谐波随机过程的四阶平稳性和四阶遍历性条件

本文分析了由随机谐波构成的复信号四阶矩的有限数据估计,得到了四阶平稳和四阶遍历的条件,给出了估计误差及其方差,以及它们大样本极限的显式表达式。最后考虑了相应于三次相位耦合的特例,说明这一情形下的方差由遍历和非遍历两部分组成。     

谐波恢复中累量估计的强收敛问题

本文讨论有噪声污染的谐波信号累量的单一记录估计。证明了样本自相关函数的强收敛性,并得到了强收敛速度。对于四阶矩估计,给出了四阶遍历条件。在这些遍历条件下,建立了四阶矩和四阶累量样本估计的强收敛性,并得到了强收敛速度。最后给出了数值仿真结果。     

基于峰度的盲自适应多用户检测

基于四阶累积量,分析一种新的优化准则,即定向最小峰度(OMK:Oriented Minimum Kur-tosis)准则。理论分析表明:该准则函数具有全局最小值且极值点满足解相关条件。由此,通过求解该优化问题,能得到一种新的盲多用户接收方案。然后,利用最速下降法,给出盲多用户检测的自适应算法。仿真结果进一步验证了本文的结论。     

Identification of nonminimum phase FIR systems via fourth-order cumulants and genetic algorithm

In this paper, the problem of estimating the parameters of an FIR system from only the fourth-order cumulants of the noisy system output is considered. The FIR system is driven by a symmetric, independent, and identically distributed (i.i.d) non-Gaussian sequence. We propose a new formula called Weighted Overdetermined C(q, k) (WOC(q, k)) by extending the conventional C(q, k) formula. The optimal selection of the weights in WOC(q, k) is performed by using the Genetic Algorithm (GA) optimization method which minimizes a nonlinear error function based on the fourth-order cumulants alone. Simulations are provided to reveal the effectiveness and the superiority of this novel technique over the C(q, k) and other existing techniques.     

基于四阶累积量的共形阵列波达方向估计算法

由于共形天线阵列流形的多极化特性(Polarization Diversity),共形阵列天线的信源方位估计需要与信源的极化状态联合进行。分析总结共形阵列天线波达方向(DOA)估计特点的基础上,针对窄带远场非高斯独立信源,提出了一种共形阵列天线盲极化DOA估计算法。该算法利用四阶累积量对阵列口径的扩展性,结合旋转不变子空间(ESPRIT)算法,在信源极化状态未知条件下实现了共形阵列天线的高分辨DOA估计。所提算法的方位估计不需要天线单元方向图以及信源极化状态的任何信息,适用于多种常用共形载体(锥面、柱面以及球面共形载体),具有较为广泛的应用环境。以柱面共形阵列天线DOA估计为例,详细推导了算法机理,给出了算法步骤,计算机Monte Carlo仿真实验验证了所提算法的有效性。     

Direction finding algorithms based on high-order statistics

Two direction finding algorithms are presented for nonGaussian signals, which are based on the fourth-order cumulants of the data received by the array. The first algorithm is similar to MUSIC, while the second is asymptotically minimum variance in a certain sense. The first algorithm requires singular value decomposition of the cumulant matrix, while the second is based on nonlinear minimization of a certain cost function. The performance of the minimum variance algorithm can be assessed by analytical means, at least for the case of discrete probability distributions of the source signals and spatially uncorrelated Gaussian noise. The numerical experiments performed seem to confirm the insensitivity of these algorithms to the (Gaussian) noise parameters     

非高斯有色噪声中基于四阶累积量噪声建模的谐波恢复方法

本文提出一种在非高斯ＡＲＭＡ噪声中谐波恢复的高阶累积量方法，该方法首先通过Ｈｉｂｌｅｒｔ变换构造复数观测值，然后使用它的一种特殊的四阶累积量建立噪声过程ＡＲ参数，由此对观测值滤波，最后通过ＳＶＤ－ＴＬＳ方法估计谐波信号参数，本文方法克服了以往对非高斯噪声分布的非对称性假设，成功地解决了对称分布非高斯有色噪声中的谐波恢复问题，并且适用于于谐波信号存在二次相应耦合情形，仿真实验验证了文中结论。     

