加权类分数傅立叶变换及其在通信系统中的应用
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摘要
本文的研究背景,来源于现实需求下影响通信系统性能的两方面主要因素:首先是复杂政治、经济因素带来的对于信息安全的威胁,更重要的是通信系统宽带化与通信环境复杂化带来的各种干扰。
传统时频域的低概率截获通信技术已经出现多年,并为大多数技术工作者熟悉,这使其对通信信号的保护性大大降低,工程中对于新型抗截获通信技术的需求十分迫切。而所谓的复杂环境,即在“高运动速率”下进行“高信息速率”传输时信号所经历的时频双弥散信道和多变的信道衰落类型。传统单载波和多载波体制在不同类型衰落信道下的性能各有优劣,但现有系统无法根据变化的通信环境自适应地选择载波体制,进而为了承载相同业务、服务相同对象却产生了使用不同技术的系统,这无疑是一种低效地资源分配方式。
针对以上传统通信系统的不足,本文提出:面对复杂的时频环境,应该通过选择恰当的时频数学工具,在多系统、多技术、多域协同的工作方式下,建立起新的通信理论和通信方式;而数学工具本身要通过理解、推广,使其适用于实际系统的工程化需求。在此,本文选择的是一种新型的时频数学工具――加权类分数傅立叶变换(Weighted-typeFractionalFourierTransform,WFRFT)。
分数傅立叶变换(FractionalFourierTransform,FRFT)是一种时频联合数学分析工具,具有丰富的定义形式。其中出现最早的是以“chirp”信号为正交基的FRFT,通常被称为“chirp类FRFT”(chirp-typeFRFT,CFRFT)。而本文所研究的,是一种有别于CFRFT、出现较晚的“加权类分数傅立叶变换”,即WFRFT。目前有关WFRFT的基础数学理论尚处发展阶段,其在通信领域中更无应用先例。本文通过揭示WFRFT蕴含的“时频对称”思想,提出利用离散傅立叶变换(Discrete Fourier Transform, DFT)计算连续函数WFRFT的离散算法及其约束条件;通过定义“序列的WFRFT”(以下简称WFRFT),推导得到WFRFT的矩阵表达形式。基于以上将WFRFT内涵向工程实用化方向拓展的工作,建立起WFRFT数字通信系统框架,论证了其与现有系统的兼容性。
在将WFRFT数学工具工程化的基础上,根据WFRFT系统结构和信号特征,本文提出WFRFT在通信系统中应用的两个主要研究方向:①提出基于WFRFT的抗截获通信新技术和方案;②提出在通信系统中,WFRFT可以视为同时包含单、多载波体制的混合调制过程,并由此提出了基于WFRFT的载波体制融合方法和协作通信方式,尝试解决不同载波体制通信系统之间的融合与协作问题。
针对现有低概率截获通信技术的不足,本文提出了利用WFRFT信号的特征进行低概率截获通信的思想,分析了WFRFT信号的抗截获性能。WFRFT信号的星座图随着参数的变化呈现出旋转、分裂等特性,其统计特性服从复高斯分布,这使得大多基于高阶累积量等统计方法的盲信号检测手段失效。在对抗参数扫描的特性上,WFRFT系统也有不错表现。与跳频、直扩技术结合,文中又提出了动态改变WFRFT参数的抗截获通信策略,而利用WFRFT作为嵌入信号的波形搭载隐蔽通信方案可以提高现有同类系统的性能。
现有通信系统中存在单载波、多载波体制不兼容的现象,而为了提高资源使用效率和系统性能,未来的通信系统将朝着不同载波体制相互融合与协同工作的方向发展。对比WFRFT系统与正交频分复用(Orthogonal Frequency-DivisionMultiplexing, OFDM)系统、单载波频域均衡(Single Carrier with Frequency DomainEqualization, SC-FDE)系统的实施方式和数学模型,文中揭示了4-WFRFT在通信系统中所蕴含的物理含义:序列的WFRFT是一个同时包含有单载波体制和多载波体制的混合载波体制调制过程。而WFRFT系统的这一特点正适应于载波体制发展的需求,有助于解决不同载波体制同时传输、协同工作的技术难题。
WFRFT信号的峰均比要小于OFDM信号,其实现复杂度与OFDM系统和SC-FDE系统相当。文中比较了衰落信道下WFRFT、OFDM和单载波系统的误码率性能,在单弥散信道中WFRFT系统性能介于OFDM和单载波系统之间,而在双弥散信道中选择恰当的参数可以使得WFRFT系统性能同时优于OFDM和单载波系统。比较的结论认为WFRFT系统在衰落信道下的系统性能鲁棒性更强,通过WFRFT参数的恰当选择,即WFRFT参数与信道的匹配,可以使得单、多载波体制获得最优的协同工作性能。同时文中还提出了基于分布式发送天线的载波体制协同通信方案与加权分数域均衡等新想法。
在论文内容之外,WFRFT应用于通信领域还有更多值得深入研究的问题,特别是利用其混合载波体制调制的特性。目前,有关利用WFRFT进行信道估计和加权分数域均衡等技术正在深入研究中,文中所述内容的WFRFT通信桌面演示系统已经初步建立。
The background of this thesis is formed from the two aspects decreasing perfor-mance of communication systems: one is the threat to information security induced bythe comprehensive political and economic factors, and a more important one is the inter-ferences caused by high information rate and complex communication environments.
