基于加权分数傅里叶变换域的2天线发射方法

为改善多天线系统误码率,提出一种基于加权分数傅里叶变换域的2天线发射方法.该方法在发射端将待发送信号送入信息调制及合成模块中进行加权分数傅里叶变换,按照时频域信号合并方式将变换后的四路信号分量合并为两路混合载波信号,经时延调整后由2根发射天线发射送入信道;接收端采用单天线接收,对接收信号进行加权分数傅里叶反变换处理后,可得到原发送信号估计值.仿真结果表明:在双弥散信道下,相比于使用空时码2天线发射方法,采用本文提出的发射方法在系统误码率及复杂度方面较有优势,可有效改善系统误码性能,抵抗信道衰落.     

分数傅里叶变换及其性质

本文介绍了近年来才提出的分数傅里叶变换的定义，较为详细地证明了分数傅里叶变换的连续变换定理，平移性质，相似性定理，翻转性质、共轭性质、微分性质和面积特性等，同时指出了这些性质与传统傅里叶变换相应性质的异同。     

广义加权分数傅里叶变换两分量组合抗衰落技术

为了在不改变载波体制的情况下,提升传统单载波（Single Carrier,SC）和多载波系统（Multi-Carrier,MC）的抗衰落能力,本文利用广义混合载波（Generalized Hybrid Carrier,GHC）系统在信号设计方面的高灵活性,提出基于广义加权分数傅里叶变换（Generalized Weighted Fractional Fourier Transform, GWFRFT）的两分量组合抗衰落方案.针对SC系统,所提两分量方案包含时域和时域反转两个分量,可以有效提升系统抗时间选择性衰落的能力;针对MC系统,所提两分量方案由频域和频域反转两个分量组成,能够有效提升系统抗频率选择性衰落的能力.为了充分挖掘两分量组合信号的潜力,本文对这种信号形式获得性能优势的机理进行了分析.分析结果表明,两分量之间的功率分配和同一符号在两分量中所经历衰落的独立性是影响两分量信号性能的关键因素.鉴于此,本文提出两分量等功率设计和半码块反转方案,进一步优化了两分量组合信号的性能.在此基础上,本文给出两分量组合信号生成方法,并分析其实现复杂度和频谱特性.仿真结果表明,两分量组合方案可以在不占用额外时间和频谱资源的前提下,实现对传统SC和MC系统抗衰落性能的有效提升,而基于分量等功率分配和半码块反转的优化可以进一步增强这种性能提升的效果.     

基于二维加权分数傅里叶变换的安全传输方法

从无线通信系统的安全性角度出发,为了进一步提升传统加权分数傅里叶(weighted fractional Fourier transform,WFR-FT)的抗截获性能,引入二维加权分数傅里叶变换(two-dimensional weighted fractional Fourier transform,2DWFRFT...     

加权分数傅里叶辅助的上行NOMA隐蔽通信

针对一个具有两阶段检测器的上行非正交多址接入系统,提出了随机功率分配和加权分数傅里叶变换来实现隐蔽通信。在该非正交多址接入系统中,存在一个可靠用户和隐蔽用户传输信息给基站,同时存在一个监听者企图侦察隐蔽用户的通信行为。设计了一种两阶段检测器,包括能量检测阶段和相似度检测阶段。通过相似度检测阶段为能量检测阶段提供先验概率,降低检错概率。针对所设计的两阶段检测器,提出了一种随机功率分配和加权分数傅里叶变换方案去掩盖隐蔽用户的传输,其中可靠用户采用随机功率分配而隐蔽用户采用加权分数傅里叶变换。给出了期望最小检错概率、可靠用户及隐蔽用户的中断概率的闭合表达式,并进行了仿真。在隐蔽约束和可靠约束下研究了最大期望隐蔽速率,以优化可靠用户的功率分配。研究表明,所设计的检测器有更低的期望最小检错概率,并改进了系统的隐蔽性能。     

