, etc.
4.1.3.3 Wideband Signal Model
To explicitly characterize the imbalance effects on the individual channel
Chapter 4
53
signals, we write the multi-channel received signal ( )y t as
2 2 2
( ) 2Re[ ( ) | ] ( ) ( )c c cj f t j f t j f ty t z t e z t e z t e
(4. 20)
Then the received signal is down converted to baseband by mixing it with
( )LOx t . Assuming that ( ) 1NOMH f for | | / 2f B and ( ) 0NOMH f for
| | / 2f B , the down converted signal ( )r t can be written as
1 2( ) ( ) ( )r t K z t K z t (4. 21)
To analyze the effect of branch mismatches, the real and image part of signal
( )r t can be written as ( ) ( )I Ir t z t and ( ) cos( ) ( ) sin( ) ( )Q Q Ir t g z t g z t
respectively. Then in terms of Fourier transforms, the received signal after branch
mismatches is given by,
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )[ cos( ) ( ) sin( ) ( )]
[ ( ) ( ) cos( )] ( ) [ ( ) cos( )] ( )
I Q
I I Q Q
I I Q Q I
I Q I Q Q
Z f Z f jZ f
H f R f jH f R f
H f Z f jH f g Z t g Z t
H f jH f g Z f j H f g Z t
(4. 22)
After some manipulations, (4.22) can be written as,
1 2( ) ( ) ( ) ( ) ( )Z f G f Z f G f Z f (4. 23)
where 1( ) [ ( ) ( ) ] / 2j
I QG f H f H f ge , 2( ) [ ( ) ( ) ] / 2j
I QG f H f H f ge .
Therefore, the impaired signal at sub-carrier k of the thi OFDM symbol can
be modeled as
*
, 1, , 2, ,i k k i k k i kZ G Z G Z (4. 24)
1, , ,
2, , ,
1
21
2
j
k I k Q k
j
k I k Q k
G H ge H
G H ge H
where { } means conjugation operation. From equation (4.24), we can see
that I/Q imbalance in OFDM system translates into a mutual interference between
sub-carriers that are located symmetrically to the DC sub-carrier. Hence, the
received signal at sub-carrier k : kZ is interfered by the received signal at
sub-carrier k : kZ , and vice versa. In Equation (4.24), last terms is the image
interference induced by I/Q imbalance. Define the Image Rejection Ratio (IRR) at
sub-carrier k
Chapter 4
54
2
1,
2,
k
k
k
GIRR
G (4. 25)
For ideal case with no I/Q imbalance, IRR is expected to be infinite. However,
with the modern manufacturing process, this value is usually in the order of 30~40
dB [32].
4.2 Performance Degradation
Based on the mathematics model presented above, we analyze the system
performance degradation due to analog front-end imperfections by metric of error
vector magnitude in this section. The first part of this section builds up the
mathematics model for analog front-end imperfections in DC-OFDM based UWB
system. The second part presents the theoretical analysis. The third part gives
simulations.
4.2.1. Mathematics Model
Knowledge about the relationship between quantitative signal degradation and
transceiver parameters (such as CFO, SFO, I/Q imbalance) is essential for the design
and implementation of wireless communication systems. Given a target signal
degradation requirement, the system architects and designers need to know the
suitable transceiver parameters to realize that goal. They should provide persuasive
evidences to validate the feasibility of their proposal. Moreover, when existent
systems break down, they might need to evaluate the performance degradation to help
find out the exact reason. Traditionally, that knowledge is achieved by rich system
design experience, strict hardware measurement or computer simulations. However,
for most situations, those approaches are very subjective, condition-limited and
time-consuming. As a result, a comprehensive theoretical analysis is in urgent need.
Error Vector Magnitude (EVM) is a common merit for assessing the quality of
digitally modulated telecommunication signals [33], [34]. EVM expresses the
difference between the expected complex voltage of a demodulated symbol and the
value of the actual received symbol. Compared to the Bit Error Rate (BER), which
gives a simple one-to-one binary decision as to whether a bit is erroneous or not,
EVM contains complete information about the non-ideal effects, such as hardware
Chapter 4
55
mismatches and channel noise as well as inevitable estimation errors. The use of
EVM as a performance metric is limited to radio frequency engineering to infer the
reception performance earlier than the BER.
The EVM is described in Figure 4.3. We define the error sequence as
( ) ( ) ( )e k s k z k , where ( )s k is the reference sequence of complex symbols,
( )z k is the measured sequence of complex symbols.
Figure 4.3: Error vector magnitude definition
Then the EVM is defined as
21
0
2
max
1 ˆK
k kkY X
KEVMS
(4. 26)
where kX denotes ideal symbol, ˆkY is the corresponding received one. maxS
represents the maximal amplitude in the constellation set. Define peak-to-mean
magnitude ratio of the given modulation scheme max rms/D S S , then (4.26) can be
rewritten as
21
0
2 2
rms
1 ˆK
k kkY X
KEVMD S
(4. 27)
Peak-to-mean magnitude ratio for some useful M-QAM schemes are listed in
Table 4.1.
At the transmitter side, we define one OFDM symbol as
/2 /2 1 /2 1, , ,T
N N NX X X X (4. 28)
Then, the baseband signal ( )x t can be denoted as
Chapter 4
56
/2 1
2 /
,
/2
1 Nj k t iMT NT
i i k
i k N
x t X eN
(4. 29)
Table 4.1: Peak-to-mean magnitude ratio for M-QAM scheme
M-QAM Format Peak-to-mean Magnitude Ratio
4 1.0
16 1.341
64 1.527
where ,i kX is the complex modulated transmission data at the thk sub-carrier
of the thi OFDM symbol. N is the IFFT size and M is the total number of
samples in one OFDM symbol including the modulated transmission data tones,
pilot tones and Zero Prefix (ZP) samples. Then involving the frequency selective
fading channel ( )h t and Additive White Gaussian Noise sample (AWGN), ( )w t ,
the received signal can be written as
i iy t x t h t w t (4. 30)
in which represents convolution operation. After CFO and SFO
impairment, the sampled discrete complex baseband signal for the thk sub-carrier
of the thi OFDM symbol after the receiver FFT processing can be written as
/2 1
, , , ,0 , , ,
/2,
N
i k i k i k i i l i l i l k k
l N l k
Z H Y I H Y I W
(4. 31)
where ,i l kI
is the ICI coefficients with joint effect of CFO and SFO. kW
represents noise sample on frequency domain.
2 /
, ,c sj iM k N
i k i kY X e
(4. 32)
1 1/
,
sin
sin /
s cj l k N s c
i l k
s c
l - kI e
N l k N
(4. 33)
For simplicity, the summation /2 1
/2,
l N
l N l k
will be abbreviated as l k later
in this section.
Combine (4.24) and (4.31), we can get the baseband representation of the signal
impaired by joint effects of CFO, SFO and I/Q imbalance.
Chapter 4
57
, 1, , , ,0 , , ,
2, , , ,0 , , ,
i k k i k i k i i l i l i l k k
l k
k i k i k i i m i m i m k k
m k
Z G H Y I H Y I W
G H Y I H Y I W
(4. 34)
It should be mentioned that different subbands may have different
characteristics in a frequency-hopping system. CFO as well as I/Q imbalance may
vary in different subbands. However, SFO is generally unchanged due to fixed
sampling clock. In the following discussion, we present the analysis and algorithm
on one subband. The situations on other subbands can be derived directly.
4.2.2. EVM Analysis
Before deriving EVM calculations, we make the following assumptions in
OFDM system:
(1) All data sub-carriers are transmitted with the same power and mutually
independent in statistics, i.e. 2 2 2
l lE X E X ,
/ 2, / 2 1l N N and * 0l kE X X , l k .
(2) Samples of individual sub-carrier are generated based on an alphabet
with equal probability to each discrete symbol.
(3) The sampled additive Gaussian channel noise is white, i.e.
2 2 2 ,l l nE W E W / 2, / 2 1l N N .
With these assumptions, we define 1,l l lT G H , (4.34) can be rewritten as
0l l l lY X T I Z (4. 35)
where the term 0l lX T I denotes the first term in (4.34) and lZ is the
summation of all the other terms.
In literature, channel impulse response and I/Q imbalance can be jointly
estimated and compensated in frequency domain [35], [36]. We model the estimation
result as ˆl l lT T V , if estimation is unbiased. For illustration, lV is additive
Gaussian noise with zero mean and variance 2 2
est {| | }V lErr E T , where estErr is
the coefficient in the order of 10-3
~10-6
according to different estimation algorithms
[37].
Applying imperfect zero-forcing equalization to (4.35), then the compensated
result ˆlY can be written as
0ˆ
ˆ ˆ ˆl l l
l l
l l l
Y T ZY X I
T T T (4. 36)
Chapter 4
58
Hence, the error vector at sub-carrier l is
ˆl l lY X (4. 37)
Submitting (4.36) and (4.37) into (4.27), and making some straight-forward
algebra operations. Equation (4.38) is obtained.
