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

Transcription

1 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

2 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.

3 2 For my parents

4 Contents Contents... 2 List of Figures... III List of Tables... V List of Abbreviations... VI 摘要... 1 Abstract... 3 Chapter Background of UWB Communication OFDM based UWB System Contributions of Thesis Organization of Thesis Chapter System Description Receiver Architectures System Architecture UWB Channel Signal Structure Frame Structure Symbol Structure System Parameters Conclusion Chapter Synchronization Errors Symbol Timing Algorithm Packet Detection Coarse Timing TFC Detection Fine Timing VLSI Implementation for Symbol Timing Auto-correlation Algorithm Cross-correlation Algorithm I

5 Real-number Divider Conclusion Chapter Analog Front-end Imperfections Carrier Offset Sampling Offset I/Q Imbalance Performance Degradation Mathematics Model EVM Analysis Simulation Results Algorithms I/Q Imbalance Estimation and Compensation Joint Estimation and Compensation VLSI Implementation for CFO Cancellation Conclusion Chapter Conclusion of Current Work Prospective Research Area Phase Noise Non-linear Power Amplification DC Offset ADCs Mismatch Reference Acknowledgments II

6 List of Figures Figure 1.1: FCC spectrum mask of UWB emission level Figure 1.2: UWB applications... 6 Figure 2.1: Superheterodyne receiver architecture Figure 2.2: Direct conversion receiver architecture Figure 2.3: Band group allocation in DC-OFDM based UWB system Figure 2.4: Block diagram for DC-OFDM base UWB system Figure 2.5: PHY frame structure for DC-OFDM based UWB system Figure 2.6: Symbol structure for DC-OFDM based UWB system Figure 2.7: Frame structure for DC-OFDM base UWB system Figure 2.8: Frequency hopping in DC-OFDM based UWB, TFC Figure 3.1: OFDM symbol structure (d i denotes synchronization error) Figure 3.2: Influence to constellation chart due to time synchronization error Figure 3.3: Channel estimation: ZP-OFDM system and CP-OFDM system Figure 3.4: Power detection method, SNR=0dB, data rate 480Mbps, CM Figure 3.5: Auto-correlation method, SNR=0dB, 480Mbps, CM Figure 3.6: Packet detection, SNR=5dB, 480Mbps, CM Figure 3.7: Packet detection, SNR=3dB, 200Mbps, CM Figure 3.8: Packet detection, SNR=3dB, 53.3Mbps, CM Figure 3.9: Timing sequence of packet detection and coarse timing Figure 3.10: Process flow diagram of dynamic searching Figure 3.11: Coarse timing, SNR=5dB, 480Mbps, CM Figure 3.12: Coarse timing, SNR=3dB, 200Mbps, CM Figure 3.13: Coarse timing, SNR=3dB, 53.3Mbps, CM Figure 3.14: TFC searching chart for DC-OFDM UWB Figure 3.15: Standard Preamble 3 for TFC 3 or Figure 3.16: Cell structure in standard Preamble Figure 3.17: Fine timing, SNR=5dB, 480Mbps, CM Figure 3.18: Fine timing, SNR=3dB, 200Mbps, CM Figure 3.19: Fine timing, SNR=3dB, 53.3Mbps, CM Figure 3.20: Timing sequence for symbol timing module Figure 3.21: Signal processing flow for auto-correlation Figure 3.22: Hardware structure of cross-correlation cell III

7 Figure 3.23: Hardware structure of cross-correlation Figure 3.24: Signal processing flow for dual-bit division Figure 4.1: OFDM symbol spectrum with 3 sub-carriers Figure 4.2: I/Q imbalance model in DCR Figure 4.3: Error vector magnitude definition Figure 4.4: Simulated and analytical EVM versus SNR, 16-QAM Figure 4.5: Simulated and analytical EVM versus IRR, SNR=20dB Figure 4.6: Power spectral arrangement in OFDMsymbol Figure 4.7: Frequency domain illustration of the effect of I/Q imbalance Figure 4.8: Training scheme for both I/Q imbalance and channel estimation Figure 4.9: QPSK modulation constellation Figure 4.10: SNR enhancement versus additional phase rotation Figure 4.11: MSE versus Eb/No for I/Q imbalance estimation, 480 Mbps Figure 4.12: PER versus Eb/No, 16-QAM, 480 Mbps Figure 4.13: MSE of CFO estimation versus SNR, 480 Mbps, CM Figure 4.14: MSE of SFO estimation versus SNR, 480 Mbps, CM Figure 4.15: PER versus SNR in DC-OFDM based UWB system Figure 4.16: Timing sequence for CFO estimation module Figure 5.1: 60-GHz wireless applications IV

8 List of Tables Table 2.1: UWB channel model characteristics Table 2.2: DC-OFDM UWB system parameters Table 2.3: Cover sequence for standard preamble Table 2.4: Time-frequency hoping code for DC-OFDM based UWB system Table 3.1: Synthesis result for symbol timing module Table 4.1: Peak-to-mean magnitude ratio for M-QAM scheme Table 4.2: I/Q imbalance profiles Table 4.3: System parameters I Table 4.4: System parameters II Table 4.5: Front-end imperfection parameters at Carrier 1 for TFC Table 4.6: Synthesis result of CORDIC unit Table 4.7: Synthesis result of CFO cancellation V

