基于分数傅立叶变换的脉冲超宽带系统研究
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摘要
脉冲超宽带(ImpulseRadioUltraWideband, IR-UWB)技术是近年来通信领域的研究热点之一。IR-UWB系统与传统的载波体制通信系统不同,它采用纳秒级的脉冲波形来传输信息。
IR-UWB研究的目的是提供一种新型的低成本、低复杂度、低功耗的的数据传输方案。但是它的应用环境为非常复杂多变的密集多径信道,在这样的信道下要采用低成本、实现简单的技术手段,有效的收集多径能量、抑制各种干扰是非常困难的。这就造成了UWB系统实现的数据速率远低于其理论速率。同样地,在精确测距与定位方面,基于时域相关的到达时间(TimeofArrival,TOA)估计方法理论上具有非常高的精度,但是由于复杂度的原因,工程实现中仍然以精度较低的非相干能量检测为主。即UWB的低成本与高性能的目标在现有技术条件下无法统一。
本文尝试从一个新的角度解决UWB系统性能与复杂度之间的矛盾:仅采用一种信号处理手段来同时抑制多用户干扰、正弦干扰、多径干扰等,在满足系统结构简单的前提下实现性能的提升。为了实现这一目标,需要设计超宽带信号使其具有和所有类型的干扰信号都不同的某些特征,并且能够用一种简单的接收机结构实现对这些特征的提取。为了满足这些要求,本文选择了分数傅立叶变换(FractionalFourierTransform,FRFT)这一数学工具。FRFT具有和FFT(FastFourier Transform)运算量相当的快速离散算法,符合超宽带对系统复杂度低、功耗小的需求。
FRFT可以看做是傅立叶变换的分数阶次推广,分数傅立叶域则可以看做是介于时域和频域之间的域。本文归纳了FRFT目前主流的两类离散算法,指出Ozaktas等人提出的采样型离散算法由于具有和FFT相当的运算量而更加适用于数字通信系统。
研究FRFT应用于通信系统时的离散算法量纲归一化问题和截断Chirp函数分数域谱扩展问题是将FRFT与UWB结合的基础。Chirp函数族是FRFT的基函数,在特定阶次的分数傅立叶域上,无限长Chirp函数对应的谱具有冲激函数的形式。但是通信系统中应用的信号一定是有限长的,即为时间截断信号。文中将其等价为无限长Chirp函数与某个窗函数的乘积,进行了截断Chirp函数的分数域谱解析表达式推导。因为计算时选用采样型离散算法,其应用前提为信号要进行量纲归一化,所以又对两种量纲归一化方法及其对计算结果的影响进行了解析表达式推导。最后结合计算结果论证了上述一系列推导的正确性。这部分研究内容为FRFT的工程应用奠定了理论基础。
为了得到与干扰信号具有不同特征的UWB脉冲波形,通过分析FRFT与截断Chirp函数的关系,提出基于Chirp函数加权叠加设计波形的方案。该波形在特定阶数的FRFT域上具有支撑区间窄、能量聚集的特性,而UWB系统的其他干扰信号则不具有这种特性,因此可以通过FRFT域滤波的手段分离二者。这里基于Chirp函数设计UWB波形的优化目标是:在满足FCC(FederalCommunicationsCommission)发射功率限制的前提下尽可能的增大发射信号功率,然后借鉴滤波器设计中的成熟算法求解该优化问题。此外,文中还分析了白噪声在相应的FRFT域的特征。
采用Chirp函数设计波形的结果保证了有用信号与干扰信号在分数傅立叶域可分离。在此基础上,为了抑制多用户干扰,提出一种分数傅立叶域多址与时域跳时(TimeHopping,TH)多址联合的新型多址方案,将FRFT阶数也作为区分多用户的参数之一。为了抑制正弦干扰及实现频谱认知,提出一种FRFT域滤波分离IR-UWB信号与正弦信号的方法。为了抑制密集多径和多径时延扩展带来的符号内多径间干扰及符号间干扰对系统性能的影响,提出一种二进制Chirp率调制及分数傅立叶域解调方法。
精确测距与定位是IR-UWB目前最为热门的研究方向,其中TOA估计算法是影响测距性能的关键。因此在研究了分数傅立叶域干扰抑制方法后,本文又研究了分数傅立叶域的TOA估计方法。主要采用的技术手段有两种:“分数相关峰值位置检测法”和“分数傅立叶域幅度谱峰值位置检测法”。与时域相关相比,分数相关的不同在于其移变特性,基于此特性可以对测距范围进行控制。针对IR-UWB测距节点对设备结构简单、功耗低,精度高的要求,提出一种分数傅立叶域峰值检测测距方法,该方法复杂度低于时域相关法,通过理论推导和仿真证明在高信噪比下二者精度相当。最后,对存在频偏条件下的时延估计问题进行了研究,指出分数傅立叶变换可以同时反映信号的时延和频偏信息,因而可以对二者进行联合估计,消除频偏的影响,提高时延估计精度。
Recent years, many researches have focused on Impulse Radio Ultra-Wideband (IR-UWB) technology. It is different from the traditional continuous carrier communicationsystems that it adopts impulse waveforms to carry the information.
The target of IR-UWB is to provide a novel data transmission technique with lowcost, low complexity and low power consumption. Nevertheless, IR-UWB usually worksin a varying and complex environment with dense multi-pathes. And to achieve the ob-jects of collecting multi-pathes energy and suppressing different kinds of interferenceswith cheap and simple techniques is very difficult. Hence, the actual data rate of UWBsystems is much lower than the theoretical one. As to the precise ranging and position-ing, although the time of arrival (TOA) estimation method based on time correlation hasa very high theoretical precision, the actual implementations of the prototypes are stilldominated by non-coherent energy detection due to complexity reasons. In a word, theIR-UWB targets for low cost and high performance could not unite under current techni-cal conditions.