空域中失调光学系统衍射的分数傅里叶变换描述

本文对失调的ABCD光学系统衍射积分公式进行了整理分析，在讨论几种特殊情况后，引进缩放变量，讨论得到了满足一定条件下，在与输出面相切的球面上的复振幅分布，可表述为输入面复振幅的分数傅里叶变换。     

分数傅里叶变换光学实现表达式的一种规范表示

给出了一种分数傅里叶变换的规范表达式，并证明了其完备性，分析表明，分数傅里叶变换的单透镜实现表达式和双透镜实现表达式均可写成规范表达式与一个常数相位因子之积，而且除去一个常数相位因子，光学分数傅里叶变换的级联可表达为其阶数和的规范分数傅里叶变换。     

傅里叶变换与小波变换在信号故障诊断中的应用

研究了傅里叶变换与小波变换在信号故障诊断中的应用。仿真表明，小波变换在检测信号突变点方面比傅里叶变换优越得多，且利用小波变换可以精确地检测出信号突变的时间与位置。最后探讨了在应用小波变换进行故障检测时小波基的选取原则。     

基于相位信息的分数傅里叶变换域超宽带接收机

现有的超宽带接收机在多径分离方面存在一定的限制,为了避免上述问题,提出了一种基于相位信息的分数傅里叶变换域超宽带接收机设计方案.采用Chirp信号作为超宽带脉冲波形,并利用其在分数傅里叶变换域上能量聚集的特性在接收端进行信号滤波,得到多径分量;同时,根据分数傅里叶变换的时移性质,利用多径到达时间及多径到达相位的估计得到模板多径处的相位校正因子;最后,将接收到的信号与相位校正因子结合起来,并利用相关判决得到对数据信息的估计.仿真结果表明,通过对相位信息的校正可以得到比传统接收机更好的系统误码性能;而且由于符号间干扰对系统的影响并不严重,可以实现高数据速率的信号传输.     

分数阶傅里叶变换在数字水印中的应用

传统的图像水印技术是基于离散余弦变换,只适用于处理平稳的信号,并且离散余弦变换属于有损的数据压缩过程。而分数阶傅里叶变换可以用来处理非平稳的信号,通过对连续型分数阶傅里叶变换进行离散化采样,得到适合数值计算的离散形式,然后在频率域对幅度中间的系数使用一个随机的正态分布序列进行修改,再经过逆变换,就得到了加入水印的图像。由此提出了改进的基于分数阶傅里叶变换的随机序列水印算法。仿真结果验证了所提出的算法显著地提高了在各种攻击下水印的健壮性。     

基于加权分数傅立叶变换的混合载波码分多址多天线系统

为实现与现有码分多址(CDMA)多天线系统的兼容,提出了一种基于加权分数傅立叶变换的混合载波CDMA多天线系统。本系统在某阶分数傅立叶变换域上采用CDMA技术对发送信号进行序列扩展,对扩展后的信号进行空时分组编码后将信号映射到对应的天线端口上去。通过选择特定的参数,本系统可以转换为单载波或多载波CDMA多天线系统。同时,本系统与现有的单载波和多载波系统相比,信号能量分布更为均匀,从而可以有效地抵抗信道衰落,取得更优的系统误码性能。     

Imaginary angle fractional Fourier transform and its optical implementation

The concept of imaginary angle fractional Fourier transform is proposed. Its existence and additive operation are proved. With this concept, FRT is expanded to the optical transform of convex lens outside the range of double focal length and that of concave lens.     

