色噪声背景下正弦参量估计的互谱矩和SVD方法

互谱估计方法是用于色噪声背景下正弦信号参量估计的一个十分有效的方法。但以往互谱估计都是采用FFT方法和互周期图法。本文首次将现代谱估计方法引入到互谱估计中,从理论上建立了互相关函数的Yule-Walker方程,并在此基础上进而提出了互谱估计的矩估计法和SVD方法。给出了仿真实例结果。     

有色随机噪声背景下互谱TLS-ESPRIT估计方法

现代互谱估计是抑制有色观测噪声的一种有效方法。对旋转不变技术估计信号参量的方法进行了深入的分析，并进而提出了有色声随机信号背景下互谱TLS-ESPRIT估计方法。这种方法的突出特点是几乎不需要任何色噪声的先验信息，并在很低信噪比下工作，避免了以往互谱估计本身所固有的在整个频域上的谱峰搜索，可直接通过特征值确定信号参数估计值。此方法只需两次SVD分解，计算量大大降低。仿真结果表明，该方法具有较好的谱估计分辨率和良好的稳定性。     

有色噪声背景下正弦信号频率估计的互谱Pisarenko和MUSIC方法

现代互谱估计是抑制有色噪声的一个有效方法。本文首次对正弦信号的扩阶互相关函数矩阵的特征结构进行了深入的分析，并进而提出了有色噪声背景下正弦信号频率估计的互谱Ｐｉｓａｒｅｎｋｏ方法和ＭＵＳＩＣ方法。     

测量噪声背景下微弱正弦信号参数估计的互功率谱方法

本文首次把近代谱估计方法引入到互谱估计中，从理论上证明了互相关函数的Ｙｕｌｅ－Ｗａｌｋｅｒ方程，并在此基础上提出了互谱参数谱估计的矩估计方法和Ｌｅｖｉｎｓｏｎ递推估计方法。该方法可以有效地克服传统的互谱ＦＦＴ算法和互周期图法存在的谱分辩率低，谱估计方差大等缺点。文中还给出了信噪比为－３０ｄＢ的正弦信号参数估计的仿真实例。     

奇异值分解带通滤波背景抑制和去噪

针对可见光图像弱小目标检测中的背景抑制和去噪问题,提出了奇异值分解(Singular Value Decomposition,SVD)带通滤波新方法.首先分析了图像奇异值与目标、噪声和图像背景的关系,结果表明奇异值的高序部分更多地反映图像噪声,中序部分更多地反映目标性质,而低序部分更多地反映图像背景.以此为依据提出了SVD-I型和SVD-II型两种带通滤波器,并给出了奇异值曲线转折点法和门限准则法两种滤波器参数确定方法.实验表明SVD带通滤波能有效抑制图像背景,去除噪声,进而提高弱小目标的信噪比.     

The reconstruction of a band-limited function and its Fouriertransform from a finite number of samples at arbitrary locations bysingular value decomposition

A method for the stable interpolation of a bandlimited function known at sample instants with arbitrary locations in the presence of noise is given. Singular value decomposition is used to provide a series expansion that, in contrast to the method of sampling functions, permits simple identification of vectors in the minimum-norm space poorly represented in the sample values. Three methods, Miller regularization, least squares estimation, and maximum a posteriori estimation, are given for obtaining regularized reconstructions when noise is present. The singular value decomposition (SVD) method is used to interrelate these methods. Examples illustrating the technique are given     

A resampling method for estimating the signal subspace of spatio-temporal EEG/MEG data

Source localization using spatio-temporal electroencephalography (EEG) and magnetoencephalography (MEG) data is usually performed by means of signal subspace methods. The first step of these methods is the estimation of a set of vectors that spans a subspace containing as well as possible the signal of interest. This estimation is usually performed by means of a singular value decomposition (SVD) of the data matrix: The rank of the signal subspace (denoted by r) is estimated from a plot in which the singular values are plotted against their rank order, and the signal subspace itself is estimated by the first r singular vectors. The main problem with this method is that it is strongly affected by spatial covariance in the noise. Therefore, two methods are proposed that are much less affected by this spatial covariance, and old and a new method. The old method involves prewhitening of the data matrix, making use of an estimate of the spatial noise covariance matrix. The new method is based on the matrix product of two average data matrices, resulting from a random partition of a set of stochastically independent replications of the spatio-temporal data matrix. The estimated signal subspace is obtained by first filtering out the asymmetric and negative definite components of this matrix product and then retaining the eigenvectors that correspond to the r largest eigenvalues of this filtered data matrix. The main advantages of the partition-based eigen decomposition over prewhited SVD is that 1) it does not require an estimate of the spatial noise covariance matrix and 2b) that it allows one to make use of a resampling distribution (the so-called partitioning distribution) as a natural quantification of the uncertainty in the estimated rank. The performance of three methods (SVD with and without prewhitening, and the partition-based method) is compared in a simulation study. From this study, it could be concluded that prewhited SVD and the partition-based eigen decomposition perform equally well when the amplitude time series are constant, but that the partition-based method performs better when the amplitude time series are variable.     

