Effects of modeling errors on the resolution threshold of the MUSICalgorithm

Subspace-based algorithms for narrowband direction-of-arrival (DOA) estimation require detailed knowledge of the array response (the array manifold) and assume that the noise covariance matrix is known up to a scaling factor. In practice, these quantities are not known precisely. Estimation accuracy can degrade significantly when the array response or the noise covariance deviate from their nominal values. In the paper the authors examine the resolution threshold of the MUSIC algorithm when the array response is perturbed from its assumed value and when the noise covariance does not match the assumed model. Analytical expressions for the resolution threshold are derived and verified by computer simulation. The authors also demonstrate the fact that preprocessing of the array data can improve somewhat the resolution in the presence of model errors. The paper makes extensive use of the contributions of various authors     

Direction finding with an array of antennas having diverse polarizations

The advantages of using diversely polarized antennas to determine bearings of multiple cochannel narrow-band signals are shown. Three bearing estimation algorithms-maximum likelihood (ML), adapted angular response (AAR), and Music (multiple signal classification)-are extended to handle antenna arrays with diverse polarizations; the maximum entropy method does not readily extend. The proposed algorithms are applicable to arbitrary antenna locations and directional characteristics and arbitrary noise correlations between the antenna outputs. The algorithms are compared on the basis of multiple signal resolution and bearing accuracy in the presence of noise. The Music algorithm exhibits superior performance at moderate to low signal-to-noise ratio (SNR).     

Direction finding for wide-band signals using an interpolated array

The authors derive a new direction-finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance. Using an interpolation technique, they generate a set of virtual arrays, each for a different frequency band, having the same array manifold. The convergence matrices of these arrays are added to produce a composite covariance matrix. Direction-of-arrival (DOA) estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband MUSIC algorithm or its variants. Closed-form expressions for the asymptotic covariance matrix of the DOA estimation errors are derived using a perturbation analysis, evaluated for specific cases, and compared with the Cramer-Rao lower bound. Special attention is given to correlated and coherent signals. The formulas for the error covariance are quite general and can be modified to provide results for other wideband DOA estimation algorithms     

Crossed-dipole arrays for asynchronous DS-CDMA systems

In this paper, the use of a crossed-dipole array is proposed in joint space-time channel estimation for asynchronous multipath direct sequence code division multiple access (DS-CDMA) systems. The polarization diversity offered by such an array, unlike linearly polarized arrays, is able to detect and estimate any arbitrary completely polarized signal path. By utilizing the polarization information inherent in the received signal to construct the polar-spatio-temporal array (polar-STAR) manifold vector, the accuracy and resolution of the polar-STAR parameters' estimation are significantly improved, and its signal detection capability is enhanced. To alleviate the need for a multidimensional search in the polarization space, a computationally efficient joint polarization-angle-delay channel parameter estimation algorithm is proposed for a "desired user" that operates in an asynchronous multiuser and multipath environment. The proposed algorithm, which can be seen as an application of MUSIC-type techniques, is based on combining a two-dimensional STAR-Subspace type technique with a set of analytical equations and is supported by representative examples and computer simulation studies.     

A performance analysis of subspace-based methods in the presence ofmodel errors. I. The MUSIC algorithm

Application of subspace-based algorithms to narrowband direction-of-arrival (DOA) estimation requires that both the array response in all directions of interest and the spatial covariance of the noise must be known. In practice, however, neither of these quantities is known precisely. Depending on the degree to which they deviate from their nominal values, serious performance degradation can result. The performance of the MUSIC algorithm is examined for situations in which the noise covariance and array response are perturbed from their assumed values. Theoretical expressions for the error in the MUSIC DOA estimates are derived and compared with simulations performed for several representative cases, and with the appropriate Cramer-Rao bound. An optimally weighted version of MUSIC is proposed for a particular class of array errors     

增益相位误差下基于部分校准嵌套阵列的DOA估计

现有的波达方向（Direction of Arrival,DOA）估计方法大多依赖于阵列导向矩阵的精确无偏条件,而实际工程中由于时钟偏移、阵元位置偏差的存在导致该条件往往难以满足.为匹配阵列实际接收条件,本文基于部分校准嵌套阵列,提出了一种增益相位误差下的DOA估计新方法.该方法首先利用连乘子函数和简单的代数运算完成初始增益相位误差估计,然后通过协方差矩阵向量化和稀疏表示理论构建具有连续自由度的稀疏表示向量模型,最后考虑有效样本的影响,在初始增益相位误差估计的基础上应用稀疏总体最小均方（Sparse total least squares,STLS）算法完成波达方向估计.本文所提方法不仅对阵列增益相位误差不敏感,而且可依靠嵌套阵列高自由度特性和STLS算法的抗扰动特性获得改进的分辨率和估计精度,计算机仿真结果验证了所提算法的有效性.     