The dissertation tries to reconcile the con?ict between performance and complexityof IR-UWB systems from a new aspect. That is the adoption of a single signal processingmethod to suppress the in?uences of Multiple Access Interference (MAI), Sinusoid signalinterference and multi-path interference simultaneously, and improve the system perfor-mance with as less additional complexity as possible. To achieve this goal, IR-UWB sig-nals must be provided with some unique characteristics in order to be distinguished fromall the different types of interferences, and extraction of these features should be able toachieve with a simple receiver structure. Fractional Fourier Transform (FRFT) is thenchosen in this dissertation, because its fast digital calculation algorithm has a comparablecomplexity to Fast Fourier Transform (FFT), which meets the needs of low complexityand low power consumption for IR-UWB systems.
FRFT which generalizes Fourier Transform in the way of eigenvalues fractionaliza-tion, and FRFT domains can be seen as the ones between time-domain and frequency-domain. The dissertation summarizes FRFT discrete algorithms and points out that thesampling-type discrete algorithm proposed by Ozaktas and others is suitable for digital communication systems for its comparable complex to FFT.
Two basic theoretical issues occurring when FRFT is introduced into digital com-munication are studied. One is the dimensional normalization of discrete algorithm andthe other one is the spectrum of chirp functions on FRFT domain. As the bases of FRFT,the time infinite chirp functions will transform into impulse functions on certain FRFTdomains. Nevertheless, signals in communication are always time finite. A time finitechirp function can be seen as a multiplication of a time infinite chirp function and a win-dow function. The analytical expression of spectrum on FRFT domains of a time finitechirp function is deduced and then verified by simulations. FRFT in simulations is imple-mented by Ozaktas’discrete algorithm, which should dimensional normalize the signalsat first. So the analytical expressions of errors caused by two different dimensional nor-malization methods are also deduced and verified by simulations. All the above works laythe theoretical foundation of the application of FRFT in engineering.
