小波提升理论及其在OFDM中的应用研究
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摘要
小波分析是在傅立叶分析的基础上发展起来的，但其比傅立叶分析有着许多本质性的进步，能够从信号中提取更多的有用信息，而且它的快速算法为分析和解决实际问题带来极大的方便。小波提升理论或策略(lifting scheme)是Sweldens和Daubechies等学者于九十年代中期提出的关于小波构造的一种新方法，用来改进某一已有小波，以使其获得特定的性质，其给出了双正交小波简单而有效的构造方法。并且，通过Eucildean算法，所有的传统小波均可以由提升方法构成。本文基于小波及其提升理论提出了一种提高小波函数消失矩的方法，并给出了利用方程组求解小波提升系数的简单方法。
M带小波不仅具有小波分析的特点而且可以放大信号的高频窄带部分，具有更好的能量集中性，本文结合提升理论，提出了利用提升方法构造M带线性小波滤波器组的方法，预期在多载波调制系统中具有更好的特性。
OFDM是一种可以应用于无线环境下的调制技术一般采用的是快速付里叶变换(FFT)的原理。能够提高系统抗衰落和抗同信道干扰的能力，但是技术存在两个问题：其一，当信道特性破坏了各载波子信道的正交性时，系统的性能会受到很大的影响；其二，对信号进行FFT变换时，实质上对信号有一个符号周期(TS)长的截断过程，这一截断过程相当于信号与一个时长为Ts的矩形脉冲相乘，而具有sinc函数形的频谱，前后两数据帧有较大的频谱重叠，在信道畸变(如相位失真)时会产生较大的码间干扰(ISI)和各子信道之间的串扰(ICI)。人们通过插入保护间隔及循环前缀后，可以基本消除符号间的干扰(ISI)及子带间的中串扰，但也会同时带来功率和信息速度的损失，因而要探索一种新的方法来改进现在的基于FFT的OFDM系统的性能。Wornell和Oppenheim提出了基于小波调制的发射机和接收机设计构想，H．Nikookar提出了将小波应用于多载波通信的构想，本实验室也相继提出离散小波OFDM调制及小波提升OFDM调制等，这些调制方式，在不同方向，对基于FFT的OFDM缺点有了一定改进。但是由于传统小波分析的局限性的原因，性能不是很理想。本文基于M带小波及其提升理论相继提出了M带小波提升多载波系统(LWMT—OFDM)和小波提升MC—CDMA系统，在此类多载波系统中不需加保护间隔，系统更简单，且数据速率更高。
本论文的组织结构如下：第一章是绪论，对研究背景及相关技术背景作出了一个概述。第二章是对小波变换与多速率滤波器组进行研究，以小波理论在通信中的应用为线索，对其基本理论、基本性质及其与多速率滤波器组的关系进行研究，包括连续和离散小波变换、小波包变换，完全重构滤波器组，离散小波变换与多速率滤波器组的关系等。第三章以小波的提升策略(理论)为研究重点，总结归纳了一套完整的提升理论，并结合滤波器的提升结构，构造新的小波，为以后其在多载波中的应用提供基础。第四章主要研究M带小波原理及其提升结构，从基本原理出发，对M带小波进行详细的理论研究，结合正则性等特性，给出正则M带尺度滤波器的公式，提出M带小波的构造方式，并利用M带滤波器组及提升结构给出M带小波的提升结构，最后利用提升来构造M带正交小波。第五章主要基于M带小波提升理论提出M带小波提升OFDM系统，从理论上推导基于QPSK调制的多载波传输系统的等效M带离散小波多载波传输模型，并对其在AWGN及多径下性能进行理论研究及软件仿真。第六章提出一种新的基于正交M带离散小波的MC-CDMA系统及其实现方法：从理论上分析其抗干扰的性能；最后进行性能仿真，并与基于DFT的MC-CDMA系统进行性能比较。
Wavelet analysis has more essential advantage than Fourier analysis such as wavelet analysis can abstract more useful information form the signal and the fast arithmetic of wavelet analysis bring more conveniences for us to settle actual problem. The wavelet lifting scheme were proposed by Sweldens and Daubechies to construct a new wavelet as a new method in 1990s. Lifting can improve a known wavelet to get a good feature and can give a good and efficient method to construct bi-orthogonal wavelet. All the traditional wavelet can be constructed through lifting scheme with Euclidean arithmetic. The dissertation proposed a method to improve the wavelet function vanishing moment, at the same time present an equation method to solve for the coefficients of the lifting scheme.