22 2 22 2
2 2 2 2 22,
0 0 02 2
1,
1 1 11 1 1
ˆ ˆ ˆll l l l l
l k k l l m m l
k l m ll l ll l ll l
GV V W V WEVM E I I H I H I H I
D X G XT T TH H
(4. 38)
Equation (4.38) deserves more detail discussion to achieve a simple result.
Firstly, 2 2
estˆ{| / | } {| / | }l l l lE V T E V T Err is hold when estimation error is relative
small, i.e. 10-3
~10-5
. Secondly, 1IRR in realistic OFDM system, therefore
2
2, 1,| / | 1l lG G .
We define ICI on sub-carrier l caused by residual CFO as lICI and the
mirrored one due to I/Q imbalance as lICI ,
2
2
l k k l
k l
l m m l
m l
ICI H I
ICI H I
(4. 39)
Though 1IRR , 2| / |l lH H could be arbitrary large value in frequency
selective fading channel, so the mirrored distortion caused by the joint effects of
CFO and I/Q imbalance can not be simply neglected in (4.38). According to
Cramer-Rao lower bound, the minimal estimation error is related to the conditional
probability density function as well as SNR in the channel. Though the estimation
error estErr is inevitable, it decades quickly with SNR in practical OFDM system
[38]. 2ˆ{| / | } 1l lE V T when SNR is large. Hence, averaging over all data
sub-carriers, (4.38) can be rewritten as (4.40). Extremely with perfect estimation,
(4.40) is reduced to the result presented in [32] when residual CFO is eliminated.
2/2 1
2 2 2
0 est 0 02 2/2
1 1 1 11
Nl l l
l N l l l ll l
ICI H ICIEVM E I Err I I
D IRR H IRR SNRH H
(4. 40)
4.2.3. Simulation Results
A typical direct conversion receiver for wideband OFDM system as shown in
Figure 2.4 is constructed to examine the accuracy of equation derived in previous
Chapter 4
59
section. Carrier frequency offset and I/Q imbalance are introduced to DCR as
illustrated in Table 4.2. System parameters are summarized: OFDM symbol length is
128, modulation orders of 4, 16, 64 are adopted. All simulations are carried out with
the perfect symbol synchronization at the receiver side. Theoretical calculation is
presented by solid line and simulation result is presented by discrete symbols.
Table 4.2: I/Q imbalance profiles
Profile1 Profile2 Profile3
Amplitude imbalance 0.3 dB 0.6 dB 0.9 dB
Phase imbalance 3° 6° 9°
Frequency dependent imbalance
-1 -2,
-1 -2,
z 0.98 0.005z +0.02z
z 1.0 0.003z +0.01z
LPF I
LPF Q
h
h
10 12 14 16 18 20 22 24 26 28 300.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Signal to Noise Ratio (dB)
Err
or
Ve
cto
r M
ag
nitu
de
Profile 1,CAL
Profile 1,SIM
Profile 2,CAL
Profile 2,SIM
Profile 3,CAL
Profile 3,SIM
Figure 4.4: Simulated and analytical EVM versus SNR, 16-QAM.
In Figure 4.4, different non-ideal impairment profiles are applied to system with
deterministic modulation scheme. For illustration, 16-QAM is used. Normalized
residual CFO is set to 0.03. Typical Rayleigh distributed wireless channel is adopted.
Applying the estimation scheme presented in Section III, estimation error is set to the
value of corresponding Cramer-Rao lower bound [38]. Three typical I/Q imbalance
parameter profiles listed in Table. II are considered. Almost perfect agreements can
Chapter 4
60
be observed. In Figure 4.4, Profile 1 generates relatively small distortion, while
Profile 3 generates much larger one. However, there are slight differences when SNR
is small. In this situation, 2ˆ{| / | } 1l lE V T does not hold and the relevant terms in
(4.38) can not be neglected.
In Figure 4.5, we consider different modulation schemes at SNR=20dB. Without
loss of generality, estimation error estErr is set to 10-4
. Normalized residual CFO is
set to 0.03. I/Q imbalance is described by the parameter IRR. Typical Raleigh
distributed wireless channel is used. We can see that the theoretical calculation
results can predict the distortion precisely. While, there are slight differences when
IRR is small. When IRR is relatively small, i.e. 10dB, the assumption that 1IRR
is no longer hold in (4.38). Fortunately, with the modern manufacturing process, IRR
is usually in the order of 30~40 dB. Also, it can be seen that EVM of QPSK is 1.84
dB higher than 64-QAM, which coincides with the peak-to-mean magnitude ratio of
these two schemes.
10 12 14 16 18 20 22 24 26 28 30
0.2
0.25
0.3
0.35
0.4
Image Rejection Ratio (dB)
Err
or
Ve
cto
r M
ag
nitu
de
QPSK,CAL
QPSK,SIM
16-QAM,CAL
16-QAM,SIM
64-QAM,CAL
64-QAM,SIM
Figure 4.5: Simulated and analytical EVM versus IRR, SNR=20dB.
4.3 Algorithms
In the previous section, we explore the cause and effect of several analog
front-end imperfections, such as CFO, SFO and I/Q imbalance. The corresponding
Chapter 4
61
mathematics model is built up for them. From the performance degradation analysis,
we can find that the analog front-end non-ideal effects introduce severe impairment
to OFDM systems. Thus, a robust estimation and compensation algorithm is required
to guarantee the system performance. In both of MB-OFDM and DC-OFDM based
UWB system, preambles are provided for non-ideal effects estimation. So, we focus
our attention on the data-aided algorithms.
This section is divided into three parts. In the first part, we investigate the
estimation problems in frequency dependent I/Q imbalance. A new training sequence
is designed for the frequency dependent I/Q imbalance in DC-OFDM based UWB
system. We target the diversity message introduced by I/Q imbalance, and try to
obtain it during the demodulation process. In the second part, we proposed a
time-domain joint CFO and I/Q imbalance estimation and compensation scheme. The
algorithm is robust to a large I/Q imbalance. In the third part, a frequency-domain
joint estimation and compensation scheme for CFO, SFO, and frequency dependent
I/Q imbalance is proposed for wideband OFDM systems. In this scheme, we utilize
the diversity message and improve the system performance comparing to existing
methods.
4.3.1. I/Q Imbalance Estimation and Compensation
In this section, we explore the diversity message introduced by the I/Q
imbalance. Though the interference from the image sub-carrier is an undesired
component, it can also be viewed as useful information when we can separate it from
the received signals. Based on this phenomenon, we design a set of new training
sequence which are suitable for frequency dependent I/Q imbalance estimation.
Simulation results confirm that diversity message is obtained to enhance the system
performance.
4.3.1.1 Diversity Message
In wireless communication system, the detection in fading channel has poor
performance even it adopts coherent detection mechanism. The reason is not because
of the lack of channel knowledge at the receiver. It is due to the fact that channel
gain is random and there is a significant probability that the channel falls in a “deep
fade”. We assume a slow fading channel, then the averaged BER can be calculated
Chapter 4
62
by averaging bit error rates through all SNR range,
0( ) ( )B BP P x p x dx
(4. 41)
where ( )BP x is the BER of certain modulation scheme at SNR x ,
2
0/bx E N . denotes the signal magnitude variation caused by fading effect.
( )p x is the probability density function for x . When the channel is in a “deep
fade”, the standard deviation of the noise and therefore the error probability becomes
significant.
A natural solution to improve the performance is to ensure that the information
symbols pass through multiple signal paths. If each path fades independently, then
the possibility of all signal paths meet “deep fade” is significantly decreased. By this
way, we make sure that reliable communication is possible as long as one of the
signal paths is strong. This technique is named as diversity, and it can dramatically
improve the system performance over fading channels.
In OFDM system, the sub-carriers are allocated around the DC point. The
typical OFDM message symbol spectral arrangement is illustrated in Figure 4.6.
Usually, the DC point is null point, and is not used for data transmission.
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Normalized Frequency (pi*rad/s)
Pow
er
Figure 4.6: Power spectral arrangement in OFDM symbol
From equation (4.24), we can see that I/Q imbalance introduces image
interference. Hence, the received signal at sub-carrier k : kZ is interfered by the
received signal at sub-carrier k : kZ , and vice versa. This phenomenon is
illustrated in Figure 4.7. From the viewpoint of sub-carrier k , the component from
sub-carrier k is undesired. However, if we can separate the original signal of
Chapter 4
63
these two sub-carriers, the interference can be changed to useful signals. As the
image interference also passes the wireless channel, it can be viewed as diversity
message during demodulation process. This is the basic idea that we transfer the
interference to the useful signal, and achieve additional diversity message.