9 List of Abbreviations ADC AGC AWGN BPF CFO CIR CMOS CP CPO DAC DCR DFT DSP DSSS ECMA FIFO EIRP EVM FCC FCS FFT HCS IBO ICI IDFT I/Q IRR ISI ITRS LNA LO LOS Analog to Digital Converter Auto Gain Control Additive White Gaussian Noise Band-Pass Filter Carrier Frequency Offset Channel Impulse Response Complementary Metal-Oxide Semiconductor Cyclic Prefix Carrier Phase Offset Digital to Analog Converter Direct Conversion Radio Discrete Fourier Transform Digital Signal Processing Direct Sequence Spread Spectrum European Computer Manufactures Association First in First out Effective Isotropic Radiated Power Error Vector Magnitude Federal Communications Commission Frame Check Sequence Fast Fourier Transform Header Check Sequence Input Power Backoff Inter-Carrier Interference Inverse Discrete Fourier Transform In-phase and Quadrature-phase Image Rejection Ratio Inter-Symbol Interference International Technology Roadmap for Semiconductors Low-Noise Amplifier Local Oscillator Light of Sight VI

10 LPF OFDM PA PAPR PLCP SFO SINR SNR SoC SPO TFC UWB VLSI ZP Low-Pass Filters Orthogonal Frequency Division Multiplexing Power Amplifier Peak to Average Power Ratio Physical Layer Convergence Protocol Sampling Frequency Offset Signal to Interference and Noise Ratio Signal to Noise Ratio System on Chip Sampling Phase Offset Time Frequency Code Ultra-wideband Very Large Scale Integrated Circuit Zero Padding VII

11 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 1

12 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;TN

13 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 3

14 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; TN

15 Chapter 1 Chapter 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 where, f c f H f /2 H f 5 L f L (1. 1) f and H f L 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 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 C Blog (1 SNR) (1. 2) 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.

16 Chapter 1 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 6

17 Chapter 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 a 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 7

18 Chapter 1 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 8

19 Chapter 1 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: 9

20 Chapter 1 (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 10

21 Chapter 1 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. 11

22 Chapter 2 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 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 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 12

23 Chapter 2 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, f f f (2. 1) IF c LO f image fc 2 fif ; flo f fc 2 fif ; flo 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 Direct Conversion Receiver The Direct Conversion Receiver (DCR), which is also known as homedyne or 13

24 Chapter 2 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 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 14

25 Chapter 2 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 UWB Channel The physical transmission medium in wireless applications, which is also known 15

26 Chapter 2 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 P 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 a 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 a UWB RF channel model is given by where l Lh K h ( t) X ( t T ) (2. 3) RF k, l l k, l l0 k0 T, kl, and X are random variables representing the delay of the l th cluster, the delay of the k th multi-path component of the l th 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 pk, llk, l. The 16

27 Chapter 2 small-scale coefficient is p kl,, 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 q th band is given by Lh K j2 fq ( Tl k, l ) q k, l s l k, l 0 l0 k0 h ( n) X e p( nt T t ) (2. 4) where the effect of the combined transmit and receive filter with the impulse response pt () whose span is [ t0, t0] has been included in the CIR, and the delay t 0 is inserted for the causality. Details of the channel models are referred to [25] and references therein. 2.2 Signal Structure 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. 17

28 Chapter 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. f sub 1 1 NT T (2. 5) where T is the sampling period, N is the number of sub-carriers and s T s is the symbol period. The structure of discrete OFDM symbol is shown in Figure 2.6. i x n denotes the n th sample in i th OFDM symbol, 0 n N xi x i xi xi N (2. 6) Traditionally, cyclic prefix is added before data symbol to form a complete OFDM symbol. The cyclic prefix for i th OFDM symbol p i is made up of the latest N g samples in x i g g 1 1 pi xi N N xi N N xi 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 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

29 Chapter 2 Table 2.2: DC-OFDM UWB system parameters Parameters Value N :Sub-carrier Number 128 B :Sub-band Bandwidth F :Sub-carrier Spacing 264MHz MHz(= BN) T FFT :IFFT/FFT Period 484.8ns(=1 F ) T ZP :Zero Padding Length 121.2ns(= 32 B ) T GI :Guard Interval Length 18.94ns(= 5 B ) T :Symbol Interval 625ns(= T FFT T ZP T GI ) SYM 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 S cover [m], TFC=1,2,8,9 S cover [m], TFC=3,4,10,11 S cover [m], TFC=5,6,7,12,

30 Chapter 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 c. 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 20

31 Chapter 2 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. 21

32 Chapter 3 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. 22

33 Chapter 3 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 yi y i yi yi N The cyclic prefix for i th OFDM symbol p i is made up of the latest samples in y i g g 1 1 pi yi N N yi N N yi N (3. 1) N g (3. 2) Therefore, the whole length for an OFDM symbol is N N. g other Figure 3.1: OFDM symbol structure (d i 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 i points in i th cyclic prefix and the N di points in i th data symbol. Here, we define di N, 1,, 1, 0, 1,, 1 wi y i N di yi N di yi N yi yi yi N di (3. 3) According to the cyclic characteristic of FFT, the signal after FFT processing can be denoted as where i i Y k j2 kdi / N Yi k e (3. 4) Y k is the FFT output when perfect synchronization is obtained. In (3.4), a phase rotation of 2 kd / N is added to the signal of k th subcarrier. This i phase rotation can be compensated during channel equalization in frequency domain. Suppose the frequency response of practical channel is estimated result is Hk H k k Y k Hk, and the i j2 kdi / N H k e (3. 5) X i 23