As to the chief question on the design of transmission waveforms in IR-UWB, thedissertation propose a scheme of weighted superposition of chirp functions, based on theanalysis of the relationship of FRFT and chirp functions. The designed waveforms willconcentrate on certain FRFT domains while the interferences will not, so filtering onthe FRFT domains is able to separate them. In this case, the designing objective is toincrease the emission power as high as possible while meeting power spectral constraintsof FCC (Federal Communications Commission). The optimization problem is solved bySDP algorithm and PM algorithm in filter designing. The dissertation also analyze thecharacteristics of Additive White Gaussian Noise (AWGN) on FRFT domains.
Waveform design with chirp functions guarantees the separation of signal and inter-ferences on the FRFT domains. For the purpose of Multiple Access Interference (MAI)suppression, a novel Multiple Access (MA) scheme combined with FRFT domain MAand time hopping MA is proposed, in which the FRFT order is also determined as a pa-rameter to distinguish multi-user. A method separating IR-UWB signals and sinusoidsignals is proposed for sine interference suppression and spectral cognition. A binarychirp rate modulation and its non-coherent demodulation are proposed in order to reducethe influences of inter symbol interference and multi-path interference in one symbol.
As to the ranging application of IR-UWB, the estimation precision of TOA is anessential parameter. So the dissertation studies and compares two TOA estimation meth- ods: (i) coherent method based on peak detection of correlation on FRFT domain and (ii)non-coherent method based on peak detection of spectrum on FRFT domain. Comparedwith correlation on time domain, correlation on FRFT domain has a shift-varying prop-erty, based on which the scope of ranging is able to be controlled. To meet the needs ofIR-UWB ranging nodes of simple device structure and low power consumption, a rangingmethod of peak detection on FRFT domain is proposed, which has lower complexity thantime correlation method. The theoretical deduction and simulation results verify that theproposed method and time correlation method have a comparable precision in high signalto noise ratio conditions. At last, the dissertation studies the estimation of time delay inthe presence of frequency offset. FRFT can display both of time delay and frequency off-set information simultaneously. So it can be used for a joint estimation of time delay andfrequency offset, in order to eliminate in?uence of frequency offset and improve precisionof time delay estimation.
IR-UWB研究的目的是提供一种新型的低成本、低复杂度、低功耗的的数据传输方案。但是它的应用环境为非常复杂多变的密集多径信道,在这样的信道下要采用低成本、实现简单的技术手段,有效的收集多径能量、抑制各种干扰是非常困难的。这就造成了UWB系统实现的数据速率远低于其理论速率。同样地,在精确测距与定位方面,基于时域相关的到达时间(TimeofArrival,TOA)估计方法理论上具有非常高的精度,但是由于复杂度的原因,工程实现中仍然以精度较低的非相干能量检测为主。即UWB的低成本与高性能的目标在现有技术条件下无法统一。