基于四阶混合累积量的CP-GTD模型参数估计方法

二维相干极化GTD（CP-GTD）模型能够精确描述高频区雷达目标的电磁散射机理。基于此模型,针对二维ESPRIT方法在色噪声情况下估计精度不高的问题,提出了一种新的二维散射中心参数估计方法。根据二维四阶混合累积量的特点和性质,用其代替观测数据实现色噪声背景下二维CP-GTD模型的位置参数估计,然后通过MUSIC谱峰搜索方法估计散射中心的类型参数,通过最小二乘法估计散射中心的相干极化散射矩阵。该方法能够实现全极化雷达目标的超分辨成像和二维CP-GTD模型参数的正确估计,与现有的二维MUSIC和二维ESPRIT方法相比,改善了估计性能,对色噪声具有较强的稳健性,同时克服了在长观测样本情况下计算量过大的缺陷。仿真和暗室测量数据实验验证了上述结论的正确性。      

基于盲波束形成的麦克风阵列语音增强方法

考虑到语音信号方向向量估计误差对传统波束形成语音增强性能的影响,该文提出一种盲波束形成语音增强方法。由于采用阵列四阶互累积量和线性约束最小方差波束形成器相结合,使得该方法对语音信号方向向量误差具有一定韧性。此外,采用多通道后置滤波去除盲波束形成器输出端的残留噪声。仿真结果表明,在语音信号波达方向等先验信息未知的情况下,该文提出的盲波束形成语音增强方法仍具有较好的噪声抑制性能。     

零均值复杂噪声背景下二维谐波的三次非线性耦合分析

该文利用一种四阶时间平均矩谱,通过对原始数据取平方的办法,改变了原始信号中噪声的统计特性,首次对零均值独立噪声背景下的二维谐波的三次耦合问题给出了解决方法,文中给出了详细的理论分析和证明。由于该方法也适合于非零均值噪声下的谐波耦合问题,因此这种方法不再需要对噪声的均值、颜色和分布作任何限制。仿真结果表明了该方法的有效性。     

基于高阶累积量实现数字调相信号调制识别

给出了基于高阶累积量进行多进制数字相位调制(MPSK)信号调制识别的特征值构造方法,对该特征值抑制多径干扰能力进行了理论分析,证明累积量阶数越高抑制多径干扰的性能越好。推导出基于6阶累积量进行MPSK信号调制识别的特征值公式,并给出具体分类方法,对4阶和6阶累积量调制识别性能进行了分析比较。计算机仿真试验证明:多径信道时,6阶累积量分类特征值优于4阶;当符号信噪比低于0dB时,4阶累积量分类特征值优于6阶。     

高斯噪声下差分跳频信号的高分辨率频率检测

差分跳频(DFH)是一种新的高速短波通信体制,它利用相邻跳变频率的变化而不是载频本身来携带信息。跳变频率检测是实现DFH的关键技术之一。本文利用四阶累积量研究了(色)高斯噪声下基于ARMA建模法的DFH信号频率检测,并针对由于模型阶数估计过高而产生的虚检频率,提出一种充分利用信号先验信息的改进算法。仿真结果证明了该方法的有效性,尤其是在低信噪比时仍然能够实现精确检测。     

Exploiting data and code interactions to reduce the power variancefor CDMA sequences

This paper investigates the effect of interactions between the Walsh codes and data sequences on the statistical moments of the forward-link CDMA signal. Of primary interest is the normalized fourth-order moment, which is referred to as the “power variance”. Several techniques for reducing the power variance of the CDMA signal are discussed that are based on Walsh code selection and data encoding. Certain groupings of Walsh codes, referred to as “active quadruples”, are shown to be useful in predicting the potential of each technique. Results demonstrate the reduction in the power variance afforded by two novel approaches referred to as “channel hopping” and “data reversal”     

Sample cumulants of stationary processes: asymptotic results

In this paper, we present the formulas of the covariances of the second-, third-, and fourth-order sample cumulants of stationary processes. These expressions are then used to obtain the analytic performance of FIR system identification methods as a function of the coefficients and the statistics of the input sequence. The lower bound in the variance is also compared for different sets of sample statistics to provide insight about the information carried by each sample statistic. Finally, the effect that the presence of noise has on the accuracy of the estimates is studied analytically. The results are illustrated graphically with plots of the variance of the estimates as a function of the parameters or the signal-to-noise ratio. Monte Carlo simulations are also included to compare their results with the predicted analytic performance     