The traditional Low Probability Interception (LPI) communication techniques de-signed on time or frequency domain have existed for a long time that they are knownto most researchers, which impairs its capability for protecting communication signals.So there are exigent demands for new LPI techniques. The so called complex environ-ments means time-frequency doubly dispersive channels and varying channel fading typeswhen delivers high data rate in a high moving speed. The single carrier scheme andmulti-carrier scheme have different performance under channels of different fading types.However, few current systems is able to vary carrier scheme automatically that systemswith different techniques have to be adopted for the same services and customers. It isno doubt the waste of resources. In order to develop the current systems, I propose inthe thesis that: the proper time-frequency mathematical analysis tools and cooperationamong systems, techniques and domains should be adopted to solve the problems oc-curring in complex time-frequency channels by building up new communication theoriesand modes; while the mathematical tools themselves should be generalized to satisfy theengineering demands. In this thesis, I consider a rather new time-frequency mathematicaltool–Weighted-type Fractional Fourier Transform (WFRFT).
Fractional Fourier Transform (FRFT), which is a mathematics tool for time-frequency analysis, has a variety of definitions. And the earliest one is chirp-type FRFT(CFRFT), which is notified by its name that has chirp signals as its orthogonal basis. Inthis thesis, whereas, we focus on a different kind of FRFT–WFRFT, which was proposedlater than CFRFT. WFRFT is a developing theory that its applications have never beenseen in communications. The thesis reveals the symmetrical time-frequency property ofWFRFT. Moreover, a creative work on the basic theory of WFRFT is done on the discretealgorithm of 4-terms WFRFT for continuous functions based on Discrete Fourier Trans-form (DFT), and also its restrict conditions for utilization. WFRFT matrix is obtained by defining the WFRFT for sequence. The structures of WFRFT digital communicationsystems are designed and proved to be compatible to current systems based on the gener-alization works on WFRFT.
On the aspect of applications in communications, there are two major scenarioswith the considerations of WFRFT’s structure and its signals’characters. One is thenew anti-interception techniques based on WFRFT. The other one is the carrier schemeconvergence and cooperation based on WFRFT’s physical structure of hybrid modulationprocess with single carrier and multi-carrier scheme.