Figure 4.7: Frequency domain illustration of the effect of I/Q imbalance
4.3.1.2 New Training Sequence
According to DC-OFDM based UWB system standard, the original training
sequence is a real number sequence on time domain. If we convert it to frequency
domain by DFT, it is composed of two parts around the DC sub-carrier. These two
parts are mutually mirror conjugated. After experiencing I/Q imbalance, the
interference adds coherently to the desired signal. Thus, training sequences with this
special structure can not be used for the estimation of frequency dependent I/Q
imbalance.
The response of frequency dependent I/Q imbalance is not flat on frequency
domain. So, frequency-domain estimation and compensation algorithms are preferred.
In literature, [13] constructs a training sequence as illustrated in Figure 4.8. “P”
stands for pilot sequence being transmitted, and “0” stands for no data being
transmitted.
Chapter 4
64
Figure 4.8: Training scheme for both I/Q imbalance and channel estimation.
Since the every OFDM training symbol is only half occupied, the receiver can
separate the desired signal and image interference directly. In the first / 2Trn
OFDM symbols, the receiver can estimate the coefficient 1,kG , 1 / 2k N as
well as 2,lG , / 2 1l N N . While in the next / 2Trn OFDM symbols, the
receiver obtains the message of 1,kG , / 2 1k N N , and 2,lG , 1 / 2l N . By
this way, the receiver is trained to frequency dependent I/Q imbalance.
However, it wastes half part of every training sequence (half sub-carriers are
assigned to “0”), and therefore it needs many training sequences to improve the
estimation performance. So it is not suit in practical DC-OFDM based UWB system.
In this section, we propose a new training sequence based on phase rotation. The
corresponding estimation scheme involves the diversity message in I/Q imbalance.
In DC-OFDM based UWB system, the number of sub-carriers in one OFDM
symbol is 128. The original training sequence employs QPSK modulation, as shown
in Figure 4.9 (a).
Re
Im
Re
Im
θ
(a) QPSK in ECMA-368 (b) QPSK based on phase rotation.
Figure 4.9: QPSK modulation constellation.
Chapter 4
65
For simplicity, we neglect the DC sub-carrier and divide the training sequence
into two parts 1,kP and 2,kP . Each of these two parts consists of 63 sub-carriers,
T
1, 2,, ,1 63k kP P k Prmb (4. 42)
where T{ } represents transposition operation. We denote the original training
sequence in polar coordinates as,
1,
2,
k
k
j
k k
j
k k
P L e
P L e
(4. 43)
where 1kL , { / 4, 3 / 4}k . If we apply additional phase rotation to the
original training sequence, like Figure 4.9 (b), we reassign the energy on signal
real-part and imaginary part without changing the overall signal energy. However, if
we select the part with higher energy, the actual SNR will be improved. Construct
four training sequences with the phase rotation i ,
1,
2,
e ,1 4ik j
k
Pi
P
iPrmb (4. 44)
where [ ,π/2 . , π/2 ]i . represents the phase rotation,
0 / 4 . Without losing generality, we analyze the SNR for I/Q imbalance
estimation when / 4k . We normalize the preamble,
π π 1
cos sin 1+4 4 2
j j
Prmb (4. 45)
In (4.45), the signal energy is equally divided into real and image part. We define
the power of AWGN samples is 2 , then the SNR for I/Q imbalance estimation is
2
2
1 10
1SNR 10log /
2
(4. 46)
Similarly, the preamble symbol with additional phase rotation is
12
π π 1cos + sin 1 D
4 4 D 1j j
Prmb (4. 47)
where D tan( / 4 ) . Since the I/Q imbalance introduces the image
interference, we can construct two preambles, and utilize the higher energy part for
estimation. For example, we utilize the image part in 1Prmb . Hence, the SNR for
I/Q imbalance estimation changes to 2
2
2 102
DSNR 10log /
D 1
(4. 48)
Chapter 4
66
Making some straight-forward algebra operations, we can get the relationship
between signal-to-noise ratio enhancement G and phase rotation ,
2 1 102
2DSNR -SNR 20log
D 1G
(4. 49)
Figure 4.10 shows the result in (4.49). We can see that G increases along with
. In this section, we set the phase rotation to / 8 for practical system
consideration.
0 5 10 15 20 25 30 35 40 450
0.5
1
1.5
2
2.5
3
3.5
Additional Phase Rotation (degree)
SN
R E
nh
an
ce
me
nt (d
B)
Figure 4.10: SNR enhancement versus additional phase rotation.
As discussed previously, I/Q imbalance introduces image interference which can
be also viewed as diversity message. Additional phase rotation reassigns the signal
energy on real part and image part. Using the higher energy part results in more
accurate estimation. After involving the diversity message during demodulation
process, the system performance achieves more improvement.
Similar to 1,kP and 2,kP , rewrite 1,kG and 2,kG as follows,
1,1, 2,1,
1, 2,
1,2, 2,2,
,k k
k k
k k
G GG G
G G
(4. 50)
Making conjugation of (4.24), we can get the following relation (with no noise
presence).
1, 2,
2, 1,
kk kk
k k kk
RG GR
G G RR
(4. 51)
Chapter 4
67
Taking (4.44) and (4.50) into (4.51), the received training sequences after I/Q
imbalance impairment are T( )i i,1 i,2T T ,T= , 1 4i .
1, 1,1, 2, 2,1,
2, 1,2, 1, 2,2,
i i
i i
j j
k k k k
j j
k k k k
P e G P e G
P e G P e G
i,1
i,2
T
T (4. 52)
For simplicity, we neglect the sub-carrier index k and denote kL as L , kL
as 'L . Notice that there are following relationships between k and
sin cos
cos sin
sin cos
cos sin
k k
k k
k k
k k
(4. 53)
Define the internal parameters k β and k γ . When 1,2i ,
(4.52) can be rewritten as
cos sin
sin cosj
1,1 1,1 2,1
1,1 2,1
T L β G β G
L β G β G (4. 54a)
cos sin
sin cosj
2,1 1,1 2,1
1,1 2,1
T L β G β G
L β G β G (4. 54b)
sin cos
cos sinj
1,2 1,2 2,2
1,2 2,2
T L' γ G γ G
L' γ G γ G (4. 54c)
sin cos
cos sinj
2,2 1,2 2,2
1,2 2,2
T L' γ G γ G
L' γ G γ G (4. 54d)
Combing (4.54a)~(4.54d), we define the intermediate variables 1J and 2J
2 sin j 1 2,1 1,1
J L β G G (4. 55a)
2 sin j 2 1,2 2,2
J L γ G G' (4. 55b)
Similarly, 3Prmb and 4Prmb can be denoted as 3J , 4J .
2 sin j 3 1,1 2,1
J L β G G (4. 55c)
2 sin j 4 2,2 1,2
J L' γ G G (4. 55d)
Combing (4.55a)~(4.55d), we can get the estimation results
ˆ ˆ4 sin 4 sin
ˆ ˆ4 sin 4 sin
j j
j j
j j
j j
1 3 1 31,1 2,1
2 4 2 41,2 2,2
J J J JG ,G
L β L β
J J J JG ,G
L' γ L' γ
(4. 56)
Chapter 4
68
in which the parameters L , L' , β and γ are known at the receiver side.
Therefore, the I/Q imbalance estimation can be denoted as ˆ1
G , ˆ2
G .
ˆ ˆˆ ˆ
ˆ ˆ
1,1 2,1
1 2
1,2 2,2
G GG = ,G =
G G (4. 57)
It should be mentioned that the proposed estimation scheme requires 4 training
sequences for I/Q imbalance estimation, which can be satisfied in some practical
UWB system, like DC-OFDM UWB system.
With the estimated information, receiver fulfills I/Q imbalance compensation.
Maximum Likelihood (ML) detector can archive the diversity gain, but the
computational complexity is too high to implement the UWB receiver. In this paper,
we adopt a sub-optimal receiver structure: ordered successive interference
cancellation (OSIC) detector. For detailed information, one can refer to [53]
As shown in (4.51), I/Q imbalance resembles a 2x2 MIMO system. We apply
the OSIC detector as in V-BLAST receiver [39] to detect the transmitted signal.
4.3.1.3 Simulation Result
To evaluate the performance of the proposed scheme, a typical DC-OFDM
based UWB system has been developed. Monte Carlo simulations are carried out
with the system parameters list in Table. I. In the simulations, channel model one
(CM1) is selected as the frequency selective UWB channel. OSIC receiver is
adopted. We consider the following simulation cases:
(1) Ideal case: no I/Q imbalance
(2) Non-ideal case: method in [13] with DC-OFDM based UWB training
sequence
(3) Non-ideal case: method in [13] with training sequence defined in [13]
(4) Non-ideal case: method in [40] with diversity message
(5) Non-ideal case: new training sequence and proposed method
In case (3), we use the frequency domain estimation scheme and special training
sequence defined in [13]. While in case (5), we apply additional phase rotation to
DC-OFDM based UWB training sequence. In all above simulation cases, we assume
perfect symbol synchronization and do not apply any channel coding schemes.