基于累量的近场源快速定位算法

本文提出了一种基于累量的近场源参数快速估计方法。具体地,本文首先构造了一个累量矩阵,对其进行奇异值分解后,利用得到的右奇异向量和左奇异向量分别使用类Root-MUSIC方法得到了近场波达方向和距离估计的闭式解。该方法利用高阶累量矩阵,减少了阵列孔径损失,提高了能分辨的最大信源数,而且与其他基于高阶累积量的方法相比,该方法在近场的波达方向与距离的估计过程中只需要构造一个累量矩阵和进行一次奇异值分解,并且使用闭式解完全避免了峰值搜索,大大降低了运算量,同时还提高了估计的分辨概率和精度。此外,该方法在几乎没有增加额外计算量的情况下可以推广到混合场源的情况。仿真结果表明,该算法的分辨率和精度都有较大的优越性。      

准正交空时分组码系统的一种盲信道估计方法

空时分组码(STBC)系统的经典信道盲估计方法,如子空间法(SS)等,都是基于接收端样本自相关矩阵的特征值分解(EVD)或奇异值分解(SVD)来实现信道估计的,而基于QR分解的信道盲估计方法是一种性能优良的新算法.文中将该算法应用到准正交空时分组码系统的信道估计中,结合准正交空时分组码的特性提出了一种新的信道盲估计算法.与以上经典的信道盲估计算法相比,文中提出的算法的计算量大为降低.同时Monte-Carlo仿真表明,当信噪比较低时,该算法比子空间法有更好的性能.     

修正的MIMO-FSO信道自适应SVD估计算法

针对多入多出(MIMO)无线光通信(FSO)中传统的奇异值分解(SVD)信道估计算法由于训练序列的单极性容易导致信号能量损失,从而引起信道估计值不准确的问题,提出了一种修正的自适应SVD估计算法。该修正算法能对SVD算法中存在的估计误差进行补偿,从而能使该估计方法更好地应用于MIMO-FSO系统中。仿真结果表明,与SVD算法相比,在信噪比为15dB时,修正的算法有2个数量级的均方误差(MSE)性能提高,在信噪比为30dB时,MSE性能有3个数量级的提高。与相同条件下的均值修正SVD算法相比,平均有1dB左右的性能改善。该修正方法可移植性强,在其他信道估计方法中也可采用类似的改进方法。     

Channel estimation for multi‐antenna mobile worldwide interoperability for microwaves access downlink partial usage of subchannels systems

In order to improve channel estimation performance, a new time domain least square method is proposed for the multi‐antenna worldwide interoperability for microwaves access system at the downlink partial usage of subchannels mode. We show that the pilots in the proposed method double those of the regular time domain least square method by establishing a hypothetical channel estimation model instead of increasing the additional pilots, in which the frequency outputs of virtual pilots in the current symbol are reconstructed at the positions where the actual pilots of the adjacent symbol are located. We also show that the border effect incurred by the uneven limited pilots, which degrades the performance of channel estimation, can be reduced by using SVD as effectively as regularization. Simulations demonstrate that the proposed method using SVD or regularization can perform better than the conventional approaches, and especially over the pedestrian‐B channel for four transmits, it only incurs the performance loss of about 2.5 dB at a 0.001 of BER compared to the ideal case, whereas the regular methods cease to be effective due to too rare pilots allocated for each transmit and cannot approach this BER value over the considered Eb ∕ N0 range. Copyright © 2013 John Wiley & Sons, Ltd.     