34 Chapter 3 After channel equalization, the baseband signal is X k Y k i X k (3. 6) H k 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 Ng di 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 wi yi di yi di yi N yi N Ng yi N Ng yi N Ng d i After FFT processing, Y k Y k ISI k e (3. 7) j2 kdi / N i i i (3. 8) d i 1 j2 km/ N i i1 g i (3. 9) m0 ISI k y m N N y m e Therefore, phase rotation as well as ISI will be added simultaneously to subcarrier of i th symbol. It is the ISI that causes sever performance degradation in OFDM system. k th 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) 24

35 Chapter 3 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 i th 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 25

36 Chapter 3 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 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 26

37 Chapter 3 calculated in (3.10). N P( n) y( n) y ( n) (3. 10) n1 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, N P( n) [ x( n) w( n)] [ x ( n) w ( n)] n1 N n1 2 2 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 Cauto( n) [ x( n m) w( n m)] [ x ( n) w ( n)] n1 (3. 12) N x( n m) x ( n) x( n m) w ( n) x ( n) w( n m) w( n m) w ( n) n1 N 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. ( n) N n1 N y( n m) y ( n) n1 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 27

38 Power Power Chapter 3 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 f c1 and c2 f 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. 3 x 104 Power detection method at Carrier 1 3 x 104 Power detection method at Carrier Discrete samples index at time domain Discrete samples index at time domain Figure 3.4: Power detection method, SNR=0dB, data rate 480Mbps, CM1. 28

39 Normalizad auto-correlation coefficient Normalizad auto-correlation coefficient Normalizad auto-correlation coefficient Normalizad auto-correlation coefficient Chapter 3 Auto-correlation method at Carrier 1 Auto-correlation method at Carrier Discrete samples index at time domain Discrete samples index at time domain 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. 1 Auto-correlation method at Carrier 1 1 Auto-correlation method at Carrier Discrete samples index at time domain Discrete samples index at time domain Figure 3.6: Packet detection, SNR=5dB, 480Mbps, CM1. 29

40 Normalizad auto-correlation coefficient Normalizad auto-correlation coefficient Normalizad auto-correlation coefficient Normalizad auto-correlation coefficient Chapter Auto-correlation method at Carrier Auto-correlation method at Carrier Discrete samples index at time domain Discrete samples index at time domain Figure 3.7: Packet detection, SNR=3dB, 200Mbps, CM2. Auto-correlation method at Carrier 1 Auto-correlation method at Carrier Discrete samples index at time domain Discrete samples index at time domain Figure 3.8: Packet detection, SNR=3dB, 53.3Mbps, CM 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 30

41 Chapter 3 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 31

42 Chapter 3 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 S d 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. 32

43 Auto-correlation coefficient Normalized auto-correlation coefficient Auto-correlation coefficient Normalized auto-correlation coefficient Auto-correlation coefficient Normalized auto-correlation coefficient Chapter Discrete samples index at time domain Discrete samples index at time domain Figure 3.11: Coarse timing, SNR=5dB, 480Mbps, CM1. 3 x Discrete samples index at time domain Discrete samples index at time domain Figure 3.12: Coarse timing, SNR=3dB, 200Mbps, CM2. 8 x Discrete samples index at time domain Discrete samples index at time domain Figure 3.13: Coarse timing, SNR=3dB, 53.3Mbps, CM3. 33

44 Chapter 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 34

45 Chapter 3 illustrated in Figure 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 35

46 Chapter 3 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 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

47 Chapter 3 Figure 3.15: Standard Preamble 3 for TFC 3 or 9. If we denote the first sample in Preamble 3 as S 0 and the last one as S 127, the whole preamble can be divided into 16 cells A 0 ~ A 15, with 8 samples in each cell, as illustrated in Figure The sequence of signal sign in the first cell C 0 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 Therefore, the sign sequence for whole samples on time domain is C { C0, C1,, C14, C15 }. 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. 37

48 Chapter 3 Figure 3.16: Cell structure in standard Preamble 3. N C ( k) y( k n) C cross (3. 14) kn, 1 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 38

49 Accumulated amplitude Accumulated amplitude Chapter 3 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 Discrete samples index at time domain Figure 3.17: Fine timing, SNR=5dB, 480Mbps, CM Discrete samples index at time domain Figure 3.18: Fine timing, SNR=3dB, 200Mbps, CM2. 39

50 Accumulated amplitude Chapter Discrete samples index at time domain Figure 3.19: Fine timing, SNR=3dB, 53.3Mbps, CM 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 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 40

51 Chapter 3 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 Noncombinational area Net Interconnect area Dynamic Power mw 41

52 Chapter 3 Cell Leakage Power Critical Path uw 4.58ns 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). xn ( ) is the input signal. -D Z means delay unit, where D=660, N=128. N 1 C( n) x( n k) x ( n k D) k0 N1 N1 P( n) x( n k D) x ( n k D) x( n k D) k0 k0 2 (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 Cn ( ) and the other to Pn. ( ) 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. Cn ( ) and Pn ( ) are characterized by 18-bits. From (3.15) we can see that Cn ( ) and Pn ( ) need to calculate summation of 128 consecutive samples. Whenever a new sample comes, we update Cn ( ) and Pn ( ) by abstracting the oddest and adding the new sample. It can be denoted as, C( n 1) C( n) x( n 127) x( n 1) 2 2 (3. 16) 42