As discussed previously, we perform joint estimation and compensation of I/Q
imbalance and channel response. In Figure 4.11, the original training sequence in
Chapter 4
69
DC-OFDM based UWB standard draft introduces error floor to the estimation of
frequency dependent I/Q imbalance. The proposed estimation scheme can reduce the
mean square error (MSE) to 60% of that in [40].
Table 4.3: System parameters I
Parameter Value
Data rate 480 Mbps
Sub-carrier number 128
Inter-carrier spacing 2.0625 MHz
Modulation order 16-QAM
Additional phase rotation π / 8
Channel model CM1 + AWGN
I/Q imbalance
0.6dBg , 4
-1 -2,
-1 -2,
z 0.98 0.03z +0.01z
z 1.0 0.005z +0.2z
LPF I
LPF Q
h
h
10 15 20 25 30 35 40 4510
-5
10-4
10-3
10-2
10-1
100
Eb/No (dB)
Me
an
Sq
ua
re E
rro
r
Non-ideal case: DC-OFDM training sequence
Non-ideal case: method in [13]
Non-ideal case: method in [40]
Non-ideal case: proposed method
Figure 4.11: MSE versus Eb/No for I/Q imbalance estimation, 480 Mbps.
In Figure 4.12, we can also find error floor when original training sequence in [8]
is used for frequency dependent I/Q imbalance estimation. Though the method and
training sequence in [13] can estimate and compensate the I/Q imbalance in UWB
Chapter 4
70
system, the estimation accuracy is limited by the number of available training
sequence. In addition, the system performance is worse than the ideal case with no
I/Q imbalance. Involving the diversity message introduced by I/Q imbalance during
the demodulation process, [40] can enhance the performance: about 4 dB Eb/No
advantage at PER=8% comparing to method in [13]. Due to the limited estimation
accuracy, the diversity gain can not be obtained completely at the receiver side. The
proposed estimation scheme improves the estimation performance by applying
additional phase rotation to the original training sequence, and thus achieve another
1 dB Eb/No advantage comparing to method in [40].
10 15 20 25 30 35 40 4510
-3
10-2
10-1
100
Eb/No (dB)
Pa
cket E
rro
r R
ate
Ideal case: no I/Q imbalance
Non-ideal case: DC-OFDM training sequence
Non-ideal case: method in [13]
Non-ideal case: method in [40]
Non-ideal case: proposed method
Figure 4.12: PER versus Eb/No, 16-QAM, 480 Mbps.
4.3.2. Joint Estimation and Compensation
In Section 4.3.1, we have investigated the problem of I/Q imbalance in OFDM
system without considering other analog front-end non-ideal effects, like CFO, SFO,
etc. However, more challenging situation is inevitable in practical DC-OFDM based
UWB system: estimation and compensation of I/Q imbalance with the influence of
CFO and SFO. In Section 4.1, we have discussed that the impairment of CFO and
SFO, such as ICI and phase rotation, will be mirrored due to I/Q imbalance. The
Chapter 4
71
image interference severely affects the performance of traditional CFO and SFO
estimation algorithms. Besides, frequency dependent I/Q imbalance will render the
time-domain joint CFO and I/Q imbalance estimation schemes hardly work. In this
section, we present details of the joint estimation and compensation algorithm for
CFO, SFO and I/Q imbalance.
4.3.2.1 CFO and SFO Estimation
As discussed in Chapter 2, identical preamble symbols are adopted in
DC-OFDM based UWB system for symbol timing and frequency synchronization.
The phase difference between successive preamble symbols has two main sources,
i.e. carrier and sampling frequency offset. Traditional data-aided carrier frequency
offset estimation algorithm employs two consecutive preamble symbols in the time
domain [12], [41]
4ˆ ,1
8 /c
angle z n z n Nn N
M N
(4. 58)
where { }angle returns the phase angle of a complex number. [ ]z n and
[ 4 ]z n N represent the discrete samples of two successive preamble symbols on
one subband. However, the accuracy of this estimation method suffers severe
degradation with the presence of I/Q imbalance. In (4.34), I/Q imbalance introduces
an opposite phase rotation, which is superimposed on the original one. This image
interference causes the correlation operation in (4.58) fails to work. Here, we
propose a joint CFO and SFO estimation method which is robust to frequency
dependent I/Q imbalance in wideband OFDM system.
Substitute (4.32) and (4.33) into (4.31). According to [14], we can obtain the
following relation with the assumption: 4 ,4 2 , 4 1 , i ki k i k
H H H
and
4 ,4 1 , i ki kX X
2 4 /
4 ,4 1 ,
c sj M k N
i ki kZ Z e
(4. 59)
Similarly,
2 8 /
4( 2), 4 ,c sj M k N
i k i kZ Z e
(4. 60)
Consider three successive received preamble symbols on one subband. After
taking the impairment of CFO, SFO and I/Q imbalance into account, the three
preambles can be written as,
Chapter 4
72
4 , 1, 4 , 2, 4 ,i k k i k k i kZ G Z G Z
(4. 61a)
1, 2,4 1 , 4 1 , 4 1 ,k ki k i k i kZ G Z G Z
(4.61b)
1, 2,4 2 , 4 2 , 4 2 ,k ki k i k i kZ G Z G Z
(4.61c)
Taken (4.59) and (4.60), then (4.61a)~(4.61c) can be rewritten as
4 , 1, 4 , 2, 4 ,i k k i k k i kZ G Z G Z
(4. 62a)
2 4 / 2 4 /
1, , 2, ,4 1 ,
c s c sj M k N j M k N
k i k k i ki kZ G Z e G Z e
(4.62b)
2 8 / 2 8 /
1, , 2, ,4 2 ,
c s c sj M k N j M k N
k i k k i ki kZ G Z e G Z e
(4.62c)
Summing (4.62a) and (4.62c), and making some straight-forward algebra
operations
2 4 / 2 4 /
4 , 4 2 ,
2 4 / 2 4 /
1, , 2, ,
c s c s
c s c s
j M k N j M k N
i k i k
j M k N j M k N
k i k k i k
Z Z e e
G Z e G Z e
(4. 63)
In (4.63), approximation has been made based on the assumption s ck .
According to DC-OFDM based UWB standard draft [8], the maximum carrier and
sampling frequency offset are limited to 40 ppm at 10.3 GHz carrier frequency and
528 MHz sampling frequency. Since 128N and 165M , the assumption is
valid in practical DC-OFDM based UWB systems. Besides, IRR usually achieves
30dB~40dB in practical DCR implementation [32], which also minimize the
approximation error.
Then (4.63) can be rewritten as
2 4 / 2 4 /
4 , 4 2 , 4 1 ,
4 1 ,2 cos 2 4 /
c s c sj M k N j M k N
i k i k i k
c si k
Z Z Z e e
Z M k N
(4. 64)
Therefore, the relation between three successive symbols can be denoted as
4 , 4 2 ,1
4 1 ,
cos8 2
i k i k
k c s
i k
Z ZNk
M Z
(4. 65)
(4.65) was derived without noise. The maximum likelihood estimate of c and
s can not be found analytically. However, an estimate of the sampling frequency
offset s can be derived by comparing the difference of two sub-carriers with
determined distance d :
4 , 4 ,4 2 , 4 2 ,1 1
,
4 1 , 4 1 ,
ˆ cos cos8 2 2
i k i li k i l
s d k l
i k i l
Z Z Z ZN
M k l Z Z
(4. 66)
To improve the estimation performance, the determined distance d in (4.66)
Chapter 4
73
selects a large number to combat the channel noise. Here, d is selected to be
maximal length in one OFDM symbol / 2 1N . The final estimated SFO can be
obtained by averaging all available estimates.
,
/2 1
2ˆ ˆ
2s s d
d NN
(4. 67)
With the estimated sampling frequency offset ˆs , the estimate of carrier
frequency offset can be derived from (4.65)
4 , 4 2 ,1
,
4 1 ,
ˆ ˆcos8 2
i k i k
c k s
i k
Z ZNk
M Z
(4. 68)
Similar to ˆs , the final estimated CFO ˆ
c is the average of the estimates on all
sub-carriers
/2 1
,
/2
1ˆ ˆ
N
c c k
k NN
(4. 69)
4.3.2.2 I/Q Imbalance Estimation
As discussed in Section 4,1, I/Q imbalance introduces image interference.
Traditional estimation algorithms explore the relationship between the two
sub-carriers that are located symmetrically to the DC sub-carrier [13], [40]. However,
this symmetrical relationship will be destroyed when CFO and SFO exist, which
introduce Inter-Carrier Interference (ICI) to the desired signal. In this part, we
propose a frequency domain I/Q imbalance estimation scheme with the presence of
CFO and SFO.