Multi-channel sampling theorems for band-limited signals with fractional Fourier transform

Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies. Supported partially by the National Natural Science Foundation of China (Grant Nos. 60232010 and 60572094) and the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104)     

分数阶Fourier变换的数值计算

以分数阶Fourier变换的定义为基础，仿真实现了其数值运算。对于线性调频信号（LFM），分析了调频斜率与分数阶数的关系，进而与匹配滤波器进行了性能比较，并且在低信噪比条件下仿真实现了LFM信号怀噪声的分离。仿真结果表明，当分数阶数与调频斜率相匹配时，LFM信号的能量会高度集中。在水声信号处理领域，分数阶Fourier变换的良好的抗多卜勒性能有利于微弱信号检测。     

Filterbank implementation for multi-channel sampling in fractional Fourier domain

Reconstruction of a continuous time signal from its periodic nonuniform samples and multi-channel samples is fundamental for multi-channel parallel A/D and MIMO systems. In this paper, with a filterbank interpretation of sampling schemes, the efficient interpolation and reconstruction methods for periodic nonuniform sampling and multi-channel sampling in the fractional Fourier domain are presented. Firstly, the interpolation and sampling identities in the fractional Fourier domain are derived by the properties of the fractional Fourier transform. Then, the particularly efficient filterbank implementations for the periodic nonuniform sampling and the multi-channel sampling in the fractional Fourier domain are introduced. At last, the relationship between the multi-channel sampling and the filterbank in the fractional Fourier domain is investigated, which shows that any perfect reconstruction filterbank can lead to new sampling and reconstruction strategies. Supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104), the National Natural Science Foundation of China (Grant Nos. 60890072, 60572094) and the National Key Basic Research Program Founded by MOST (Grant No. 2009CB724003)     

FRFT域LFM雷达回波信号的压缩采样模型

针对宽带雷达线性调频信号(Linear Frequency Modulated,LFM)带宽大、采样率高、存储容量要求高的问题,设计了一种基于压缩感知的 LFM雷达回波信号的欠采样整体方案。首先,利用 LFM信号在分数阶傅里叶变换(FRactional Fourier Transform,FRFT)域上良好的能量聚集特点,提出了一种基于DFRFT核矩阵的正交基字典构造方法,在此基字典的基础上利用随机解调器和匹配追踪类算法构建了一个 LFM雷达回波信号的压缩采样和重构系统模型。仿真结果验证了 FRFT域处理 LFM雷达回波信号的可行性和有效性,LFM雷达信号在该正交基字典上的稀疏表示效果要优于现有的波形匹配字典,而且具有更好的抗噪性能和自适应性能。     

Constellation splitting security transmission technology based on the multi-parameter weighted-type fractional Fourier transform for dual-polarized satellites

In order to improve the security transmission performance of dual-polarized satellites, a constellation splitting security transmission system based on the multi-parameter weighted-type Fractional Fourier Transform (MP-WFRFT) is proposed. By analyzing the time-frequency characteristics of signals, the constellation splitting function is constructed and solved by the Genetic Algorithm (GA). The constellation splitting criteria of the MP-WFRFT in the two-dimensional surface and three-dimensional sphere are mainly explored. Simulation results show that the splitting pattern is determined by the ratio of time-domain terms on the MP-WFRFT and the transmitting signal can be camouflaged by setting different time-domain terms ratio constrains to prevent the eavesdropper from acquiring the correct message. The error in the transform parameter can improve the security performance. The larger the parameter error of the MP-WFRFT is, the higher secrecy capacity can be achieved, which verifies the rationality and effectiveness of the proposed scheme.     

Performance analysis of hybrid carrier DS CDMA communication system

A hybrid carrier (HC) DS CDMA communication system is proposed, combining 4-weighted fractional Fourier transform (4-WFRFT) with code division multiple access (CDMA) technique. The signals are modulated in a certain order fractional Fourier domain and transformed by 4-WFRFT to compose the hybrid carrier signals. In the time domain CDMA technique is adopted for multiple accesses and time diversity gain. Compared to orthogonal frequency division multiplexing (OFDM) system, in which Fourier transform is adopted, the signal energy in HC system is distributed on the time-frequency plane more evenly and symmetrically. Thus, when there is a deep fading notch or single-frequency interference in the channel, the proposed method can split the interference to a broader range in order to reduce the influence, resulting in the better system performance. Moreover, the performances of the proposed system, such as peak-to-average power rate (PAPR) and security are also discussed in the paper.