基于四阶累积量的相干信号频率和二维到达角联合估计的新算法

该文提出了一种基于四阶累积量的相干信号频率和二维到达角联合估计的新算法-CTSS算法.CTSS算法利用双平行线阵的时空数据以及平滑技术构造了一个时空平滑矩阵,通过对其进行特征分解,并利用分解得到的特征值和特征矢量估计出空间相干信号的三维参数.在色噪声环境下,该算法能够精确地估计空间相干信号的三维参数,无需多维谱峰搜索,能实现信号三维参数的自动配对,并有效地解决了信源参数兼并问题.计算机仿真结果验证了算法的有效性.     

一种非等间距线阵的DOA估计方法

针对非等间距线阵测向中的测向精度和相位模糊之间的矛盾,该文提出了一种基于四阶累积量的波达角(DOA)估计算法。该算法利用基线间的参差关系解相位模糊,以突破VESPA算法中参考阵元间距不大于半波长的限制,从而有效地提高了测向精度。依靠导向矢量、累积量矩阵特征值以及其对应的特征向量三者之间的关系,该算法实现了各基线的相位差与信号源的配对。仿真实验验证了该算法的有效性。     

基于四阶累积量虚拟阵列扩展的运算量分析

在阵列信号处理中,利用四阶累积量可以使阵列虚拟扩展,增大了天线阵的孔径,但同时也增加了算法的计算量。该文通过分析四阶累积量矩阵中各元素之间的关系,剔除掉相同或互为共轭的冗余元素,避免了冗余元素的重复计算,极大地降低了四阶累积量矩阵计算的复杂度,并阐述了计算复杂度与阵元数目之间的关系。另外,针对均匀直线阵这种特殊情况进行了单独讨论。该文得出的相关结论对实际工程应用具有指导性的意义。     

基于四阶累积过的阵列扩展

在阵列测向问题中应用高阶累积量除了信息利用更充分和抑制高斯噪声等优点之外还具有阵列扩展的功能.本文推导了基于四阶累积量的阵列扩展方法,研究了虚拟阵的结构.放宽了协方差方法对信源数目的限制.但该方法在窄带多信号方向估计应用中存在局限.本文还推导了四阶相干问题和阵列扩展的限制条件.最后给出了实验举例.     

A sinusoidal contrast function for the blind separation of statistically independent sources

The authors propose a new solution to the blind separation of sources (BSS) based on statistical independence. In the two-dimensional (2-D) case, we prove that, under the whiteness constraint, the fourth-order moment-based approximation of the marginal entropy (ME) cost function yields a sinusoidal objective function. Therefore, we can minimize it by simply estimating its phase. We prove that this estimator is consistent for any source distribution. In addition, such results are useful for interpreting other algorithms such as the cumulant-based independent component analysis (CuBICA) and the weighted approximate maximum likelihood (WAML) [or weighted estimator (WE)]. Based on the WAML, we provide a general unifying form for several previous approximations to the ME contrast. The bias and the variance of this estimator have been included. Finally, simulations illustrate the good consistency, convergence, and accuracy of the proposed method.     

A higher order FDTD method for EM propagation in a collisionlesscold plasma

A fourth-order in time and space, finite-difference time-domain (FDTD) scheme is presented for radio-wave propagation in a lossless cold plasma. As with previously reported fourth-order schemes, the methodology is founded on the principle that correction derivatives (i.e., three derivatives in time) can be converted into vector spatial derivatives. From the error analysis and phase-velocity data, it is argued that this approach will significantly minimize the dispersion errors while still maintaining minimal memory requirements. This claim is also supported by data obtained from FDTD simulations. Using a one-dimensional plasma slab problem as the test case, we show that the bandwidth and dynamic range associated with this fourth-order scheme are significantly improved with respect to its second-order counterpart. The impact of other error mechanisms, namely material boundary-related errors, is also discussed