With the estimated information of carrier frequency offset ˆc and sampling
frequency offset ˆs , the received preamble symbols can be either positive partially
compensated { }POS or negative partially compensated { }NEG . Consider
(4.62b), the positive and negative partially compensated result is
2 4 / 2 8 /*
1, 4 , 2, 4 ,4 1 , 4 1 ,
2 4 / 2 8 / *
1, 4 , 2, 4 ,4 1 , 4 1 ,
c s c
c s c
j M k N j M N
k i k k i ki k i k
j M k N j M N
k i k k i ki k i k
POS Z Z e G Z G Z e
NEG Z Z e G Z e G Z
(4. 70)
According to the preamble structure presented in [8], the symbol index of the
channel estimation preamble is known after frame synchronization. Referring to
(4.32), the information of 4 ,i kY and *
4 ,i kY can be obtained after symbol timing.
Chapter 4
74
Therefore, the channel response and I/Q imbalance on one subband can be jointly
estimated. Comparing (4.61a) and (4.70), we can get the estimate of joint channel
response and I/Q imbalance parameters as follows
4 ,4 1 ,
1, 2 8 /
4 ,
4 ,4 1 ,
2, 2 8 /
4 ,
ˆ
1
ˆ
1
c
c
i ki k
k j M N
i k
i ki k
k j M N
i k
NEG Z ZG
Y e
POS Z ZG
Y e
(4. 71)
It should be pointed out that the proposed I/Q imbalance estimation scheme
works properly with the constraint that the carrier frequency offset could not be zero,
which leads (4.71) to a poor estimation accuracy. Though the frequency offset can be
limited within tens of ppm (point per million) with state of art analog technique,
CFO and SFO can not be avoid in practical OFDM systems. With the specification
in [8]: 128N and 165M , this constraint is generally satisfied in practical
implementation. If CFO indeed approaches to zero, partially compensation presented
above can be passed by.
4.3.2.3 Data Pre-compensation
So far, the estimation stage of the proposed joint estimation and compensation
scheme has been fulfilled. In previous discussion, the estimation of the CFO, SFO
and I/Q imbalance parameters have been performed on the frequency domain using
preamble symbols. In this part, we present data pre-compensation scheme. The
proposed scheme jointly compensated the effects of the CFO, SFO, I/Q imbalance as
well as fading channels. The received signals are firstly positive and negative
partially compensated similar to (4.70)
2 4 / 2 8 /
4 , 4 , 1, 4 , 4 , 2, 4 , 4 ,
2 4 / 2 8 /
4 , 4 , 1, 4 , 4 , 2, 4 , 4 ,
c s c
c s c
j iM k N j iM N
i k i k k i k i k k i k i k
j iM k N j iM N
i k i k k i k i k k i k i k
POS Z Z e G H X G H X e
NEG Z Z e G H X e G H X
(4. 72)
where 4 ,i kX is the desired signal. In (4.72), we neglect the impact of ICI during
compensation. The approximation is the trade-off between complexity and
performance. As stated previously, the maximum carrier and sampling frequency
offset are limited to 40ppm in [8]. Therefore, after fulfilling partially compensation,
the approximation here will make only moderate performance degradation. The
simulation results confirm this approximation.
Chapter 4
75
Taking the complex conjugation of the negative partially compensated result,
we can get the following equation
2 8 /4 , 4 ,1, 4 , 2, 4 ,
2 8 /4 ,2, 4 , 1, 4 ,4 ,
c
c
j iM Ni k i kk i k k i k
j iM Ni kk i k k i ki k
POS Z XG H G H e
XG H G H eNEG Z
(4. 73)
With the estimated parameters ˆc , ˆ
s , 1,ˆ
kG and 2,ˆ
kG , the distortion can be
corrected by (4.74). Note that 1,ˆ
kG and 2,ˆ
kG are the jointly estimate of channel
response and I/Q imbalance.
4 , 1, 4 , 2,
4 ,
1, 1, 2, 2,
ˆ ˆˆ
ˆ ˆ ˆ ˆ
i k k i k k
i k
k k k k
POS Z G NEG Z GX
G G G G
(4. 74)
Similar to (4.74), if we take the complex conjugation of the positive partially
compensated result, the following relation can be obtained.
4 , 1, 4 , 2,
4 ,
1, 1, 2, 2,
ˆ ˆˆ
ˆ ˆ ˆ ˆ
i k k i k k
i k
k k k k
POS Z G NEG Z GX
G G G G
(4. 75)
The final pre-compensation result is the average of (4.74) and the complex
conjugation of (4.75). For detailed information, one can refer to [54].
4.3.2.4 Phase Tracking and Compensation
Though pre-compensation has been carried out, the residual carrier frequency
offset c and sampling frequency offset s still affects the system performance,
especially when the length of the transmission packet is long. In the part, we use the
simplified carrier and sampling frequency offset estimation procedure presented in
the preceding discussion. The pilot after pre-compensation is
2 /
, ,ˆ c sj iM k N
i p i pX X e
(4. 76)
The phase rotation caused by residual CFO and SFO is
, , ,ˆ ˆ2 / /i p c s i p i piM p N angle X X (4. 77)
With linear interpolation, the compensation result is
, , ,ˆ ˆ
i k i k i pX X (4. 78)
4.3.2.5 Simulation Result
To evaluate the performance of the proposed scheme, a typical DC-OFDM
Chapter 4
76
based UWB system has been developed based on standard draft [8]. In the
simulations, different channel environments are adopted as the frequency selective
UWB channel at three typical data rate: 53.3 Mbps in CM4, 200 Mbps in CM2 and
480 Mbps in CM1. For each simulation, 1000 packets are transmitted, each
containing 1024 bytes of the information bits. For frequency hopping, we use TFC 9
for Band Group 2 as illustrated in Figure 2.8. The CFO is set to 40 ppm at each
carrier frequency and the SFO is set to 40 ppm at a sampling frequency of 264 MHz.
The minimal and maximal gain and phase imbalance are set to 0.6 dB, 6 degree and
1 dB, 10 degree respectively. The system parameters and non-ideal analog front-end
effects used in the simulations are listed in Table 4.4 and Table 4.5. In all
simulations, we assume perfect symbol synchronization at the receiver side.
Table 4.4: System parameters II
Parameters Value
Frame Length 1024 bytes
Packet Number 1000
TFC TFC 9 for Band Group 2
Data Rate 53.3 Mbps, 200 Mbps, 480 Mbps
Channel Model CM4 for 53.3 Mbps, CM2 for 200 Mbps, CM1 for 480 Mbps
Table 4.5: Front-end imperfection parameters at Carrier 1 for TFC 9
Parameters Subband #3 Subband #4 Subband #5 Subband #6
SFO 40 ppm at 528 MHz
CFO 40 ppm at 6636 MHz 40 ppm at 6600 MHz 40 ppm at 6864 MHz 40 ppm at 7128 MHz
I/Q Imbalance
g =0.6 dB, =6 degree
-1 -2
-1 -2
z 1.05 0.01z +0.01z
z 1.0 0.02z -0.05z
I
Q
h
h
g =0.8 dB, =8 degree
-1 -2
-1 -2
z 0.98 0.03z +0.01z
z 1.0 0.005z +0.2z
I
Q
h
h
g =0.8 dB, =10 degree
-1 -2
-1 -2
z 1.0 0.05z +0.01z
z 1.0 0.005z +0.2z
I
Q
h
h
g =1.0 dB, =10 degree
-1 -2
-1 -2
z 0.97 0.01z -0.005z
z 1.0 0.002z +0.02z
I
Q
h
h
The simulated mean square error (MSE) of CFO and SFO estimation versus
SNR is shown in Figure 4.13 and Figure 4.14 respectively. The proposed CFO and
SFO estimation algorithm is compared with the traditional method in [41] for data
rate 480Mbps scenario in CM1. In Figure 4.13, CFO 1~ CFO 4 represent CFO
estimation on different subbands. In Figure 4.13 and Figure 4.14, the traditional
method introduces an error floor to both CFO and SFO estimation. As discussed in
Chapter 4
77
Section 4.3.2, I/Q imbalance causes image interference which degrades the
performance of traditional CFO and SFO estimation. While the proposed estimation
scheme promises accurate CFO and SFO estimations in DC-OFDM based UWB
system with frequency dependent I/Q imbalance.
Figure 4.15 shows the Packet Error Rate (PER) performance of the DC-OFDM
based UWB system versus SNR. For comparison, Ideal case: no analog front-end
imperfections and Non-ideal case: non-ideal imperfections listed in Table 4.5 are
considered in simulations. Three typical data rates: 53.3 Mbps in CM4, 200 Mbps in
CM2 and 480 Mbps in CM1 are adopted in simulations. From Figure 4.15, we can see
that the proposed estimation and compensation scheme can achieve the system PER
performance (8% specified in [8]) at SNR 5.7 dB, 7 dB and 9 dB for three data rates
respectively, which is competent for practical applications. Meanwhile, Figure 4.15
demonstrates that the approximation in proposed joint estimation and compensation
scheme only results in limited performance degradation, less than 0.5 dB at PER=8%,
comparing to the ideal case without non-ideal analog front-end effects. Besides, the
proposed scheme achieves 0.3 dB SNR advantage comparing to the method in [42]
due to the proper management of SFO and frequency dependent I/Q imbalance, which
is inevitable in practical DC-OFDM UWB systems, but neglected in [42].