本文尝试从一个新的角度解决UWB系统性能与复杂度之间的矛盾:仅采用一种信号处理手段来同时抑制多用户干扰、正弦干扰、多径干扰等,在满足系统结构简单的前提下实现性能的提升。为了实现这一目标,需要设计超宽带信号使其具有和所有类型的干扰信号都不同的某些特征,并且能够用一种简单的接收机结构实现对这些特征的提取。为了满足这些要求,本文选择了分数傅立叶变换(FractionalFourierTransform,FRFT)这一数学工具。FRFT具有和FFT(FastFourier Transform)运算量相当的快速离散算法,符合超宽带对系统复杂度低、功耗小的需求。
FRFT可以看做是傅立叶变换的分数阶次推广,分数傅立叶域则可以看做是介于时域和频域之间的域。本文归纳了FRFT目前主流的两类离散算法,指出Ozaktas等人提出的采样型离散算法由于具有和FFT相当的运算量而更加适用于数字通信系统。
研究FRFT应用于通信系统时的离散算法量纲归一化问题和截断Chirp函数分数域谱扩展问题是将FRFT与UWB结合的基础。Chirp函数族是FRFT的基函数,在特定阶次的分数傅立叶域上,无限长Chirp函数对应的谱具有冲激函数的形式。但是通信系统中应用的信号一定是有限长的,即为时间截断信号。文中将其等价为无限长Chirp函数与某个窗函数的乘积,进行了截断Chirp函数的分数域谱解析表达式推导。因为计算时选用采样型离散算法,其应用前提为信号要进行量纲归一化,所以又对两种量纲归一化方法及其对计算结果的影响进行了解析表达式推导。最后结合计算结果论证了上述一系列推导的正确性。这部分研究内容为FRFT的工程应用奠定了理论基础。
为了得到与干扰信号具有不同特征的UWB脉冲波形,通过分析FRFT与截断Chirp函数的关系,提出基于Chirp函数加权叠加设计波形的方案。该波形在特定阶数的FRFT域上具有支撑区间窄、能量聚集的特性,而UWB系统的其他干扰信号则不具有这种特性,因此可以通过FRFT域滤波的手段分离二者。这里基于Chirp函数设计UWB波形的优化目标是:在满足FCC(FederalCommunicationsCommission)发射功率限制的前提下尽可能的增大发射信号功率,然后借鉴滤波器设计中的成熟算法求解该优化问题。此外,文中还分析了白噪声在相应的FRFT域的特征。
采用Chirp函数设计波形的结果保证了有用信号与干扰信号在分数傅立叶域可分离。在此基础上,为了抑制多用户干扰,提出一种分数傅立叶域多址与时域跳时(TimeHopping,TH)多址联合的新型多址方案,将FRFT阶数也作为区分多用户的参数之一。为了抑制正弦干扰及实现频谱认知,提出一种FRFT域滤波分离IR-UWB信号与正弦信号的方法。为了抑制密集多径和多径时延扩展带来的符号内多径间干扰及符号间干扰对系统性能的影响,提出一种二进制Chirp率调制及分数傅立叶域解调方法。
精确测距与定位是IR-UWB目前最为热门的研究方向,其中TOA估计算法是影响测距性能的关键。因此在研究了分数傅立叶域干扰抑制方法后,本文又研究了分数傅立叶域的TOA估计方法。主要采用的技术手段有两种:“分数相关峰值位置检测法”和“分数傅立叶域幅度谱峰值位置检测法”。与时域相关相比,分数相关的不同在于其移变特性,基于此特性可以对测距范围进行控制。针对IR-UWB测距节点对设备结构简单、功耗低,精度高的要求,提出一种分数傅立叶域峰值检测测距方法,该方法复杂度低于时域相关法,通过理论推导和仿真证明在高信噪比下二者精度相当。最后,对存在频偏条件下的时延估计问题进行了研究,指出分数傅立叶变换可以同时反映信号的时延和频偏信息,因而可以对二者进行联合估计,消除频偏的影响,提高时延估计精度。
Recent years, many researches have focused on Impulse Radio Ultra-Wideband (IR-UWB) technology. It is different from the traditional continuous carrier communicationsystems that it adopts impulse waveforms to carry the information.
The target of IR-UWB is to provide a novel data transmission technique with lowcost, low complexity and low power consumption. Nevertheless, IR-UWB usually worksin a varying and complex environment with dense multi-pathes. And to achieve the ob-jects of collecting multi-pathes energy and suppressing different kinds of interferenceswith cheap and simple techniques is very difficult. Hence, the actual data rate of UWBsystems is much lower than the theoretical one. As to the precise ranging and position-ing, although the time of arrival (TOA) estimation method based on time correlation hasa very high theoretical precision, the actual implementations of the prototypes are stilldominated by non-coherent energy detection due to complexity reasons. In a word, theIR-UWB targets for low cost and high performance could not unite under current techni-cal conditions.