53 Chapter 3 P( n 1) P( n) x( n 127) x( n 1) 2 2 (3. 17) Cross-correlation Algorithm Cross-correlation is used in fine timing process. It need two signal inputs: one is received signal yn, ( ) 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 C 0 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 yn ( ). Then the result is stored in reg8. By this method, we calculate the cross-correlation of 128 samples yn ( ) and C. Note that, this cross-correlation result is divided into 16 parts, from reg0 to reg120 as illustrated in Figure 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 A 0 ~ A 15, 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 43

54 Chapter 3 cross-correlation in DC-OFDM based UWB system. Figure 3.23: Hardware structure of cross-correlation Real-number Divider We need a real-number divider to calculate the normalized auto-correlation coefficient in (3.13). Since the input Cn ( ) and Pn ( ) 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. 44

55 Chapter 3 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. 45

56 Chapter 4 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 Carrier Offset In OFDM system, carrier offset consists of CFO and Carrier Phase Offset 46

57 Chapter 4 (CPO). Normally, these non-ideal effects are caused by mismatch of local oscillators between transmitter and receiver 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 f n. 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 fc fc fc ', 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 fc 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 N /2 0 power spectrum density. Let us introduce the normalized CFO coefficient carrier frequency offset fc to the inter-carrier spacing f CFO as the ratio of the actual f sub c CFO (4. 1) fsub 47

58 Chapter 4 Generally, the normalized CFO coefficient can be divided into two parts: CFO z (4. 2) where z is an integer, which indicates a coarse carrier frequency offset, i.e. the integral multiple of sub-carrier spacing. c c denotes fine carrier frequency offset, which is no bigger than half of sub-carrier space, 0.5 c 0.5. 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 c 0 in the following discussion. Then after FFT processing, the received signal on symbol can be denoted as, Y k X l e W k N1 N1 ( lkc ) 1 j2 n N i( ) i( ) ( ) N l0 n0 k th sub-carrier of i th (4. 3) where Wk ( ) presents the sample of Gaussian noise. In (4.3), we can find that if 0, we have Y k X k W k. Rewrite (4.3) as, c i N 1 k i i k i l0, lk i l Y ( k) X ( k) I X ( l) I W ( k) k 0,1,, N 1 (4. 4) k in which l I k is the ICI coefficient between the two sub-carriers l and k. l sin( ( l k)) N 1 I exp j ( l k) k N sin( ( l k) / N) N (4. 5) In equation (4.4), the first term is the expected signal. If there is no CFO ( c 0 ), the ICI coefficient ICI part. As coefficient c l I k l I k achieve the maximal value 1. The second term is increasing, the magnitude of desired signal decrease, while ICI increases. Thus, the Signal to Interference and Noise Ratio (SINR) is where SINR 2 k E I k N 1 2 l N 0 / Es I k i0, jk (4. 6) E s denotes the power of an OFDM symbol, N 0 denotes the noise power. Comparing (4.6) with the equation without CFO SNR Es N0, we can get the degradation on system SNR as 48

59 Chapter 4 2 N 1 2 SINR k Es l Dc 10log log E I 10log 1 E I k k SNR N 0 (4. 7) l0, lk 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 Es Dc 1 ln10 3 N 0 (4. 8) The data rate for transmission is R N / T for OFDM system. While for single carrier system, the data rate is R 1/ T. Since the CFO can be rewritten as fc/ f fc T, we have, c sub fc Es 1, OFDM system ln10 3 N R N 0 Dc fc Es 1 single carrier system ln10 3 R, N0 (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 Carrier Phase Offset If we assume the phase offset between carrier frequency signals is, the discrete signals at receiver side can be written as, y n j y n e (4. 10) After FFT processing, the signal is transferred to frequency domain, * j Y 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. 49

60 Chapter 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) 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 ' s s s f f 1, and the first same at receiver side is coincide with the first one at transmitter side, then the signal of domain is, k th samples in m th OFDM symbol on time m kf s mn n N 1 j2 N ' f s m k 0 y n X k e 1 s N1 k mn n 2 1 kn k smn j N j2 N N X mk e X mk e k0 k0 (4. 12) After FFT processing, (4.12) can be written as, 1 ik N N1 1 s Ym k ym i e e X m k I k X m k I k Wm k N i0 i0 ik 2 N j2km k i (4. 13) where Generally, i k I denotes the ICI coefficient, k i sin k 1s i i N 1 I k exp j k 1 s i 1 N s N sin N s is smaller than 100ppm. For example, when k k 1 127, we have i k I k k I k, and I k (4. 14) 100ppm, arg The ICI component N 1 X m is so small that we can neglect the effect of it. Therefore, the i0, ik impact of SFO can be viewed as the 2km phase rotation on received signals, s s 50

61 Chapter 4 j2 km Ym k X m 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 Sampling Phase Offset We assume the normalized sampling phase offset is 0, then the received signal is denoted as, m kf 1 s mn n 0 N j2 N fs m k 0 y n X k e kmn n 0 N kn k 0 N1 j2 1 j2 j2 N N N X mk e X mk e e k0 k0 (4. 16) After FFT processing, the received signal on frequency domain is m m Y k X k e 0 j2 k N (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 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. 51