0 2 4 6 8 10 1210
-8
10-7
10-6
10-5
10-4
Signal-to-Noise Ratio(dB)
MS
E o
f C
FO
estim
atio
n
CFO 1: Method in [41]
CFO 2: Method in [41]
CFO 3: Method in [41]
CFO 4: Method in [41]
CFO 1: Method in [42]
CFO 2: Method in [42]
CFO 3: Method in [42]
CFO 4: Method in [42]
CFO 1: Proposed
CFO 2: Proposed
CFO 3: Proposed
CFO 4: Proposed
Figure 4.13: MSE of CFO estimation versus SNR, 480 Mbps, CM1
Chapter 4
78
0 2 4 6 8 10 1210
-11
10-10
10-9
10-8
10-7
10-6
Signal-to-Noise Ratio(dB)
MS
E o
f S
FO
estim
atio
n
SFO: Traditional
SFO: Proposed
Figure 4.14: MSE of SFO estimation versus SNR, 480 Mbps, CM1
0 2 4 6 8 10 1210
-3
10-2
10-1
100
Signal-to-Noise Ratio(dB)
Pa
cket E
rro
r R
ate
53.3 Mbps in CM4: Ideal
53.3 Mbps in CM4: Method in [42]
53.3 Mbps in CM4: Proposed
200 Mbps in CM2: Ideal
200 Mbps in CM2: Method in [42]
200 Mbps in CM2: Proposed
480 Mbps in CM1: Ideal
480 Mbps in CM1: Method in [42]
480 Mbps in CM1: Proposed
Figure 4.15: PER versus SNR in DC-OFDM based UWB system.
Chapter 4
79
4.4 VLSI Implementation for CFO Cancellation
In Chapter 2, we introduce the system architecture as well as the system
resources assigned for synchronization. According to the DC-OFDM based UWB
standard draft [8], we have only four identical OFDM preamble sets for symbol
timing and frequency synchronization in standard transmission mode. It results in a
very tight timing sequence in algorithm development. For system design, we use the
first two preamble sets for symbol timing, while the last two sets for CFO estimation.
The received signal with CFO compensation starts at the channel estimation
sequence.
Traditionally, CFO is estimated by auto-correlation of two identical symbols on
time domain, which is known as Moose algorithm [43]. CFO introduces phase
rotation 2 /c FFTn N to thn sample on time domain. Thus, the phase rotation
between two consecutive OFDM symbols on the same subband is 2 660 /128c .
Since cyclic characteristic of phase rotation, the maximal phase rotation is allowed to
. Then, we can get the maximal normalized CFO coefficient c is 0.097. If
we assume the carrier frequency is 4GHz, carrier frequency offset satisfies the
50ppm requirement in DC-OFDM based UWB system. We choose Moose algorithm
for CFO cancellation. Note that, CFO estimation and compensation in each subband
is independent with each other.
Figure 4.16 shows the timing sequence for CFO estimation module in
DC-OFDM based UWB system. As we can see, Preamble set 3 is used for fine
timing as well as CFO estimation. Note that, though the multi-path effect causes the
distance between two symbols in different subband varies from each other, the
distance between two symbols in the same subband remains the same, which equals
to 660, 4 times of OFDM symbol length. Thus, if we prepare a FIFO with 660
sample-depth, we can start the auto-correlation calculation with the fine timing
result.
Equation (4.58) characterizes Moose algorithm, in which we can find
auto-correlation, arc tangent and division. Besides, CFO compensation involves
vector rotation. The hardware design for auto-correlation and division modules have
been presented in section 3.3. In the following section, we present VLSI
implementation for arc tangent and vector rotation.
Chapter 4
80
Figure 4.16: Timing sequence for CFO estimation module
Both of arc tangent and vector rotation are classified to triangle calculation..
Basically, there are two VLSI implementation methods for triangle calculation:
lookup table method and CORDIC method. The former method explicitly lists all
results in a table to cover all possible inputs. Obviously, it will cost a great deal of
storage cells to cover the input range and to achieve the required precision. The
CORDIC method fulfills angle calculation and vector rotation by simple operations
like addition and shift. The targeted precision can be achieved by increasing iteration
times. In DC-OFDM based UWB system, we need a dual-mode CORDIC unit for
angle calculation and vector rotation. The two mode are named as vector mode and
rotation mode respectively.
Intrinsically, CORDIC algorithm adopts an iterative method to approximate the
final result. The iterative formula in CORDIC algorithm is
1 2
1 2
1 arctan 2
n
n
n
n
n
n
y n y n x n
x n x n y n
z n z n
(4. 79)
where n equals to either 1 or -1. In vector mode, the value of n makes y
approximate to zero, while z approximate to angle 0 0arctan y x . In rotation
mode, the value of n makes z approximate to zero, while ( , )x y approximate
to new coordinate ( ', ')x y . In order to keep the vector norm unchanged, the iteration
result should multiple by an adjusting factor 21 2 i
n
n
A .
Chapter 4
81
n
sign z n in rotation mode
sign y n in vector mode
(4. 80)
' tan cos
' tan cos
x x y
y y x
(4. 81)
The iteration process in vector mode and rotation mode are same, except the
value of n . Therefore, the dual-mode CORDIC unit can be realized by simply
adding some MUX and registers.
According to the requirements of speed and cost, CORDIC algorithm can be
implemented by folding structure or pipeline structure. We expect the CORDIC unit
is able to achieve 132MS/s throughput rate in DC-OFDM based UWB system. We
adopt the pipeline structure.
During the CFO estimation period, the CORDIC unit is set to vector mode. We
calculate the auto-correlation result and thus obtain the normalized CFO coefficient
ˆc . Then the CORDIC unit is set to rotation mode to compensate the CFO effect.
We adopt SMIC 0.13us technology library. The synthesis result of CORDIC unit
from Design Compiler is presented in Table 4.6. The synthesis result of CFO
cancellation module is presented in Table 4.7.
Table 4.6: Synthesis result of CORDIC unit
Combinational area 16745.097656
Noncombinational area 5595.010742
Net Interconnect area 103507.187500
Table 4.7: Synthesis result of CFO cancellation
Combinational area 659962.789263
Noncombinational area 662081.999834
Net Interconnect area 9525836.198914
Dynamic Power 90.8949 mW
Cell Leakage Power 500.0925 uW
Critical Path 4.64ns
Chapter 4
82
4.5 Conclusion
In this chapter, we study the frequency synchronization problem in DC-OFDM
based UWB system systematically. Firstly, we investigate multiple analog front-end
imperfections which are inevitable in practical OFDM system. CFO and SFO are
known as frequency offset which introduce ICI. I/Q imbalance introduces image
interference that renders the traditional CFO estimation hardly work. Secondly, we
build mathematics models of CFO, SFO and I/Q imbalance in OFDM system, and
analyze the performance degradation due to these analog front-end imperfections by
the metric of EVM. RF designer can set up connection between mismatch
parameters and performance degradation. Thirdly, we explore the intrinsic character
of I/Q imbalance which causes the image interference. Then, we design a set of new
training sequences based on phase rotation and give the corresponding estimation
algorithm. The simulation result shows that the new training sequence is able to
obtain the diversity message introduced by I/Q imbalance and therefore achieve the
diversity gain during demodulation process. In order to deal with the challenging
situation where multiple analog front-end imperfections co-exist, we propose a joint
estimation and compensation scheme. In the aspect of hardware implementation, we
present the hardware structure of CFO estimation and compensation module catered
for DC-OFDM based UWB system, with the emphasis on CORDIC unit that is
responsible for triangle calculations. The VLSI implementation result shows that the
proposed CFO estimation and compensation module satisfies the timing and
resource requirements in DC-OFDM based UWB system.
Chapter 5
83
Chapter 5.
5.1 Conclusion of Current Work
In this thesis, we systematically study the synchronization problem in
DC-OFDM based UWB system. We derive the performance analysis for multiple
synchronization errors, and address the estimation and compensation algorithms for
analog front-end non-ideal effects. The hardware implementation of synchronization
modules is also presented.
Chapter 1 introduces the background of UWB technology, and its development
in recent years. Subsequently, we presents the synchronization issues in DC-OFDM
based UWB system which we are interested in, including symbol timing and
frequency synchronization.
Chapter 2 introduces the fundamental information of DC-OFDM based UWB
system with the emphasis on receiver architecture and signal structure. The essential
points in synchronization issues are addressed according to DC-OFDM based UWB
PHY standard draft. The characteristics of UWB channel are also presented.
Chapter 3 discusses symbol timing problem in target system. We firstly derive
the performance analysis for symbol timing errors. Then we present the complete
symbol timing scheme tailored for DC-OFDM based UWB system. Simulation
result shows that the proposed scheme achieve good robustness in UWB channels. In
the last, we address the VLSI implementation of symbol timing algorithm. Both
detailed timing sequence and some key modules are presented.
