Low-Complexity Estimation of DOA and Angular Spread for an Incoherently Distributed Source

In this paper, a low-complexity method is proposed for the parametric estimation of an incoherently distributed (ID) source, using a uniform linear array. Based on the Taylor approximation property of the noise-free covariance matrix, the proposed method firstly decouples the estimation of the nominal direction-of-arrival (DOA) from that of the angular spread. And then utilizing the nominal DOA estimation and a special cost function, the angular spread can be estimated by constructing one-dimensional (1-D) searching spectrum. Compared with some existing techniques, our approach requires a much lower computational cost and can exhibit a better estimation performance in a single ID source case, especially for low signal-to-noise ratio. Simulation results illustrate the performance of the proposed method.     

基于互相关抽样分解的分布式非圆信号DOA快速估计

在非相干分布式非圆信号波达方向(DOA)估计中,针对利用信号非圆特性后输出矩阵维数扩展带来的较大运算量问题,该文提出一种基于互相关抽样分解的DOA快速估计算法。该算法仅需要从子阵间的扩展互相关矩阵中抽样出少量行元素和列元素,构成两个低维子矩阵,进而通过低秩近似分解便可快速地同时求出左右奇异矢量,即分别对应两个子阵的信号子空间,避免了计算整个互相关矩阵及其奇异值分解运算;最后利用两个子阵信号子空间的旋转不变性通过最小二乘得到DOA估计。仿真分析表明,当行列抽样数大于信源数的两倍时,所提算法与直接基于互相关矩阵奇异值分解的非相干分布式非圆信号DOA估计算法性能相近,但复杂度得到了大幅度降低;而相比于传统的低复杂度非相干分布源DOA估计算法,所提算法利用信号非圆特性具有更高的估计性能。     

Direction of Arrival Estimation in the Presence of Noise Coupling in Antenna Arrays

The direction of arrival (DOA) estimation problem in the presence of signal and noise coupling in antenna arrays is addressed. In many applications, such as smart antenna, radar and navigation systems, the noise coupling between different antenna array elements is often neglected in the antenna modeling and thus, may significantly degrade the system performance. Utilizing the exact noise covariance matrix enables to achieve high-performance source localization by taking into account the colored properties of the array noise. The noise covariance matrix of the antenna array consists of both the external noise sources from sky, ground and interference, and the internal noise sources from amplifiers and loads. Computation of the internal noise covariance matrix is implemented using the theory of noisy linear networks combined with the method of moments (MoM). Based on this noise statistical analysis, a new four-port antenna element consisting of two orthogonal loops is proposed with enhanced source localization performance. The maximum likelihood (ML) estimator and the Cramer-Rao lower bound (CRLB) for DOA estimation in the presence of noise coupling is derived. Simulation results show that the noise coupling in antenna arrays may substantially alter the source localization performance. The performance of a mismatched ML estimator based on a model which ignores the noise coupling shows significant performance degradation due to noise coupling. These results demonstrate the importance of the noise coupling modeling in the DOA estimation algorithms.     

非相干分布源DOA和角度扩展去耦估计方法

该文提出了一种新的非相干分布源的DOA和角度扩展估计算法。根据空间频率模型下的非相干分布源协方差矩阵的结构特点,可将协方差矩阵分离成两个分别由相位信息和幅度信息重建的矩阵。对矩阵的各主次对角线元素均进行平滑,可得到包含相位信息和幅度信息的平滑向量。利用最小均方拟合方法,可从相位信息中估计得到方位角;估计得到的方位角信息代入到幅度信息中即可获得角度扩展信息的估计,实现非相干分布源的DOA和角度扩展去耦估计。计算机仿真验证了算法的性能。     

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.     