With a view to the weakness of current LPI communication techniques, I suggest tomake WFRFT involve and analyze the anti-interception capability for WFRFT’s signals.The constellation of WFRFT signals appears the rotation and fission property along withthe variation of WFRFT parameter. Meanwhile, when WFRFT parameter satisfies certainconditions, the signal constellation on the complex plane appears to have a quasi Gaus-sian probability density, which invalidates most of the blind detection methods based onhigher order cumulants. When the WFRFT parameter is scanned and detected one byone, WFRFT signals also appears convinced security. In With the combination of fre-quency hopping or Directed Sequence Spread Spectrum techniques, alterable parametersschemes are proposed in order to enhance the anti-interception capability of WFRFT sys-tems. Covert communication based on waveform overlay with WFRFT signals wouldalso improve the efficiency of traditional overlay systems.
Although the single carrier and multi-carrier scheme are not compatible in currentcommunication systems, the convergence and cooperation of systems with different car-rier schemes is moving on. By analogy with Orthogonal Frequency-Division Multiplex-ing (OFDM) and Single Carrier with Frequency Domain Equalization (SC-FDE) system,the physical meaning of 4-WFRFT in digital communication is revealed: 4-WFRFT is acompatible process of multi-carrier and single carrier modulation. With respect to carrierschemes in current communication systems and the popular researches on relative tech-niques, I believe that convergence and cooperation of different carrier schemes are theforeseeing requirements which WFRFT can satisfy.
The Peak-to-Average Power Rate of WFRFT signals is smaller than that of OFDMsignals. And WFRFT system has a comparative hardware complexity to that of OFDM orSC-FDE. The comparisons of bit error rate performance among different carrier schemes under fading channels are made in the thesis. WFRFT takes the second place under singledispersive channels, while it outperforms both of OFDM and single carrier system underdouble dispersive channels. The simulation results show that WFRFT system has the mostrobust performance under different kinds of fading channels. And the proper parameterof WFRFT that matches the channel will lead to the optimal cooperative carrier scheme.More creative works, such as cooperative carrier scheme communication system based ondistributed transmission antennae and equalization on the weighting fractional domain,can also be seen in the thesis.
Beyond the contents of this thesis, there are more worthy subjects about the appli-cations of WFRFT in communications, especially when the property of hybrid carrierscheme modulation is considered. Channel estimation and equalization based on WFRFTare in the processes and the rudiments of WFRFT demo system have been established.
传统时频域的低概率截获通信技术已经出现多年,并为大多数技术工作者熟悉,这使其对通信信号的保护性大大降低,工程中对于新型抗截获通信技术的需求十分迫切。而所谓的复杂环境,即在“高运动速率”下进行“高信息速率”传输时信号所经历的时频双弥散信道和多变的信道衰落类型。传统单载波和多载波体制在不同类型衰落信道下的性能各有优劣,但现有系统无法根据变化的通信环境自适应地选择载波体制,进而为了承载相同业务、服务相同对象却产生了使用不同技术的系统,这无疑是一种低效地资源分配方式。
针对以上传统通信系统的不足,本文提出:面对复杂的时频环境,应该通过选择恰当的时频数学工具,在多系统、多技术、多域协同的工作方式下,建立起新的通信理论和通信方式;而数学工具本身要通过理解、推广,使其适用于实际系统的工程化需求。在此,本文选择的是一种新型的时频数学工具――加权类分数傅立叶变换(Weighted-typeFractionalFourierTransform,WFRFT)。