一种改进的快速高分辨DOA估计方法

快速子空间类高分辨DOA估计方法(Propagator Method,PM)算法是从阵列接收数据的协方差矩阵中提取噪声子空间的基,此方法是利用被噪声污染的数据来实现对噪声子空间的逼近。利用阵列分割的消噪预处理原理对PM算法进行改进,改进后的算法是在剔除噪声之后的数据协方差矩阵中提取噪声子空间的基。仿真试验表明改进的算法会带来阵列孔径损失,但是在大快拍数的条件下DOA估计的分辨力有明显的提高而算法的计算量没有增加。     

基于内插阵列变换的非圆信号MUSIC算法

针对非圆信号的波达方向(DOA)估计问题,提出一种基于内插阵列变换的非圆信号MUSIC算法(VIA-NC-MUSIC算法)。利用真实阵列流型与虚拟阵列流型之间的变换矩阵,将真实协方差矩阵变换为虚拟协方差矩阵,再对虚拟协方差矩阵进行奇异值分解(SVD),利用信号子空间与噪声子空间的正交性,得出算法的空间谱函数。仿真实验表明:存在阵元位置误差的情况下,新算法通过对阵元位置校准数据进行内插阵列变换(VIA),取得与阵元位置校准的非圆信号MUSIC算法(NC-MUSIC算法)相当的估计性能,保持了高估计精度、阵列扩展能力等优点。     

Higher Order Direction Finding From Arrays With Diversely Polarized Antennas: The PD-2q-MUSIC Algorithms

Fourth-order (FO) and, a short while ago, 2qth-order, q ges 2, high-resolution methods exploiting the information contained in the FO and the 2qth-order, q ges 2, statistics of the data, respectively, are now available for direction finding of non-Gaussian signals. Among these methods, the 2q-MUSIC methods, q ges 2, are the most popular. These methods are asymptotically robust to a Gaussian background noise whose spatial coherence is unknown and offer increasing resolution and robustness to modeling errors jointly with an increasing processing capacity as q increases. However, these methods have been mainly developed for arrays with identical sensors only and cannot put up with arrays of diversely polarized sensors in the presence of diversely polarized sources. In this context, the purpose of this paper is to introduce, for arbitrary values of q, q ges 1, three extensions of the 2q-MUSIC method, able to put up with arrays having diversely polarized sensors for diversely polarized sources. This gives rise to the so-called polarization diversity 2q-MUSIC (PD-2q-MUSIC) algorithms. For a given value of q, these algorithms are shown to increase the resolution, the robustness to modeling errors, and the processing capacity of the 2q-MUSIC method in the presence of diversely polarized sources. Besides, some PD-2q-MUSIC algorithms are shown to offer increasing performances with q when resolution in both direction of arrival and polarization is required.     

毫米波热辐射阵列的空间谱估计阵列误差模型研究

将空间谱估计算法应用于毫米波热辐射阵列接收系统对目标进行超分辨率探测,需要解决目标热辐射信号弱及阵列误差使性能下降这两个主要问题.为此,建立了低信噪比阵列误差模型,该模型综合考虑了通道幅相误差对信源和通道噪声的影响,推导出由它们所造成的阵列接收数据自相关矩阵的特征值扰动范围和信号特征向量空间误差距离.利用该模型提出了一种通道幅相误差校正算法,使得高分辨率的空间谱估计算法能够很好地应用于毫米波热辐射阵列接收系统,并通过实验验证了新模型及校正算法的正确性和有效性.     

一种基于波束空间的非相关信号源DOA估计方法

针对非相关信号源的到达角估计,本文基于波束空间信号输出协方差矩阵的对角阵特性,建立了信号到达角估计的最小化代价函数.采用DFT波束形成矩阵,借助于矩阵分解变换,保持了阵列流形的Vandermonde结构,并由此将代价函数转换为二次函数形式,得到信号源到达角的精确估计.仿真结果表明该算法具有更快的运算速度,更低的分辨力门限及高的估计精度.     

Subspace fitting with diversely polarized antenna arrays

Diversely polarized antenna arrays are widely used in RF applications. The diversity of response provided by diversely polarized antenna arrays can greatly improve direction-finding performance over arrays sensitive to only one polarization component. For d emitters, directly implementing a multidimensional estimation algorithm would require a search for 3d parameters: d directions of arrival (DOAs), and 2d polarization parameters. A more efficient solution is presented based on the noise subspace fitting (NSF) algorithm. It is shown how to decouple the NSF search into a two-step procedure, where the DOAs are estimated separately. The polarization parameters are then obtained by solving a linear system of equations. The advantage of this approach is that the search dimension is reduced by a factor of three, and no initial polarization estimate is required. The algorithm can be shown to yield asymptotically minimum variance estimates: provided no perfectly coherent signals are present. Simulation examples are included     

A performance analysis of subspace-based methods in the presence ofmodel error. II. Multidimensional algorithms

For pt.I, see ibid., vol.40, no.7, p.1758-74 (1992). In pt.I the performance of the MUSIC algorithms for narrowband direction-of-arrival (DOA) estimation when the array manifold and noise covariance are not correctly modeled was investigated. This analysis is extended to multidimensional subspace-based algorithms including deterministic (or conditional) maximum likelihood, MD-MUSIC, weighted subspace fitting (WSF), MODE, and ESPRIT. A general expression for the variance of the DOA estimates that can be applied to any of the above algorithms and to any of a wide variety of scenarios is presented. Optimally weighted subspace fitting algorithms are presented for special cases involving random unstructured errors of the array manifold and noise covariance. It is shown that one-dimensional MUSIC outperforms all of the above multidimensional algorithms for random angle-independent array perturbations     