A Simplified Estimator for Tridimensional Localization of Single Incoherently Distributed Source

In this paper, a simplified parametric estimator for tridimensional localization of single incoherently distributed (ID) source with small angular spread is proposed. The proposed estimator firstly obtains two sample covariance matrices using the observation data of a L-shape array. And then the secondary diagonal elements of the sample covariance matrices are used to estimate the nominal azimuth and elevation of single ID source. Our technique does not involve any spectrum searching and the eigen-decomposition of the sample covariance matrix, and thus the computational burden has been significantly alleviated. Moreover, it is also a blind estimator which doesn’t require any prior knowledge about the angular power density of the ID source. Numerical examples illustrate the performance of the proposed estimator.     

A Fast Decoupled Nominal 2-D Direction-of-Arrival Estimation for Coherently Distributed Source

In this paper, we consider the problem of the nominal 2-D (azimuth and elevation) direction-of-arrival (DOA) estimation for coherently distributed source. This new approach is based on the rotation matrices of three parallel uniform linear arrays as deduced, which has decoupled the nominal 2-D DOA from those of angular spreads. The estimator makes use of the eigenvalue decomposition to beamspace data to estimate the nominal elevation DOA. And then using a new cross-correlation matrix, the nominal azimuth DOA estimates are decoupled from the elevation estimates and can be obtained with no searching. The proposed algorithm has lower computational complexity particularly when the radio of array size to the number of source is large, at the expense of negligible performance loss. Simulation results verify the effectiveness of the proposed method.     

Maximum likelihood estimation and Cramer-Rao bounds for directionof arrival parameters of a large sensor array

A maximum likelihood (ML) method is developed for estimation of direction of arrival (DOA) and associated parameters of narrowband signals based on the Taylor's series expansion of the inverse of the data covariance matrix R for large M, M specifying number of sensors in the array. The stochastic ML criterion function can thus be simplified resulting in a computationally efficient algorithm for DOA estimation. The more important result is the derivation of asymptotic (large M) expressions for the Cramer-Rao lower bound (CRB) on the covariance matrix of all unknown DOA angles for the general D source case. The derived bound is expressed explicitly as a function of snapshots, signal-to-noise ratio (SNR), sensors, separation, and correlation between signal sources. Using the condition of positive definiteness of the Fisher information matrix a resolution criterion is proposed which gives a tight lower limit on the minimum resolvable angle     

Efficient Subspace-Based Estimator for Localization of Multiple Incoherently Distributed Sources

In this paper, a new subspace-based algorithm for parametric estimation of angular parameters of multiple incoherently distributed sources is proposed. This approach consists of using the subspace principle without any eigendecomposition of the covariance matrix, so that it does not require the knowledge of the effective dimension of the pseudosignal subspace, and therefore the main difficulty of the existing subspace estimators can be avoided. The proposed idea relies on the use of the property of the inverse of the covariance matrix to exploit approximately the orthogonality property between column vectors of the noise-free covariance matrix and the sample pseudonoise subspace. The resulting estimator can be considered as a generalization of the Pisarenko's extended version of Capon's estimator from the case of point sources to the case of incoherently distributed sources. Theoretical expressions are derived for the variance and the bias of the proposed estimator due to finite sample effect. Compared with other known methods with comparable complexity, the proposed algorithm exhibits a better estimation performance, especially for close source separation, for large angular spread and for low signal-to-noise ratio.     

Decoupled estimation of DOA and angular spread for a spatiallydistributed source

In mobile communications, local scattering in the vicinity of the mobile results in angular spreading as seen from a base station antenna array. In this paper, we consider the problem of estimating the parameters [direction-of-arrival (DOA) and angular spread] of a spatially distributed source, using a uniform linear array (ULA). A two-step procedure enabling decoupling the estimation of DOA from that of the angular spread is proposed. This method combines a covariance matching algorithm with the use of the extended invariance principle (EXIP). More exactly, the first step makes use of an unstructured model for the part of the covariance matrix that depends on the angular spread. Then, the solution is refined by invoking EXIP. Instead of a 2-D search, the proposed scheme requires two successive 1-D searches. Additionally, the DOA estimate is robust to mismodeling the spatial distribution of the scatterers. A statistical analysis is carried out, and a formula for the asymptotic variance of the estimates is derived. Numerical examples illustrate the performance of the method     