分数傅立叶变换(FractionalFourierTransform,FRFT)是一种时频联合数学分析工具,具有丰富的定义形式。其中出现最早的是以“chirp”信号为正交基的FRFT,通常被称为“chirp类FRFT”(chirp-typeFRFT,CFRFT)。而本文所研究的,是一种有别于CFRFT、出现较晚的“加权类分数傅立叶变换”,即WFRFT。目前有关WFRFT的基础数学理论尚处发展阶段,其在通信领域中更无应用先例。本文通过揭示WFRFT蕴含的“时频对称”思想,提出利用离散傅立叶变换(Discrete Fourier Transform, DFT)计算连续函数WFRFT的离散算法及其约束条件;通过定义“序列的WFRFT”(以下简称WFRFT),推导得到WFRFT的矩阵表达形式。基于以上将WFRFT内涵向工程实用化方向拓展的工作,建立起WFRFT数字通信系统框架,论证了其与现有系统的兼容性。
在将WFRFT数学工具工程化的基础上,根据WFRFT系统结构和信号特征,本文提出WFRFT在通信系统中应用的两个主要研究方向:①提出基于WFRFT的抗截获通信新技术和方案;②提出在通信系统中,WFRFT可以视为同时包含单、多载波体制的混合调制过程,并由此提出了基于WFRFT的载波体制融合方法和协作通信方式,尝试解决不同载波体制通信系统之间的融合与协作问题。
针对现有低概率截获通信技术的不足,本文提出了利用WFRFT信号的特征进行低概率截获通信的思想,分析了WFRFT信号的抗截获性能。WFRFT信号的星座图随着参数的变化呈现出旋转、分裂等特性,其统计特性服从复高斯分布,这使得大多基于高阶累积量等统计方法的盲信号检测手段失效。在对抗参数扫描的特性上,WFRFT系统也有不错表现。与跳频、直扩技术结合,文中又提出了动态改变WFRFT参数的抗截获通信策略,而利用WFRFT作为嵌入信号的波形搭载隐蔽通信方案可以提高现有同类系统的性能。
现有通信系统中存在单载波、多载波体制不兼容的现象,而为了提高资源使用效率和系统性能,未来的通信系统将朝着不同载波体制相互融合与协同工作的方向发展。对比WFRFT系统与正交频分复用(Orthogonal Frequency-DivisionMultiplexing, OFDM)系统、单载波频域均衡(Single Carrier with Frequency DomainEqualization, SC-FDE)系统的实施方式和数学模型,文中揭示了4-WFRFT在通信系统中所蕴含的物理含义:序列的WFRFT是一个同时包含有单载波体制和多载波体制的混合载波体制调制过程。而WFRFT系统的这一特点正适应于载波体制发展的需求,有助于解决不同载波体制同时传输、协同工作的技术难题。
WFRFT信号的峰均比要小于OFDM信号,其实现复杂度与OFDM系统和SC-FDE系统相当。文中比较了衰落信道下WFRFT、OFDM和单载波系统的误码率性能,在单弥散信道中WFRFT系统性能介于OFDM和单载波系统之间,而在双弥散信道中选择恰当的参数可以使得WFRFT系统性能同时优于OFDM和单载波系统。比较的结论认为WFRFT系统在衰落信道下的系统性能鲁棒性更强,通过WFRFT参数的恰当选择,即WFRFT参数与信道的匹配,可以使得单、多载波体制获得最优的协同工作性能。同时文中还提出了基于分布式发送天线的载波体制协同通信方案与加权分数域均衡等新想法。
在论文内容之外,WFRFT应用于通信领域还有更多值得深入研究的问题,特别是利用其混合载波体制调制的特性。目前,有关利用WFRFT进行信道估计和加权分数域均衡等技术正在深入研究中,文中所述内容的WFRFT通信桌面演示系统已经初步建立。
The background of this thesis is formed from the two aspects decreasing perfor-mance of communication systems: one is the threat to information security induced bythe comprehensive political and economic factors, and a more important one is the inter-ferences caused by high information rate and complex communication environments.
The traditional Low Probability Interception (LPI) communication techniques de-signed on time or frequency domain have existed for a long time that they are knownto most researchers, which impairs its capability for protecting communication signals.So there are exigent demands for new LPI techniques. The so called complex environ-ments means time-frequency doubly dispersive channels and varying channel fading typeswhen delivers high data rate in a high moving speed. The single carrier scheme andmulti-carrier scheme have different performance under channels of different fading types.However, few current systems is able to vary carrier scheme automatically that systemswith different techniques have to be adopted for the same services and customers. It isno doubt the waste of resources. In order to develop the current systems, I propose inthe thesis that: the proper time-frequency mathematical analysis tools and cooperationamong systems, techniques and domains should be adopted to solve the problems oc-curring in complex time-frequency channels by building up new communication theoriesand modes; while the mathematical tools themselves should be generalized to satisfy theengineering demands. In this thesis, I consider a rather new time-frequency mathematicaltool–Weighted-type Fractional Fourier Transform (WFRFT).