The dissertation tries to reconcile the con?ict between performance and complexityof IR-UWB systems from a new aspect. That is the adoption of a single signal processingmethod to suppress the in?uences of Multiple Access Interference (MAI), Sinusoid signalinterference and multi-path interference simultaneously, and improve the system perfor-mance with as less additional complexity as possible. To achieve this goal, IR-UWB sig-nals must be provided with some unique characteristics in order to be distinguished fromall the different types of interferences, and extraction of these features should be able toachieve with a simple receiver structure. Fractional Fourier Transform (FRFT) is thenchosen in this dissertation, because its fast digital calculation algorithm has a comparablecomplexity to Fast Fourier Transform (FFT), which meets the needs of low complexityand low power consumption for IR-UWB systems.
FRFT which generalizes Fourier Transform in the way of eigenvalues fractionaliza-tion, and FRFT domains can be seen as the ones between time-domain and frequency-domain. The dissertation summarizes FRFT discrete algorithms and points out that thesampling-type discrete algorithm proposed by Ozaktas and others is suitable for digital communication systems for its comparable complex to FFT.
Two basic theoretical issues occurring when FRFT is introduced into digital com-munication are studied. One is the dimensional normalization of discrete algorithm andthe other one is the spectrum of chirp functions on FRFT domain. As the bases of FRFT,the time infinite chirp functions will transform into impulse functions on certain FRFTdomains. Nevertheless, signals in communication are always time finite. A time finitechirp function can be seen as a multiplication of a time infinite chirp function and a win-dow function. The analytical expression of spectrum on FRFT domains of a time finitechirp function is deduced and then verified by simulations. FRFT in simulations is imple-mented by Ozaktas’discrete algorithm, which should dimensional normalize the signalsat first. So the analytical expressions of errors caused by two different dimensional nor-malization methods are also deduced and verified by simulations. All the above works laythe theoretical foundation of the application of FRFT in engineering.
As to the chief question on the design of transmission waveforms in IR-UWB, thedissertation propose a scheme of weighted superposition of chirp functions, based on theanalysis of the relationship of FRFT and chirp functions. The designed waveforms willconcentrate on certain FRFT domains while the interferences will not, so filtering onthe FRFT domains is able to separate them. In this case, the designing objective is toincrease the emission power as high as possible while meeting power spectral constraintsof FCC (Federal Communications Commission). The optimization problem is solved bySDP algorithm and PM algorithm in filter designing. The dissertation also analyze thecharacteristics of Additive White Gaussian Noise (AWGN) on FRFT domains.
Waveform design with chirp functions guarantees the separation of signal and inter-ferences on the FRFT domains. For the purpose of Multiple Access Interference (MAI)suppression, a novel Multiple Access (MA) scheme combined with FRFT domain MAand time hopping MA is proposed, in which the FRFT order is also determined as a pa-rameter to distinguish multi-user. A method separating IR-UWB signals and sinusoidsignals is proposed for sine interference suppression and spectral cognition. A binarychirp rate modulation and its non-coherent demodulation are proposed in order to reducethe influences of inter symbol interference and multi-path interference in one symbol.
As to the ranging application of IR-UWB, the estimation precision of TOA is anessential parameter. So the dissertation studies and compares two TOA estimation meth- ods: (i) coherent method based on peak detection of correlation on FRFT domain and (ii)non-coherent method based on peak detection of spectrum on FRFT domain. Comparedwith correlation on time domain, correlation on FRFT domain has a shift-varying prop-erty, based on which the scope of ranging is able to be controlled. To meet the needs ofIR-UWB ranging nodes of simple device structure and low power consumption, a rangingmethod of peak detection on FRFT domain is proposed, which has lower complexity thantime correlation method. The theoretical deduction and simulation results verify that theproposed method and time correlation method have a comparable precision in high signalto noise ratio conditions. At last, the dissertation studies the estimation of time delay inthe presence of frequency offset. FRFT can display both of time delay and frequency off-set information simultaneously. So it can be used for a joint estimation of time delay andfrequency offset, in order to eliminate in?uence of frequency offset and improve precisionof time delay estimation.
引文
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