Chapter 4 presents the frequency synchronization issues in DC-OFDM based
UWB system. We discuss multiple analog front-end imperfections in target system,
such as CFO, SFO, I/Q imbalance. We analyze the performance degradation due to
these imperfections by the metric of EVM. With this help, RF designers can figure
out the system parameters at the early stage of system design. After that, we study
the intrinsic characteristic of I/Q imbalance, and design a new training sequence
which is able to achieve the diversity gain during demodulation process. A joint
estimation and compensation scheme is presented for more challenging scenario:
CFO and SFO cancellation with the presence of frequency dependent I/Q imbalance.
Simulation result shows that the proposed scheme exhibits good performance even
Chapter 5
84
with severe mismatch. In the last, the hardware implementation of CFO estimation is
presented.
This chapter discusses some prospective research areas in future 60-GHz
technology, with the emphasis on non-ideal effects in front-end signal processing.
5.2 Prospective Research Area
In the past decade, explosion in internet services and wide spread usage of
electronic devices call for high data rates communication systems. The availability
of unlicensed 60-GHz band provides a great opportunity for multi-Gb/s short-range
wireless communication [44]. IEEE 802.15.3 Task Group 3c (TG3c) was formed in
March 2005 to develop a millimeter-wave-based alternative physical layer (PHY) for
the existing 802.15.3 WPAN standard 802.15.3-2003 [45]. The proposed standard
will allow a mandatory data rate of 2 Gb/s and an optional data rate of 3 Gb/s.
Moreover, many industrial partners have joined together to form WirelessHD or
WiHDTM
, a specification for the next generation wireless digital network interface
for consumer electronics products [46].
60-GHz gigabit WPAN systems are suitable for numerous short-range
applications in residential areas, conference rooms, offices, etc. The typical
applications are shown in Figure 5.1, which include wireless gigabit Ethernet,
wireless high-speed download, wireless streaming of high definition video, etc [47].
Figure 5.1: 60-GHz wireless applications
Chapter 5
85
Though owning various merits, 60-GHz technology has a number of challenges
to be overcome due to the huge data throughput and ultra-high carrier frequency. The
challenges involve the aspects of channel propagation issues, baseband modulation
schemes, as well as antennas and integrated circuit technologies. These problems are
strongly related when aiming at a low-cost system design. In this chapter, we focus
on the analog front-end device and several imperfections in 60-GHz applications.
5.2.1. Phase Noise
OFDM system suffers greatly by the presence of random phase noise in
oscillators, especially when the system operates at high carrier frequency for high
data rate applications. In practical systems, the amplitude and phase of the oscillator
are randomly disturbed by the thermal noise. Usually, the frequency fluctuations
dominate the influence of the oscillator imperfection on the systems [48]. These
random frequency fluctuations are often referred as phase noise. Phase noise will
impact the transmission by two effects: rotation of all demodulated sub-carriers by a
random common angle, and the occurrence of ICI.
Phase noise problem in 60-GHz applications needs more investigation. The
thermal noise in devices will affect the performance of local oscillator greatly. How
to model the phase noise? Is it a Guassian distributed random process or Wiener
process, or some else? And what about the corresponding compensation schemes
with moderate complexity?
5.2.2. Non-linear Power Amplification
In time domain, an OFDM symbol is the superposition of many carriers by
means of an Inverse Discrete Fourier Transform (IDFT). Hence, OFDM systems
require the signal processing blocks at transmitter and receiver side have a high
dynamic range, which leads to costly RF components. The high Peak to Average
Power Ratio (PAPR) in OFDM system is especially problematic for the Power
Amplifier (PA) [49].
A PA exhibits non-linear transfer behavior when the PA works in the range up to
its saturation point. The non-linear distortion cause signal compression and create
interference between sub-carriers [50]. Though several methods have been proposed
to reduce PAPR, such as improved modulation, Single Carrier OFDM (SC-OFDM),
Chapter 5
86
etc, the complexity is usually high. One way to eliminate the non-linearity is to apply
an Input Power Backoff (IBO) such that the amplifier works in a more linear region.
However, large IBO may result in low power efficiency. Besides the non-linearity in
different amplitude, the non-linearity in different frequency band may also exist in
60-GHz applications. How to calibrate the non-linearity and make proper
compensation needs more research.
5.2.3. DC Offset
Direct Conversion Radio (DCR) is well known for its low cost, high integration.
However, the direct conversion architecture severely suffers from DC offset problem,
which reduces the desired signal power over undesired signal power ratio. Moreover,
DC offset also affects symbol timing in OFDM system. Usually, auto-correlation
algorithm is adopted to pick up signal from noise. Certain DC offset may simply
render the this method hardly work.
Cancellation algorithm for DC offset is actively researched in literature. For
example, [51] proposes to eliminate the DC offset by the HPF composed from
feedback loop. However, the HPF degrades the BER performance due to the fact that
the desired signal power near the DC components is also decreased. One improvement
is to lower the cut-off frequency of HPF. However, this approach results in time
convergence problem due to the long time constant. Another method is to eliminate
the DC offset by estimation [52], which is obtained by averaging the received signal.
Due to the limited time duration, the estimation is not equal to the accurate one.
In 60-GHz applications, DC offset will be even more severe due to DCR
architecture and high carrier frequency. How to fulfill DC offset cancellation fast and
efficiently still needs more research.
5.2.4. ADCs Mismatch
All digital gigabit baseband architectures need ADCs of sufficient rate and
precision. The precision requirements are increased in case multiple antennas are
used to obtain spatial multiplexing, higher constellations are used for spectral
efficiency or digital equalization is done to combat dispersion. Since these scenarios
arise in the communication protocol design for the 60 GHz unlicensed band, ADCs
with high precision (8-10 bits) sampling at 5 GS/s are needed. Time-interleaving
Chapter 5
87
several low rate ADCs is a good option to meet these requirements. This architecture
can also result in power reduction due to the use of power efficient low rate ADCs,
such as SAR.
However, the time-interleaving architecture comes with the issue of mismatch
between the interleaved ADCs. To the first order, the mismatch can be classified as
gain, timing and voltage offset mismatch. We can estimate the mismatch by using the
already available channel training sequence and then the mismatch can be jointly
compensated with the channel equalization. Current research challenges are
integration of mismatch compensation with the space-time equalization MIMO
systems with the compensation of chromatic dispersion in the optical transceivers
and how we can scale the compensation algorithms with the number of interleaved
ADCs.
Reference
88
Reference
[1] FCC, “The report and order, revision of part 15 of the commission’s rules
regarding ultra-wideband transmission systems,” ET Docket 98-153, February
14, 2002.
[2] S. Roy, J. Foerster, V. Somayazulu, and D. Leeper, “Ultra wideband radio
design: the promise of high-speed, short-range wireless connectivity,” Proc.
IEEE, vol. 92, no. 2, pp. 295–311, Feb. 2004.
[3] XtremeSpectrum CFP Document, IEEE 802.15-03/ 154r3, 2003.A.
[4] Batra a, et al. Multi-band OFDM physical layer proposal for IEEE 802.15 task
group 3a [S]. IEEE P802.15-03/268r3, 2004.
[5] ECMA Standard 368: High rate ultra wideband PHY and MAC standard, 1st
Edition, December 2005.
[6] ISO/IEC 26907: 2007(E), High Rate Ultra Wideband PHY and MAC
Standard, 1st Edition, March 2007.
[7] WiMedia Alliance, http://www.wimedia.org/
[8] People’s Republic of China Standard: High-Speed Ultra Wideband
Communication PHY and MAC (draft)
[9] B. R. Saltzberg, “Performance of an efficient parallel data transmission
system,” IEEE Trans. Commu. COM-15(6):805-811, Dec. 1967.
[10] S. B. Weinstein, P.M. Ebert, “Data transmission by frequency division
multiplexing using the discrete Fourier transform,” IEEE Trans. Commun,
COM-19(5):628-634, Oct. 1971.
[11] A. Peled, A. Ruiz, “Frequency domain data transmission using reduced
computational complexity algorithms,” Proc. IEEE Int. Conf. Acoust, Speech,
Signal processing, pp. 964-967, Denver, CO, 1980.
[12] L. Yinghui, H. MInn, T. Jacobs and M. Z. Win, “Frequency offset estimation
estimation for MB-OFDM-based UWB systems,” IEEE Trans.
Communications, vol. 56, no. 6, pp. 968-979, Jun. 2008.
[13] A. Tarighat, R. Bagheri and A. H. Sayed, “Compensation schemes and
performance analysis of IQ imbalances in OFDM receivers,” IEEE Trans.
Signal Processing, vol. 53, no. 8, pp. 3257-3268, Aug. 2005.
[14] M. Sliskovic, “Carrier and Sampling Frequency Offset Estimation and
Correction in Multicarrier Systems,” IEEE Globecom Tele Conference, vol. 1,
Reference
89
25-29, pp. 285-289, Nov. 2001.