Fractional Fourier Transform (FRFT), which is a mathematics tool for time-frequency analysis, has a variety of definitions. And the earliest one is chirp-type FRFT(CFRFT), which is notified by its name that has chirp signals as its orthogonal basis. Inthis thesis, whereas, we focus on a different kind of FRFT–WFRFT, which was proposedlater than CFRFT. WFRFT is a developing theory that its applications have never beenseen in communications. The thesis reveals the symmetrical time-frequency property ofWFRFT. Moreover, a creative work on the basic theory of WFRFT is done on the discretealgorithm of 4-terms WFRFT for continuous functions based on Discrete Fourier Trans-form (DFT), and also its restrict conditions for utilization. WFRFT matrix is obtained by defining the WFRFT for sequence. The structures of WFRFT digital communicationsystems are designed and proved to be compatible to current systems based on the gener-alization works on WFRFT.
On the aspect of applications in communications, there are two major scenarioswith the considerations of WFRFT’s structure and its signals’characters. One is thenew anti-interception techniques based on WFRFT. The other one is the carrier schemeconvergence and cooperation based on WFRFT’s physical structure of hybrid modulationprocess with single carrier and multi-carrier scheme.
With a view to the weakness of current LPI communication techniques, I suggest tomake WFRFT involve and analyze the anti-interception capability for WFRFT’s signals.The constellation of WFRFT signals appears the rotation and fission property along withthe variation of WFRFT parameter. Meanwhile, when WFRFT parameter satisfies certainconditions, the signal constellation on the complex plane appears to have a quasi Gaus-sian probability density, which invalidates most of the blind detection methods based onhigher order cumulants. When the WFRFT parameter is scanned and detected one byone, WFRFT signals also appears convinced security. In With the combination of fre-quency hopping or Directed Sequence Spread Spectrum techniques, alterable parametersschemes are proposed in order to enhance the anti-interception capability of WFRFT sys-tems. Covert communication based on waveform overlay with WFRFT signals wouldalso improve the efficiency of traditional overlay systems.
Although the single carrier and multi-carrier scheme are not compatible in currentcommunication systems, the convergence and cooperation of systems with different car-rier schemes is moving on. By analogy with Orthogonal Frequency-Division Multiplex-ing (OFDM) and Single Carrier with Frequency Domain Equalization (SC-FDE) system,the physical meaning of 4-WFRFT in digital communication is revealed: 4-WFRFT is acompatible process of multi-carrier and single carrier modulation. With respect to carrierschemes in current communication systems and the popular researches on relative tech-niques, I believe that convergence and cooperation of different carrier schemes are theforeseeing requirements which WFRFT can satisfy.
The Peak-to-Average Power Rate of WFRFT signals is smaller than that of OFDMsignals. And WFRFT system has a comparative hardware complexity to that of OFDM orSC-FDE. The comparisons of bit error rate performance among different carrier schemes under fading channels are made in the thesis. WFRFT takes the second place under singledispersive channels, while it outperforms both of OFDM and single carrier system underdouble dispersive channels. The simulation results show that WFRFT system has the mostrobust performance under different kinds of fading channels. And the proper parameterof WFRFT that matches the channel will lead to the optimal cooperative carrier scheme.More creative works, such as cooperative carrier scheme communication system based ondistributed transmission antennae and equalization on the weighting fractional domain,can also be seen in the thesis.
Beyond the contents of this thesis, there are more worthy subjects about the appli-cations of WFRFT in communications, especially when the property of hybrid carrierscheme modulation is considered. Channel estimation and equalization based on WFRFTare in the processes and the rudiments of WFRFT demo system have been established.
引文
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