62 Chapter 4 HNOM f HI f yi t yt x LO, I t cos2 fct xlo, Q t g sin 2 fct HNOM f HQ f yq t Figure 4.2: I/Q imbalance model in DCR Frequency Independent Mismatch The frequency independent I/Q imbalance is caused by the mismatch in quadrature demodulator. The local oscillator signal x () t of an imbalanced quadrature demodulator is here modeled as c c x ( t) cos(2 f t) jgsin(2 f t ) K e K e (4. 18) LO c c LO j2 f t j2 f t 1 2 where parameter g and characterizes the magnitude and phase imbalance between the two local oscillator signals, x LO, I and x LO, Q in Figure 4.2. The mismatch coefficients are given by K1 (1 ge j ) / 2, K2 (1 ge j ) / 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), H f H f H f I NOM I LPF H f H f H f Q NOM Q, LPF (4. 19) where H ( f ) is the nominal LPF response rejecting the high-frequency NOM components, HI, LPF ( f ) and H, ( f ) represent the actual mismatch effects due to branch filters, AGCs, A/Ds, etc. Q LPF Wideband Signal Model To explicitly characterize the imbalance effects on the individual channel 52

63 Chapter 4 signals, we write the multi-channel received signal yt () as LO () y( t) 2Re[ z( t) e ] z( t) e z ( t) e j2 fct j2 fct j2 fct (4. 20) Then the received signal is down converted to baseband by mixing it with x t. Assuming that H ( f) 1 for f B/ 2 and H ( f) 0 for NOM f B/ 2, the down converted signal rt () can be written as 1 2 NOM r( t) K z( t) K z ( t) (4. 21) To analyze the effect of branch mismatches, the real and image part of signal rt () can be written as r ( t) z ( t) and r ( t) g cos( ) z ( t) g sin( ) z ( t) I I Q Q I respectively. Then in terms of Fourier transforms, the received signal after branch mismatches is given by, Z( f ) Z ( f ) jz ( f ) I Q H ( f ) R ( f ) jh ( f ) R ( f ) I I Q Q H ( f ) Z ( f ) jh ( f )[ g cos( ) Z ( t) g sin( ) Z ( t)] I I Q Q I (4. 22) [ H ( f ) jh ( f ) g cos( )] Z ( f ) j[ H ( f ) g cos( )] Z ( t) I Q I Q Q After some manipulations, (4.22) can be written as, Z( f ) G ( f ) Z( f ) G ( f ) Z ( f ) (4. 23) 1 2 where ( ) [ ( ) ( ) j G ]/ 2 1 f H f H f ge, ( ) [ ( ) ( ) j G ]/ 2 2 f H f H f ge. I Q Therefore, the impaired signal at sub-carrier k of the i th OFDM symbol can be modeled as * Zi, k G1, kzi, k G2, kzi, k (4. 24) 1 j G1, k I, k Q, k 2 H ge H 1 j G2, k H I, k ge H Q, k 2 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 : sub-carrier k : Z k I Z k is interfered by the received signal at, 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 Q 53

64 Chapter 4 IRR k G 2 1, k (4. 25) G 2, k 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 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 54

65 Chapter 4 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 sk ( ) is the reference sequence of complex symbols, zk ( ) is the measured sequence of complex symbols. Then the EVM is defined as Figure 4.3: Error vector magnitude definition EVM 1 K 1 Yˆ k0 k K S 2 max X k 2 (4. 26) where X k denotes ideal symbol, Y ˆk is the corresponding received one. represents the maximal amplitude in the constellation set. Define peak-to-mean magnitude ratio of the given modulation scheme D Smax / Srms, then (4.26) can be rewritten as S max EVM 1 K 1 Yˆ k0 k K D S 2 2 rms X k 2 (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 X X, X,, X (4. 28) N /2 N /21 N /21 Then, the baseband signal xt () can be denoted as T 55

66 Chapter 4 i N /21 1 j2 ktimt / NT i, k (4. 29) N i kn /2 x t X e Table 4.1: Peak-to-mean magnitude ratio for M-QAM scheme M-QAM Format Peak-to-mean Magnitude Ratio where X ik, is the complex modulated transmission data at the k th sub-carrier of the i th 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 ht () and Additive White Gaussian Noise sample (AWGN), wt (), the received signal can be written as in which i y t x t h t w t (4. 30) i represents convolution operation. After CFO and SFO impairment, the sampled discrete complex baseband signal for the k th sub-carrier of the i th OFDM symbol after the receiver FFT processing can be written as N /21 Z H Y I H Y I W (4. 31) i, k i, k i, k i,0 i, l i, l i, lk k ln /2, lk where Ii, l k is the ICI coefficients with joint effect of CFO and SFO. W k represents noise sample on frequency domain. I i, lk For simplicity, the summation in this section. i, k i, k j2 im c k s / N Y X e (4. 32) 1 1/ sin s c l - k j l k N s c e N sin l k / N s ln/21 ln /2, lk will be abbreviated as lk c (4. 33) later 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. 56

67 Chapter 4 Zi, k G1, k Hi, kyi, k Ii,0 Hi, lyi, lii, l k Wk lk G H Y I H Y I W 2, k i, k i, k i,0 i, m i, m i, mk k mk (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 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. l l / 2, / 2 1 and l k l N N E X X * 0, l k E X E X,. (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 l l n, l N / 2, N / 2 1 E W E W. With these assumptions, we define Tl G1, lhl, (4.34) can be rewritten as Y X T I Z (4. 35) l l l 0 l where the term XlTlI 0 denotes the first term in (4.34) and summation of all the other terms. Z l is the 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 Tˆl T l V l, if estimation is unbiased. For illustration, V l is additive Gaussian noise with zero mean and variance 2 2 V Errest E{ Tl }, where Err est 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 Y ˆl can be written as ˆ Y T Z Yl X I (4. 36) T T T l l l l 0 ˆ ˆ ˆ l l l