基于联合奇异值分解的二维DOA估计

文章设计了一种新型三维立体阵列并基于该阵列形式提出了一种基于联合奇异值分解的二维DOA（Direction Of Arrival）估计算法。该方法利用三维立体阵,与平面阵相比大大提高某些方向上的测角精度,在方法中使用了子阵列之间的互相关而不是传统的子阵自相关,有效减小了噪声的影响,提高了估计精度,并且利用联合奇异值分解实现了快速配对。最后数值仿真结果证实了所提方法在增加了估计范围,提高了估计精度。     

三元阵被动定位中时延差估计算法研究

为了提高三元阵被动定位精度,该文对互谱法时延差估计进行了研究改进。改进算法解决了单独采用互谱法进行时延差估计存在的相位模糊问题,增强了互谱法在实际应用的鲁棒性。该算法所得时延差由周期值和修正值构成;时延差周期值是通过对阵元间互谱信号进行时延补偿所得,时延差修正值是采用最小二乘法对补偿后互谱信号拟合所得。理论分析和实验结果表明:采样率为103 Hz时的时延差估计精度可以达到10-6 s,该方法具有很强的实用性。能有效提高三元阵被动定位精度。     

Low-complexity video coding based on two-dimensional singular value decomposition

In this paper, we propose a low-complexity video coding scheme based upon 2-D singular value decomposition (2-D SVD), which exploits basic temporal correlation in visual signals without resorting to motion estimation (ME). By exploring the energy compaction property of 2-D SVD coefficient matrices, high coding efficiency is achieved. The proposed scheme is for the better compromise of computational complexity and temporal redundancy reduction, i.e., compared with the existing video coding methods. In addition, the problems caused by frame decoding dependence in hybrid video coding, such as unavailability of random access, are avoided. The comparison of the proposed 2-D SVD coding scheme with the existing relevant non-ME-based low-complexity codecs shows its advantages and potential in applications.     

Bearing estimation in the bispectrum domain

A new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data. The method is based on the asymptotic distribution of cross-bispectrum estimates and uses maximum likelihood theory. It is demonstrated that, when the noise additive sources are spatially correlated Gaussian with unknown cross-spectral matrix (CSM), the cross-bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known CSM. Analytical studies and simulations are given to document the performance of the new method     

The hyperbolic singular value decomposition and applications

A new generalization of the singular value decomposition (SVD), the hyperbolic SVD, is advanced, and its existence is established under mild restrictions. The hyperbolic SVD accurately and efficiently finds the eigenstructure of any matrix that is expressed as the difference of two matrix outer products. Signal processing applications where this task arises include the covariance differencing algorithm for bearing estimation in sensor arrays, sliding rectangular windowing, and array calibration. Two algorithms for effecting this decomposition are detailed. One is sequential and follows a similar pattern to the sequential bidiagonal based SVD algorithm. The other is for parallel implementation and mimics Hestenes' SVD algorithm (1958). Numerical examples demonstrate that like its conventional counterpart, the hyperbolic SVD exhibits superior numerical behavior relative to explicit formation and solution of the normal equations. Furthermore, the hyperbolic SVD applies in problems where the conventional SVD cannot be employed     

Analysis of Brain-Wave Generators as Multiple Statistical Time Series

An illustrative example of the spectral analysis of simultaneously recorded electroencephalograms(EEG's) is presented. The first topic is that of auto-spectral analysis, which is very similar to frequency analysis; then cross-spectral analysis is used to show that the major relationship among three of the traces analyzed is a linear one, while a fourth trace is nonlinearly activated. Two hypotheses suggested by this analysis are tested by methods of multivariate spectral analysis, a recently developed extension of the cross-spectral method.     

Filtering and frequency estimation using perturbation formulas

A new method for updating the SVD is introduced, based on perturbation formulas. The complexity of the method is O(n²). Applications are made to frequency estimation and filtering     

MIMO-OFDM系统中基于导频辅助的信道估计

该文对MIMO-OFDM系统中基于导频辅助的LMMSE信道估计算法进行了研究,导出了其估计均方差的下界。为降低算法复杂度,首先利用奇异值分解给出一种低阶近似的信道估计器结构;其次提出了一种基于最优导频设计的简化算法。该简化算法不仅降低了算法复杂度,且能有效地获得最优估计性能。最后文中给出了估计信道特性的方法。     

一种改进的LTE下行系统信道估计算法

基于3GPP长期演进（LTE）下行链路系统,在比较了现有几种不同信道估计算法的基础上,提出了一种适用于LTE下行系统的时频二维联合维纳迭代滤波信道估计算法。具体步骤如下：首先,采用基于奇异值分解（SVD）的线性最小均方误差（LMMSE）算法在频域进行维纳迭代滤波;然后,再利用频域估计出来的值在时域进行一次维纳迭代滤波。仿真结果表明,该算法能够有效地改善信道估计的误比特率（BER）性能,与传统的方法相比,性能更加接近于理想信道估计,同时也没有显著增加算法的运算复杂度。