Synchronization Algorithms and VLSI Implementation for DC-OFDM based UWB System

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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 L c H L f f f f f    (1. 1) where, f and _H f are the upper and lower -10 dB corner frequencies, _L

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

2

log (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.

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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].

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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

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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

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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:

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(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

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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.

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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

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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 LO f  f  f (2. 1) 2 ; 2 ; c IF LO image c IF LO f f f f f 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

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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.

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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

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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 ( ) ( ) h L K RF k l l k l l k h t X   t T    



  (2. 3) where T_l, _{k l}_, and X are random variables representing the delay of the lth

cluster, the delay of the kth multi-path component of the lth 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}_,  p_{k l}_, _l _{k l}_, . The

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small-scale coefficient is p_{k l}_, , 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 qth band is given by

, 2 ( ) , , 0 0 0 ( ) ( ) h q l k l L K j 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 [t t₀, ]₀ has been included in the CIR, and the delay

0

t 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.

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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 f_sub equals 2.062MHz.

1 1 sub s f NT T   (2. 5) where T is the sampling period, N is the number of sub-carriers and T is _s

the symbol period. The structure of discrete OFDM symbol is shown in Figure 2.6.

 

i

x n denotes the nth sample in ith OFDM symbol, 0  n N 1.

 

0

 

1



1



i i i i

x _x x x N _ (2. 6) Traditionally, cyclic prefix is added before data symbol to form a complete OFDM symbol. The cyclic prefix for ith OFDM symbol p_i is made up of the latest N_g samples in x _i



g

 

g 1





1



i i i i

p _x NN x NN  x N _ (2. 7) Therefore, the whole length for an OFDM symbol is NN_g.

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.

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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 ) FFT T ：IFFT/FFT Period 484.8ns(=1_F ) ZP

T ：Zero Padding Length 121.2ns(= 32 B )

GI

T ：Guard Interval Length 18.94ns(= 5 B ) SYM

T ：Symbol Interval 625ns(=T_FFTT_ZPT_GI)

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

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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 f . In the every moment c 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].

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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.

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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.

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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  n N 1.

 

0

 

1



1



i i i i

y _y y y N _ (3. 1) The cyclic prefix for ith OFDM symbol p_i is made up of the latest N _g

samples in y _i



g

 

g 1





1



i i i i

p _y NN y NN  y N _ (3. 2)

Therefore, the whole length for an OFDM symbol is NN_g.

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 d points in _i ith cyclic prefix and the other Nd_i points in ith data symbol. Here, we define d_i N



 

, 1 ,



,



1 ,

    

0 , 1 , ,



1



i i i i i i i i i i

w _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

 

j2 kd N_i/

i i

Y k Y k e  (3. 4) where Y k is the FFT output when perfect synchronization is obtained. In i

 

(3.4), a phase rotation of 2kdi /N is added to the signal of kth 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

 

i

 

_{ }

 

j2 kd N_i/ i Y k H k H k e X k     (3. 5)

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After channel equalization, the baseband signal is

 

Y ki

 

_{ }

 

X k X k

H 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 N_g  d_i 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



1



i i i i i i i g i g i g i w _y d y d  y N y_ NN y_ NN  y_ NN  d _ (3. 7) After FFT processing,

 

j2 kd_i/N i i i Y k _Y k ISI k _e  (3. 8)

 

1





 

2 / 1 0 i d j 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 kth

subcarrier of ith 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)

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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 N_g samples in ith data symbol should add the ZP samples in (i1)th 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

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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

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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

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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

1

c

f and f are set to Subband 3 and Subband 5 respectively. 500 discrete noise _c₂

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 1200 0 0.5 1 1.5 2 2.5 3x 10 4

Discrete samples index at time domain

P

o

w

e

r

Power detection method at Carrier 1

0 200 400 600 800 1000 1200 0 0.5 1 1.5 2 2.5 3x 10 4

P

o

w

e

r

Power detection method at Carrier 2

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0 200 400 600 800 1000 1200 0 0.1 0.2 0.3 0.4 0.5

N o rm a li za d a u to -co rr e la ti o n co e ff ici e n t

Auto-correlation method at Carrier 1

0 200 400 600 800 1000 1200 0 0.1 0.2 0.3 0.4 0.5

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 1200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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0 200 400 600 800 1000 1200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Figure 3.7: Packet detection, SNR=3dB, 200Mbps, CM2.

0 200 400 600 800 1000 1200 0 0.1 0.2 0.3 0.4 0.5 0.6

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

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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.

Synchronization Algorithms and VLSI Implementation for DC-OFDM based UWB System