[15] B. Razavi, “Design considerations for direct-conversion receivers,” IEEE
Trans. Circuits and Systems II, vol. 44, no. 6, pp. 428-435, Jun. 1997.
[16] A. Batra, J. Balakrishnan, G. R. Aiello, J. R. Foerster and A. Dabak, “Design
of a Multiband OFDM System for Realistic UWB Channel Environments,”
IEEE Trans. Microwave theory and technology, vol. 52, no. 9, pp. 2123-2138,
Sep. 2004.
[17] M. J. M. Pelgrom, A. C. J. Duinmaijer, and A. P. G.Welbers, “Matching
properties of MOS transistors,” IEEE J. Solid-State Circuits, vol. 24, no. 5, pp.
1433–1439, Oct. 1989.
[18] International Technology Roadmap for Semiconductors (ITRS), Yield
Enhancement, 2008 update. http://www.itrs.net/
[19] Leon W. Couch II, Digital and Analog Communication Systems, Prentice
Hall, Inc., 6th Edition, 2001.
[20] J.Foerster and Q. Li, “UWB channel modeling contribution from Intel,” IEEE
P802.15-02/279-SG3a.
[21] J.M Cramer, R. Scholtz, M. Win, “Evaluation of an Indoor Ultra-Wideband
Propagation Channel,” IEEE P802.15-02/286-SG3a and IEEE
P802.15-02/325-SG3a.
[22] S.Ghassemzadeh and V. Tarokh, “The Ultra-wideband Indoor Multipath Loss
Model,” IEEE P802.15-02/282-SG3a and IEEE P802.15-02/283-SG3a.
[23] J. Foerster, “Channel Modelling Sub-committee Report Final,” IEEE
P802.15-02/490-SG3a.
[24] M. Pendergrass, “Empirically Based Statistical Ultra-Wideband Channel
Model,” IEEE P802.15-02/240-SG
[25] Y. Li, H. Minn and R. M. A. P. Rajatheva, “Synchronization, Channel
Estimation, and Equalization in MB-OFDM Systems”, IEEE Trans. On
Wireless Communication, vol. 7, no. 11, pp. 4341-4352, Nov 2008.
[26] M. Speth, F. Classen and H. Meyr, “Frame synchronization of OFDM systems
in frequency selective fading channels," Proc. of IEEE VTC'97, May 1997, pp.
1807-1811.
[27] M. Speth, D. Daecke and H. Meyr, “Minimum overhead burst synchronization
for OFDM based broadband transmission," Proc. of IEEE Globecom 98, 1998,
pp. 3227-3232.
Reference
90
[28] D. Lee and K. Cheun, “Coarse symbol synchronization algorithms for OFDM
systems in multipath channels," IEEE Commun. Letters, vol. 6, pp. 446-448,
Oct. 2002.
[29] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization
for OFDM," IEEE Trans. Commun., vol. 45, pp. 1613-1621, Dec. 1997.
[30] T. Keller, L. Piazzo, P. Mandarini and L. Hanzo, “Orthogonal frequency
division multiplex synchronization techniques for frequency-selective fading
channels," IEEE J. Select. Areas in Commun., vol. 19, pp. 999-1008, June
2001.
[31] C. L. Liu, “Impacts of I/Q imbalance on QPSK-OFDM-QAM detection,”
IEEE Transactions on Consumer Electronics, vol. 44, no. 3, pp.984-989,
Aug.1998.
[32] M. Windisch and G. Fettweis, “Performance Degradation due to I/Q
Imbalance in Multi-Carrier Direct Conversion Receivers: A Theoretical
Analysis,” Proc. IEEE International Conference on Communications
(ICC’06), Istanbul, Turkey,2006.
[33] IEEE Standard for Wireless LAN Medium Access Control (MAC) and
Physical Layer (PHY) Specifications: High-Speed Physical Layer in the 5
GHz Band, IEEE Standard 802.11aTM-1999.
[34] ETSI, “Digital Video Broadcasting(DVB); Measurement guidelines for DVB
systems,” Tech. Rep, May 2001.
[35] M. Valkama, M. Renfors and V. Koivunen, “Compensation of
Frequency-selective I/Q Imbalances in Wideband Receivers: Models and
Algorithms,” Wireless Communications, 2001 (SPAWC 01’), Pages 42-45,
20-23 Mar. 2001.
[36] P. Rykaczewski, M. Valkama and M. Renfors, “On the Connection of I/Q
Imbalance and Channel Equalization in Direct-Conversion Transceivers[J],”
IEEE Trans. Vehicular Technology, vol.57, no.3, pp.1630-1636, May.2008.
[37] J. P. Delmas, “Closed-Form Expressions of the Exact Cramer–Rao Bound for
Parameter Estimation of BPSK, MSK, or QPSK Waveforms,” IEEE Signal
Processing Letters, vol.15, pp.405-408, 2008.
[38] A. Barbieri and G. Colavolpe, “ On the Cramer-Rao Bound for Carrier
Frequency Estimation in the Presence of Phase Noise,” IEEE Tran. Wireless
Communications, vol.6, no.2, pp.575-582, Feb.2007.
Reference
91
[39] P.W. Wolniansky, G.J. Fonshini, G.D. Golden, R.A. Valenzulea, “V-BLAST:
an architecture for realizing very high data rates over the rich-scattering
wireless channel,” invited paper, International Symposium on Signals,
Systems, and Electronics’98, Pisa, Italy, Sept. 1998.
[40] Y. H. Jin, J. H. Kwon and Y. Lee, “Additional Diversity Gain in OFDM
Receivers under the Influence of IQ Imbalances,” IEEE ICC’07.
[41] K. B. Png, P. Xiaoming, S. Chattong, H. T. Francis and F. Chin, “Joint Carrier
and Sampling Frequency Offset Estimation for MB-OFDM UWB System,”
IEEE Radio and Wireless Symposium, pp. 29-32, Jan. 2008.
[42] F. Horlin, A. Bourdoux, and L. V. der Perre, “Low-complexity EM-based Joint
Acquisition of the Carrier Frequency Offset and I/Q imbalance,” IEEE Trans.
Wireless Communications, pp. 2212-2220, Jun. 2008.
[43] Moose, P.H.; “A technique for orthogonal frequency division multiplexing
frequency offset correction,” IEEE Transactions on Communications, Vol. 42,
Issue 10, pp. 2908-2914.
[44] P. Smulders, “Exploiting the 60 GHz band for local wireless multimedia access:
prospects and future directions,” IEEE Commun. Mag., vol. 40, pp. 140–147,
Jan. 2002.
[45] IEEE 802.15 WPAN Millimeter Wave Alternative PHY Task Group 3c (TG3c).
Online available: http://www.ieee802.org/15/pub/TG3c.html.
[46] WirelessHD, “WirelessHD Specification Version 1.0 Overview,” Res. Lab.
Electron., M.I.T., Cambridge, MA, Tech. Rep., October 9, 2007.
[47] A. Sadri, “802.15.3c Usage Model Document (UMD), Draft,” Tech. Rep., Jan.
2006, IEEE 802.15 TG3c document: 15-06-0055-14-003c.
[48] T. Lee and A. Hajimiri, “Oscillator Phase Noise: A Tutorial,” IEEE J.
Solid-State Circuits, vol. 35, no. 3, pp. 326–336, Mar. 2000.
[49] S. C. Cripps, RFPower Amplifiers for Wireless Comnunications. Artech House,
1999.
[50] A. Vaccardi D. Dardari, V. Tralli, “A theoretical characterization of nonlinear
distortion effects in ofdm systems,” in IEICE Transactions Communications.
IEEE, Oct. 2000, vol. 48, pp. 1755–1764.
[51] H. Yoshida, T. Kato, T. Toyoda, I. Seto, R. Fujimoto, T.Kimura, O. Watanabe,
T. Arai, T. Itakura, and H. Tsurumi, “Fully Differential Direct Conversion
Receiver for W-CDMA using an active harmonic mixer,” Radio Frequency
Reference
92
Integrated Circuits Symposium, 2003 IEEE, pp. 395–398, June 2003.
[52] H. Yoshida, H. Tsurumi, and Y. Suzuki, “DC offset canceller in a direct
conversion receiver for QPSK signal reception,” 9th IEEE Personal, Indoor,
Mobile Commun. Symp., vol. 3, pp. 1314–1318, Sep. 1998.
[53] Jun Zhou, Liang Liu, Fan Ye, Junyan Ren, “Design of New Training Sequence
and Estimation Scheme for Frequency Dependent I/Q Imbalance in
MB-OFDM based UWB Systems”, IEEE 8th
International Conference on
ASIC, Oct. 2009.
[54] Jun Zhou, Liang Liu, Fan Ye, Junyan Ren, “Joint Estimation and
Compensation for Front-end Imperfection in MB-OFDM UWB Systems”,
IEEE International Symposium on Circuits and Systems, May 2010.