68 Chapter 4 Hence, the error vector at sub-carrier l is Yˆ X (4. 37) l l l Submitting (4.36) and (4.37) into (4.27), and making some straight-forward algebra operations. Equation (4.38) is obtained Vl 2 1 Vl 2 W 1 G l 2, l Vl 2 2 W l EVM l E I0 1 I0 1 H 1 2 kik l H 2 li0 HmIml D Tˆ ˆ ˆ l H T l l k l X l H G l 1, l T l ml X l (4. 38) Equation (4.38) deserves more detail discussion to achieve a simple result. 2 2 Firstly, E{ V / Tˆ } E{ V / T } Err is hold when estimation error is relative l l l l est small, i.e ~10-5. Secondly, IRR 1 in realistic OFDM system, therefore 2 2, l / 1, l 1 G G. We define ICI on sub-carrier l caused by residual CFO as mirrored one due to I/Q imbalance as Though IRR 1, ICI ICI H / ICI l, H I l k k l kl H I l m ml ml 2 2 ICI l and the (4. 39) 2 l Hl 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 [38]. Err est is inevitable, it decades quickly with SNR in practical OFDM system ˆ 2 E{ V / T } 1 when SNR is large. Hence, averaging over all data l l 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 N / ICIl 1 H l 2 1 ICI 1 l EVM E I0 1 Errest I0 I D ln/2 H IRR l l Hl IRRl H SNR l l (4. 40) 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 58

69 Error Vector Magnitude Chapter 4 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 Frequency dependent imbalance h h LPF, I LPF, Q -1-2 z z +0.02z -1-2 z z +0.01z Profile 1,CAL Profile 1,SIM Profile 2,CAL Profile 2,SIM Profile 3,CAL Profile 3,SIM Signal to Noise Ratio (db) 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 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 59

70 Error Vector Magnitude Chapter 4 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 2 is small. In this situation, E{ V / T ˆ } 1 does not hold and the relevant terms in (4.38) can not be neglected. l l In Figure 4.5, we consider different modulation schemes at SNR=20dB. Without loss of generality, estimation error Err est is set to Normalized residual CFO is set to 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 IRR 1 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 QPSK,CAL QPSK,SIM 16-QAM,CAL 16-QAM,SIM 64-QAM,CAL 64-QAM,SIM Image Rejection Ratio (db) 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 60

71 Chapter 4 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 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 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 61

72 Power Chapter 4 by averaging bit error rates through all SNR range, P ( ) ( ) B PB x p x dx (4. 41) 0 where PB ( x ) is the BER of certain modulation scheme at SNR x, 2 x Eb / N0. denotes the signal magnitude variation caused by fading effect. px ( ) 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 Normalized Frequency (pi*rad/s) 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 : received signal at sub-carrier Z k is interfered by the k : Z k, 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 62

73 Chapter 4 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 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. 63

74 Chapter 4 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 n Tr /2 OFDM symbols, the receiver can estimate the coefficient G 1,k, k 1 N/ 2 as well as G 2,l, l N / 2 1 N. While in the next n /2 OFDM symbols, the receiver obtains the message of G 1,k, k N / 2 1 N, and G 2,l, l 1 N/ 2. 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). Im Tr Im θ Re Re (a) QPSK in ECMA-368 (b) QPSK based on phase rotation. Figure 4.9: QPSK modulation constellation. 64

75 Chapter 4 For simplicity, we neglect the DC sub-carrier and divide the training sequence into two parts P 1,k and P 2,k. Each of these two parts consists of 63 sub-carriers, where T Prmb P 1, k, P2, k,1 k 63 (4. 42) T {} represents transposition operation. We denote the original training sequence in polar coordinates as, P 1, k P 2, k L e k k j k L e jk (4. 43) where Lk 1, k { / 4, 3 / 4}. 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, P1, k ji Prmb i e,1 i 4 (4. 44) P2, k where [,π/2., π/2 ]. represents the phase rotation, i 0 / 4. Without losing generality, we analyze the SNR for I/Q imbalance estimation when /4. We normalize the preamble, k Prmb π π 1 cos jsin 1+ j (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 SNR 10log / Similarly, the preamble symbol with additional phase rotation is (4. 46) Prmb π π 1 1 cos + jsin 1 Dj D 1 (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 Prmb 1. Hence, the SNR for I/Q imbalance estimation changes to 2 D 2 SNR 2 10log 10 / 2 D 1 (4. 48) 65

76 SNR Enhancement (db) Chapter 4 Making some straight-forward algebra operations, we can get the relationship between signal-to-noise ratio enhancement G and phase rotation, G SNR -SNR 20log D 2 D 1 (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 Additional Phase Rotation (degree) 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 P 1,k and P 2,k, rewrite G 1,k and G 2,k as follows, G G1,1, k G2,1, k, G 1, k 2, k G1,2, k G2,2, k 66 (4. 50) Making conjugation of (4.24), we can get the following relation (with no noise presence). R k G1, k G2, k Rk R G k 2, k G1, k R k (4. 51)