协方差矩阵稀疏表示在网格失配波达方向估计中的应用

该文利用了入射信号在空域的稀疏性,将波达方向（DOA）估计问题描述为在网格划分的空间协方差矩阵稀疏表示模型,并将其松弛为一个凸问题,从而提出了一种网格匹配下的交替迭代方法（AIEGM）。传统的基于稀疏重构的波达方向估计算法由于其模型的局限性,一旦入射角不在预先设定的离散化网格上,就会造成估计性能的急剧恶化。针对这个问题,该算法可以在离散化网格比较粗糙的前提下,通过交替迭代的方法求解一系列基追踪去噪（BPDN）问题,对于不在网格上的真实角度估计值进行修正,从而达到更精确的波达方向估计。仿真结果证明了AIEGM算法的有效性。      

Simplified Estimation of 2D DOA for Coherently Distributed Sources

In mobile communications, local scattering in the vicinity of the mobile results in angular spreading as seen from a base station antenna array. In this paper, we consider the problem of estimating the two-dimensional (azimuth and elevation) direction-of-arrival (DOA) parameters of spatially distributed sources. Based on double parallel uniform linear arrays (ULAs), a simplified method without spectrum-peak searching is proposed for the 2D DOA estimation of multiple coherently distributed (CD) sources. The proposed method firstly obtains two approximate rotational invariance relations with respect to the nominal DOAs of CD sources by using one-order Taylor approximation to the generalized steering vectors (GSVs) of two pairs of shifted subarrays. And then a new ESPRIT-based method is utilized to estimate the nominal azimuth DOA and nominal elevation DOA. In addition, a simple parameter matching approach is also given. Compared with the conventional methods, our method has significantly reduced the computational cost and can sustain the estimation performance within a tolerable level. Moreover, our method is a blind estimator without any prior knowledge about angular distribution shape. Numerical examples illustrate the performance of the method.     

相干分布源DOA与角度扩展估计求根算法

论文提出了一种具有低复杂度的相干分布源波达方向和角度扩展估计算法。该算法将点源模型中的求根MUSIC算法推广应用至分布源模型。利用空间频率下的相干分布源广义方向矢量可以表示成参数去耦形式的结构特点,并根据相干分布源的角信号密度函数,构造参数估计的多项式求根形式,然后通过交替迭代的求根方法得到分布源的中心波达方向和角度扩展的估计值。该算法参数估计性能与DSPE算法相当,其计算复杂度要远小于DSPE算法,并且适用于不同分布类型的相干分布源同时存在的情况。计算机仿真验证了算法的性能。      

Estimation of directions of arrival of multiple scattered sources

We consider the problem of estimating the directions of arrival (DOA) of multiple sources in the presence of local scattering. This problem is encountered in wireless communications due to the presence of scatterers in the vicinity of the mobile or when the signals propagate through a random inhomogeneous medium. Assuming a uniform linear array (ULA), we develop DOA estimation algorithms based on covariance matching applied to a reduced-size statistic obtained from the sample covariance matrix after redundancy averaging. Next, a computationally efficient estimator based on AR modelling of the coherence loss function is derived. A theoretical expression for the asymptotic covariance matrix of this estimator is derived. Finally, the corresponding Cramer-Rao bounds (CRBs) are derived. Despite its simplicity, the AR-based estimator is shown to possess performance that is nearly as good as that of the covariance matching method     

Maximum-likelihood direction-of-arrival estimation in the presenceof unknown nonuniform noise

