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.