77 Chapter 4 Taking (4.44) and (4.50) into (4.51), the received training sequences after I/Q imbalance impairment are T T,T T T T i = ( i,1 i,2), 1 i 4 i,1 i,2. P e G P e G ji ji 1, k 1,1, k 2, k 2,1, k P e G P e G ji ji 2, k 1,2, k 1, k 2,2, k (4. 52) as For simplicity, we neglect the sub-carrier index k and denote L '. Notice that there are following relationships between k and sin cos sin cos k cosk k sin k k cosk sin k k L k as L, L k (4. 53) Define the internal parameters (4.52) can be rewritten as β and γ k. When i 1, 2, sin T Lcos β G β G 1,1 1,1 2,1 k cos Lj sin β G β G 1,1 2,1 sin T L cos β G β G 2,1 1,1 2,1 cos Lj sin β G β G 1,1 2,1 T L' sin γ G cos γ G 1,2 1,2 2,2 L' j cos γ G sin γ G 1,2 2,2 T L' sin γ G cos γ G 2,2 1,2 2,2 L' j cos γ G sin γ G 1,2 2,2 Combing (4.54a)~(4.54d), we define the intermediate variables J 1 and J 2 (4. 54a) (4. 54b) (4. 54c) (4. 54d) J 2Lsin β G jg (4. 55a) 1 2,1 1,1 J 2L' sin γ G jg (4. 55b) 2 1,2 2,2 Similarly, Prmb 3 and Prmb 4 can be denoted as J 3, J 4. J 2Lsin β G jg (4. 55c) 3 1,1 2,1 J 2L' sin γ G jg (4. 55d) 4 2,2 1,2 Combing (4.55a)~(4.55d), we can get the estimation results ˆ J1 jj 3 ˆ J1 jj 3 G 1,1,G2,1 4 jlsin β 4 Lsin β j ˆ J2 jj4 ˆ J 2 jj4 G 1,2,G2,2 4 jl' sin γ 4 jl' sin γ (4. 56) 67

78 Chapter 4 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 G ˆ 1, G ˆ 2. Gˆ ˆ 1,1 G2,1 G ˆ ˆ 1 =,G 2 = (4. 57) ˆ ˆ G1,2 G2,2 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 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 68

79 Mean Square Error Chapter 4 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]. Parameter Data rate Table 4.3: System parameters I Value 480 Mbps Sub-carrier number 128 Inter-carrier spacing Modulation order MHz 16-QAM Additional phase rotation π /8 Channel model CM1 + AWGN I/Q imbalance h h LPF, I LPF, Q g 0.6dB, z z +0.01z -1-2 z z +0.2z Non-ideal case: DC-OFDM training sequence Non-ideal case: method in [13] Non-ideal case: method in [40] Non-ideal case: proposed method Eb/No (db) 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 69

80 Packet Error Rate Chapter 4 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] 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 Eb/No (db) Figure 4.12: PER versus Eb/No, 16-QAM, 480 Mbps 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 70

81 Chapter 4 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 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] 4 angle z n z n N ˆ c,1 n N (4. 58) 8 M / N where angle{} returns the phase angle of a complex number. zn [ ] and z[ n 4 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: H H H4, and X X 4 1, ik i k 4, 4 i2, k 4 i1, k ik j2 4 M c k s / N 4 i1, k 4, ik (4. 59) Z Z e Similarly, j2 8 M c k s / N Z4( i 2), k Z4 i, ke (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, 71

82 Chapter 4 Z4 i, k G1, kz4 i, k G2, kz 4 i, k (4. 61a) Z G Z G Z (4.61b) 1, k 2, k 4 i1, k 4 i1, k 4 i1, k Z G Z G Z (4.61c) 1, k 2, k 4 i2, k 4 i2, k 4 i2, k Taken (4.59) and (4.60), then (4.61a)~(4.61c) can be rewritten as Z4 i, k G1, kz4 i, k G2, kz 4 i, k (4. 62a) j2 4 M c k s / N j2 4 M c k s / N 4 1, 1, k i, k i k 2, k i, k (4.62b) Z G Z e G Z e j2 8 M c k s / N j2 8 M c k s / N 4 2, 1, k i, k i k 2, k i, k (4.62c) Z G Z e G Z e Summing (4.62a) and (4.62c), and making some straight-forward algebra operations 4, ik 4 i2, k j2 4 M c k s / N j2 4 M c k s / N Z Z e e j2 4 M c k s / N j2 4 M c k s / N 1, k i, k 2, k i, k G Z e G Z e (4. 63) In (4.63), approximation has been made based on the assumption ks c. 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 N 128 and M 165, 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 4, ik 4 i 2, k 4 i 1, k j2 4 M c k s / N j2 4 M c k s / N Z Z Z e e 2Z cos 2 4 M k / N i k c s 4 1, Therefore, the relation between three successive symbols can be denoted as N Z Z 1 k c k s cos 8 M 2Z 4, ik 4 i2, k 4 i1, k (4. 64) (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 : N Z 1 4 i, k Z 4 2 Z, 1 4 i, l Z i k 4i2, l ˆ s, d k l cos cos 8 M k l 2Z 4 1 2Z i, k 4i1, l To improve the estimation performance, the determined distance (4. 66) d in (4.66) 72

83 Chapter 4 selects a large number to combat the channel noise. Here, d is selected to be maximal length in one OFDM symbol N / 2 1. The final estimated SFO can be obtained by averaging all available estimates. ˆ 2 ˆ (4. 67) s s, d N 2 dn/21 With the estimated sampling frequency offset ˆs, the estimate of carrier frequency offset can be derived from (4.65) ˆ c, k N Z Z 1 cos 8 M 2Z 4, ik 4 i2, k 4 i1, k k ˆ s (4. 68) Similar to ˆs, the final estimated CFO ˆc is the average of the estimates on all sub-carriers N /21 1 ˆ ˆ (4. 69) c N k N /2 c, k 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 4i1, k 4i1, k 4i1, k 4i1, k * j2 4 M ck s / N j2 8 M c / N 1, k 4 i, k 2, k 4 i, k POS Z Z e G Z G Z e j2 4 M c k s / N j2 8 M c / N * 1, k 4 i, k 2, k 4 i, k 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 Y 4, ik and Y can be obtained after symbol timing. * 4, i k 73