We consider the problem of estimating directions of arrival (DOAs) of multiple sources observed on the background of nonuniform white noise with an arbitrary diagonal covariance matrix. A new deterministic maximum likelihood (ML) DOA estimator is derived. Its implementation is based on an iterative procedure which includes a stepwise concentration of the log-likelihood (LL) function with respect to the signal and noise nuisance parameters and requires only a few iterations to converge. New closed-form expressions for the deterministic and stochastic direction estimation Cramer-Rao bounds (CRBs) are derived for the considered nonuniform model. Our expressions can be viewed as an extension of the well-known results by Stoica and Nehorai (1989, 1990) and Weiss and Friedlander (1993) to a more general noise model than the commonly used uniform one. In addition, these expressions extend the results obtained by Matveyev et al. (see Circuits, Syst., Signal Process., vol.18, p.479-87, 1999) to the multiple source case. Comparisons with the above-mentioned earlier results help to discover several interesting properties of DOA estimation in the nonuniform noise case. To compare the estimation performance of the proposed ML technique with the results of our CRB analysis and with the performance of conventional “uniform” ML, simulation results are presented. Additionally, we test our technique using experimental seismic array data. Our simulations and experimental results both validate essential performance improvements achieved by means of the approach proposed     

Subspace-based direction-of-arrival estimation using nonparametricstatistics

The problem of subspace estimation using multivariate nonparametric statistics is addressed. We introduce new high-resolution direction-of-arrival (DOA) estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy-tailed noise. The extensions of the techniques for the case of coherent sources are considered as well. The proposed techniques are based on spatial sign and rank concepts. We show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces. In the proofs, the noise is assumed to be spherically symmetric. Moreover, we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance. The performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric. The results show that the algorithms perform near optimally in the case of Gaussian noise and highly reliably if the noise is non-Gaussian     

基于稀疏表示的相干分布式非圆信号的参数估计

基于稀疏表示技术,该文提出一种相干分布式非圆信号的参数估计新方法。该方法将信号的非圆特性引入分布式信源模型,充分利用非圆信号的特性,联合阵列输出协方差矩阵和椭圆协方差矩阵,并将其矢量化之后表示在受制于稀疏限制的过完备字典上;然后将DOA估计转化为一个稀疏重构问题,能够一次性求解出中心DOA和角度扩展。仿真结果表明,该方法适用于各种非圆率的非圆信号,具有较好的信噪比性能和分辨力,所提出的方法还能对圆和非圆信号同时存在的情况进行有效估计。     

Accurate direction‐of‐arrival estimation of multiple sources using a genetic approach

In this paper, we present an accurate direction‐of‐arrival (DOA) estimation method, which is based on the maximum likelihood (ML) principle and implemented using a modified and refined genetic algorithm (GA). With the newly introduced features—intelligent initialization and the emperor‐selective (EMS) mating scheme, carefully selected crossover and mutation operators and fine‐tuned parameters such as the population size, the probability of crossover and mutation etc., the GA‐ML estimator achieves fast global convergence. A GA operator and parameter standard is suggested for this application, which is independent of the source and array configurations except the number of sources. Simulation results demonstrate that in general scenarios, the proposed estimator is the most efficient in computation and its statistical performance is the best among all popular ML‐based DOA estimation methods. Copyright © 2004 John Wiley & Sons, Ltd.     

High-resolution direction finding: the missing data case

This paper considers the problem of estimating the direction-of-arrival (DOA) of one or more signals using an array of sensors, where some of the sensors fail to work before the measurement is completed. Methods for estimating the array output covariance matrix are discussed. In particular, the maximum-likelihood (ML) estimate of this covariance matrix and its asymptotic accuracy are derived and discussed. Different covariance matrix estimates are used for DOA estimation together with the MUSIC algorithm and with a covariance matching technique. In contrast to MUSIC, the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix, and it is demonstrated that this yields a significant performance gain     

非均匀噪声环境下宽带近场源定位的两种改进方法

研究了宽带近场信号源基于最大似然方法和相关信号子空间方法在非均匀噪声下的被动定位算法，并进行了比较。这两种算法均可在传感器任意分布的情况下有效地进行信号源定位。最大似然法采用了迭代的方法来估计噪声的协方差矩。而信号子空间法给出了聚焦阵构造的新方法。仿真试验证明了方法的有效性和稳健性。