M band wavelet not only has the wavelet feature but also can amplify high frequency narrow band part, so it could centralize more energy. The dissertation proposed a new lifting scheme to construct linear phase wavelet filter banks.
It is well known that the OFDM (Orthogonal Frequency Division Multiplexing) system has a high ability to overcome the effect of multipath and can obtain high spectral efficiency in the wireless communication channel. However, to avoid interchannel interference (ICI) and intersymbol interference (ISI) in wireless channel, a guard interval longer than channel delay is used in conventional OFDM system, which cause the efficiency of bandwidth usage reduced. Due to the superior spectral containment of wavelets, this dissertation proposed a new OFDM system based on M band Lifting Wavelet Transform (LWMT-OFDM), which adopts M band lifting wavelet transform to replace the conventional Fourier transform. The new LWMT-OFDM system doesn抰need the Cyclic Prefix (CP) so its structure is more simply than FFT-OFDM and its algorithm is as simply as FFT-OFDM. The new LWMT-OFDM system can mitigates some disadvantages of FFT-OFDM system, such as a relatively large peak-to朼verage power ratio, more sensitive to carrier frequency offset and phase noise. Simulations show that the LWMT-OFDM system is more effective and attractive than conversional FFT-OFDM in wireless channel.
The organization of the dissertation as follow: the first chapter focuses on the studying background and the relative technology. The second chapter focuses on wavelet and Multirate filter banks study. Given a conclusive of wavelet essential theory, essential feature and the relativity of Multirate filter banks. The third chapter focused on wavelet lifting structure study, proposed a new method to improve the wavelet function vanishing moment, at the same time present an equation method to solve for the coefficients of the lifting scheme. The fourth chapter focused on M band wavelet and M band filter banks lifting theory, proposed a new lifting scheme to construct linear phase wavelet filter banks. The fifth chapters based on M band lifting wavelet theory proposed a new OFDM system - M band lifting wavelet mutlicarrier system (LWMT-OFDM), at the same time gives the simulation result. In the end, the dissertation proposed a MC-CDMA system based on M band lifting wavelet and give the compare result of OFDM based MC-CDMA.
M带小波不仅具有小波分析的特点而且可以放大信号的高频窄带部分，具有更好的能量集中性，本文结合提升理论，提出了利用提升方法构造M带线性小波滤波器组的方法，预期在多载波调制系统中具有更好的特性。
OFDM是一种可以应用于无线环境下的调制技术一般采用的是快速付里叶变换(FFT)的原理。能够提高系统抗衰落和抗同信道干扰的能力，但是技术存在两个问题：其一，当信道特性破坏了各载波子信道的正交性时，系统的性能会受到很大的影响；其二，对信号进行FFT变换时，实质上对信号有一个符号周期(TS)长的截断过程，这一截断过程相当于信号与一个时长为Ts的矩形脉冲相乘，而具有sinc函数形的频谱，前后两数据帧有较大的频谱重叠，在信道畸变(如相位失真)时会产生较大的码间干扰(ISI)和各子信道之间的串扰(ICI)。人们通过插入保护间隔及循环前缀后，可以基本消除符号间的干扰(ISI)及子带间的中串扰，但也会同时带来功率和信息速度的损失，因而要探索一种新的方法来改进现在的基于FFT的OFDM系统的性能。Wornell和Oppenheim提出了基于小波调制的发射机和接收机设计构想，H．Nikookar提出了将小波应用于多载波通信的构想，本实验室也相继提出离散小波OFDM调制及小波提升OFDM调制等，这些调制方式，在不同方向，对基于FFT的OFDM缺点有了一定改进。但是由于传统小波分析的局限性的原因，性能不是很理想。本文基于M带小波及其提升理论相继提出了M带小波提升多载波系统(LWMT—OFDM)和小波提升MC—CDMA系统，在此类多载波系统中不需加保护间隔，系统更简单，且数据速率更高。
本论文的组织结构如下：第一章是绪论，对研究背景及相关技术背景作出了一个概述。第二章是对小波变换与多速率滤波器组进行研究，以小波理论在通信中的应用为线索，对其基本理论、基本性质及其与多速率滤波器组的关系进行研究，包括连续和离散小波变换、小波包变换，完全重构滤波器组，离散小波变换与多速率滤波器组的关系等。第三章以小波的提升策略(理论)为研究重点，总结归纳了一套完整的提升理论，并结合滤波器的提升结构，构造新的小波，为以后其在多载波中的应用提供基础。第四章主要研究M带小波原理及其提升结构，从基本原理出发，对M带小波进行详细的理论研究，结合正则性等特性，给出正则M带尺度滤波器的公式，提出M带小波的构造方式，并利用M带滤波器组及提升结构给出M带小波的提升结构，最后利用提升来构造M带正交小波。第五章主要基于M带小波提升理论提出M带小波提升OFDM系统，从理论上推导基于QPSK调制的多载波传输系统的等效M带离散小波多载波传输模型，并对其在AWGN及多径下性能进行理论研究及软件仿真。第六章提出一种新的基于正交M带离散小波的MC-CDMA系统及其实现方法：从理论上分析其抗干扰的性能；最后进行性能仿真，并与基于DFT的MC-CDMA系统进行性能比较。