平面极化天线阵列的DOA及极化参数降维估计方法

基于极化阵列的长矢量数据模型,提出了一种适用于平面极化天线阵列的DOA和极化参数联合估计的方法。通过利用谱函数的偏导数条件进行降维优化,从而大大降低在搜索过程中的运算量,同时保证了分辨能力与估计精度。通过仿真实验可以看出,所提算法相比于目前较有效的基于四元数的Q-MUSIC算法有着更好的分辨力与较小的均方误差,且减少了运算量。     

利用局域子空间投影提高子空间类DOA 估计算法的谱分辨力

本文提出一种新的用于子空间类DOA估计算法的阵列协方差矩阵噪声子空间投影矢量的选取方法——局域子空间投影(LSP).该投影矢量选取方法有利于压低真实信源方位附近,非信源方位对应的谱曲线高度,从而提高子空间类高分辨DOA估计算法的分辨力.LSP算法的估计偏差和信噪比分辨门限明显低于MUSIC算法,而估计方差几乎与MUSIC相同.计算机仿真结果证明了文中对LSP算法性能理论分析的正确性和LSP算法的有效性.     

Analysis of a signal estimation algorithm for diversely polarizedarrays

The problem of separating and estimating the waveforms of superimposed signals received by a diversely polarized array is considered. Signal estimation is accomplished by a two-step procedure: (1) The directions of arrival and polarization parameters of all the signals are estimated using an eigenstructure-based technique; (2) The estimated signal is obtained as a linear combination of the array outputs, with weights that are computed from the estimated direction/polarization parameters. The objective is to analyze the quality of the estimated signal in terms of the output signal-to-interference ratio (SIR) and output signal-to-noise ratio (SNR). Closed-form expressions are derived for the output SIR and SNR of a general diversely polarized array. By evaluating these expressions for selected test cases it is shown that polarization sensitive arrays can provide significantly higher output SIR and SNR than uniformly polarized arrays. The performance improvement is especially significant for closely spaced sources with sufficiently different polarization characteristics     

Direction-of-arrival and polarization estimation with uniform circular arrays in the presence of mutual coupling

A modified Root-MUSIC algorithm is proposed to estimate the directions-of-arrival (DOAs) and the polarization of plane waves, which impinge at a fixed elevation angle, using a diversely polarized uniform circular array (UCA). Special attention is devoted to the presence of mutual coupling effects in antenna arrays. By describing the electromagnetic characteristics on the basis of a phase-mode expansion for the open-circuit voltages and the mutual coupling matrix, the modified Root-multiple signal classification (MUSIC) algorithm takes mutual coupling effects into account by a limited number of phase modes. Finally, the efficiency of the new algorithm is verified based on synthetic antenna data.     

基于平行互质虚拟阵列的低复杂度二维DOA联合估计算法

针对传统平行阵列2维测向自由度低、分辨能力差和小快拍情况下估计误差大等问题,该文提出基于平行互质虚拟阵列的低复杂度2维波达角(DOA)估计算法。该算法利用两个相互平行的互质线阵扩展生成虚拟阵列,并通过协方差矩阵和互协方差矩阵构造具有增强2维角度自由度的扩展矩阵,最后通过奇异值分解(SVD)和旋转不变技术(ESPRIT)获得自动匹配的2维角度估计。相比于传统的2维DOA估计方法,所提算法更好地利用了阵列接收数据信息,能识别更多的入射信号,分辨能力高,不需要进行2维线性搜索或者角度参数匹配,在低信噪比 (SNR)和小快拍情况下也有很好的估计效果。实验仿真结果验证了提出算法的有效性和可靠性。     

Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays

We address the problem of maximum likelihood (ML) direction-of-arrival (DOA) estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays. In such arrays, intersubarray spacings are substantially larger than the signal wavelength, and therefore, sensor noises can be assumed to be uncorrelated between different subarrays. This leads to a block-diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying DOA estimation problem. A new deterministic ML DOA estimator is derived for this class of sparse sensor arrays. The proposed approach concentrates the ML estimation problem with respect to all nuisance parameters. In contrast to the analytic concentration used in conventional ML techniques, the implementation of the proposed estimator is based on an iterative procedure, which includes a stepwise concentration of the log-likelihood (LL) function. The proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases. It is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ML-based approaches to DOA estimation in spatially correlated noise.     

Direction finding for diversely polarized signals using polynomialrooting

A direction finding algorithm for diversely polarized arrays that is based on polynomial rooting is presented. Using polynomial rooting instead of search reduces significantly the computational requirements of the algorithm and enhances resolution. The basic method is limited to linear uniformly spaced arrays. However, using an interpolation technique, the algorithm is extended to a larger class of arrays. The performance of the proposed algorithm is analyzed. Computer simulations are used to demonstrate the performance of the new technique and to verify the performance analysis