84 Chapter 4 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 Gˆ Gˆ NEG Z 4 i1, k 1, k j28 Mc / N Y4, ik e POS Z 4 i1, k Z 2, k j28 Mc / N Y4, i k e 4, ik 1 Z 4, ik 1 (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]: N 128 and M 165, this constraint is generally satisfied in practical implementation. If CFO indeed approaches to zero, partially compensation presented above can be passed by 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) j2 4 im cks / N j28 imc / N 4 i, k 4 i, k 1, k 4 i, k 4 i, k 2, k 4 i, k 4 i, k POS Z Z e G H X G H X e j2 4 im cks / N j28 imc / N 4 i, k 4 i, k 1, k 4 i, k 4 i, k 2, k 4 i, k 4 i, k NEG Z Z e G H X e G H X (4. 72) where X 4, ik 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. 74

85 Chapter 4 Taking the complex conjugation of the negative partially compensated result, we can get the following equation k POS Z j28 imc / N 4, ik G1, kh4 i, k G2, kh X 4 i, ke 4, ik j28 imc / N NEG Z G X 4, i 2, kh4 i, k G1, kh4 i, ke 4, i k ˆ k ˆ k (4. 73) With the estimated parameters ˆc, ˆs, G 1, and G 2,, the distortion can be corrected by (4.74). Note that G ˆ 1, k and G ˆ 2, k are the jointly estimate of channel response and I/Q imbalance. Xˆ 4, ik ˆ POS Z G NEG Z Gˆ Gˆ Gˆ Gˆ Gˆ 4 i, k 1, k 4 i, k 2, k 1, k 1, k 2, k 2, k (4. 74) Similar to (4.74), if we take the complex conjugation of the positive partially compensated result, the following relation can be obtained. Xˆ ˆ POS Z G NEG Z Gˆ 4 i, k 1, k 4 i, k 2, k 4, i k ˆ ˆ ˆ ˆ G1, kg1, k G2, kg2, k (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] Phase Tracking and Compensation offset Though pre-compensation has been carried out, the residual carrier frequency 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 ˆ c s j2 im k / N X X e (4. 76) i, p i, p The phase rotation caused by residual CFO and SFO is ˆ ˆ 2 im p / N angle X / X (4. 77) i, p c s i, p i, p With linear interpolation, the compensation result is X Xˆ ˆ (4. 78) i, k i, k i, p Simulation Result To evaluate the performance of the proposed scheme, a typical DC-OFDM 75

86 Chapter 4 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 Frame Length Packet Number TFC Data Rate Channel Model Value 1024 bytes 1000 TFC 9 for Band Group Mbps, 200 Mbps, 480 Mbps 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 hi z z +0.01z -1-2 h z z -0.05z Q -1-2 g =0.8 db, =8 degree -1-2 hi z z +0.01z -1-2 h z z +0.2z Q g =0.8 db, =10 degree -1-2 hi z z +0.01z -1-2 h z z +0.2z 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 Q g =1.0 db, =10 degree -1-2 hi z z z -1-2 h z z +0.02z Q 76

87 MSE of CFO estimation Chapter 4 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] 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 Signal-to-Noise Ratio(dB) Figure 4.13: MSE of CFO estimation versus SNR, 480 Mbps, CM1 77

88 Packet Error Rate MSE of SFO estimation Chapter SFO: Traditional SFO: Proposed Signal-to-Noise Ratio(dB) Figure 4.14: MSE of SFO estimation versus SNR, 480 Mbps, CM 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 Signal-to-Noise Ratio(dB) Figure 4.15: PER versus SNR in DC-OFDM based UWB system. 78

89 Chapter 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 n / N to n th sample on time domain. Thus, the phase rotation c FFT between two consecutive OFDM symbols on the same subband is c /128. Since cyclic characteristic of phase rotation, the maximal phase rotation is allowed to. Then, we can get the maximal normalized CFO coefficient c is 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. 79

90 Chapter 4 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 where 1 n n 2 1 n 2 y n y n x n x n x n y n n 1 z n n arctan 2 z n n equals to either 1 or -1. In vector mode, the value of n (4. 79) n makes y approximate to zero, while z approximate to angle arctan y0 x 0. In rotation mode, the value of n makes z approximate to zero, while ( xy, ) approximate to new coordinate ( x', y '). In order to keep the vector norm unchanged, the iteration 2 result should multiple by an adjusting factor A 1 2 i n. n 80

91 Chapter 4 sign z n in rotation mode n sign y n in vector mode x' x y tan cos y ' y x tan cos (4. 80) (4. 81) value of The iteration process in vector mode and rotation mode are same, except the 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 Noncombinational area Net Interconnect area Table 4.7: Synthesis result of CFO cancellation Combinational area Noncombinational area Net Interconnect area Dynamic Power Cell Leakage Power Critical Path mw uw 4.64ns 81

92 Chapter 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. 82

93 Chapter 5 Chapter 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 83

94 Chapter 5 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 Task Group 3c (TG3c) was formed in March 2005 to develop a millimeter-wave-based alternative physical layer (PHY) for the existing WPAN standard [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 WiHD TM, 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 84