Wavelet analysis has more essential advantage than Fourier analysis such as wavelet analysis can abstract more useful information form the signal and the fast arithmetic of wavelet analysis bring more conveniences for us to settle actual problem. The wavelet lifting scheme were proposed by Sweldens and Daubechies to construct a new wavelet as a new method in 1990s. Lifting can improve a known wavelet to get a good feature and can give a good and efficient method to construct bi-orthogonal wavelet. All the traditional wavelet can be constructed through lifting scheme with Euclidean arithmetic. The dissertation proposed a method to improve the wavelet function vanishing moment, at the same time present an equation method to solve for the coefficients of the lifting scheme.
M band wavelet not only has the wavelet feature but also can amplify high frequency narrow band part, so it could centralize more energy. The dissertation proposed a new lifting scheme to construct linear phase wavelet filter banks.
It is well known that the OFDM (Orthogonal Frequency Division Multiplexing) system has a high ability to overcome the effect of multipath and can obtain high spectral efficiency in the wireless communication channel. However, to avoid interchannel interference (ICI) and intersymbol interference (ISI) in wireless channel, a guard interval longer than channel delay is used in conventional OFDM system, which cause the efficiency of bandwidth usage reduced. Due to the superior spectral containment of wavelets, this dissertation proposed a new OFDM system based on M band Lifting Wavelet Transform (LWMT-OFDM), which adopts M band lifting wavelet transform to replace the conventional Fourier transform. The new LWMT-OFDM system doesn抰need the Cyclic Prefix (CP) so its structure is more simply than FFT-OFDM and its algorithm is as simply as FFT-OFDM. The new LWMT-OFDM system can mitigates some disadvantages of FFT-OFDM system, such as a relatively large peak-to朼verage power ratio, more sensitive to carrier frequency offset and phase noise. Simulations show that the LWMT-OFDM system is more effective and attractive than conversional FFT-OFDM in wireless channel.
The organization of the dissertation as follow: the first chapter focuses on the studying background and the relative technology. The second chapter focuses on wavelet and Multirate filter banks study. Given a conclusive of wavelet essential theory, essential feature and the relativity of Multirate filter banks. The third chapter focused on wavelet lifting structure study, proposed a new method to improve the wavelet function vanishing moment, at the same time present an equation method to solve for the coefficients of the lifting scheme. The fourth chapter focused on M band wavelet and M band filter banks lifting theory, proposed a new lifting scheme to construct linear phase wavelet filter banks. The fifth chapters based on M band lifting wavelet theory proposed a new OFDM system - M band lifting wavelet mutlicarrier system (LWMT-OFDM), at the same time gives the simulation result. In the end, the dissertation proposed a MC-CDMA system based on M band lifting wavelet and give the compare result of OFDM based MC-CDMA.
引文
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[1] W. Sweldens, 揟he Lifting Scheme: A new philosophy in biorthogonal wavelet constructions? downloaded from the website http://cm.bell-labs.com/who/wim
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