Direction-of-arrival estimation for a lens-based array

In this paper, we describe a high-resolution direction-of-arrival (DOA) estimation algorithm for the enhancement of a lens-based array system. In such a system, the antenna array is followed by an electromagnetic lens and a bank of power detectors (crystal video receivers). This system can handle sources over a large bandwidth and is capable of detecting pulsed sources that exist for short periods of time. The proposed algorithm operates directly on the power estimates provided by a bank of crystal video receivers (CVRs), yielding accurate DOA estimates for multiple narrowband sources. This approach is most effective when the sources are uncorrelated, and it potentially is capable of operating in environments where the signals are highly correlated. We present computer simulations to demonstrate the improved performance achieved by the algorithm for different source scenarios     

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.     

Parametric localization of distributed sources

Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method     

Distributed source localization using ESPRIT algorithm

A new algorithm based on ESPRIT is proposed for the estimation of the central angle and angular extension of distributed sources. The central angles are estimated using TLS-ESPRIT for both incoherently distributed (ID) and coherently distributed (CD) sources. For CD sources, the extension width is estimated by constructing a one-dimensional (1-D) distributed source parameter estimator (DSPE) spectrum for each source. For ID sources, the extension widths are estimated using the central moments of the distribution. The algorithm can be used for sources with different angular distributions     

Efficiency Evaluation of the Unconditional Maximum Likelihood Estimator for Near‐Field DOA Estimation

In this paper, we address the problem of closely spaced source localization using sensor array processing. In particular, the performance efficiency (measured in terms of the root mean square error) of the unconditional maximum likelihood (UML) algorithm for estimating the direction of arrival (DOA) of near‐field sources is evaluated. Four parameters are considered in this evaluation: angular separation among sources, signal‐to‐noise ratio (SNR), number of snapshots, and number of sources (multiple sources). Simulations are conducted to illustrate the UML performance to compute the DOA of sources in the near‐field. Finally, results are also presented that compare the performance of the UML DOA estimator with the existing multiple signal classification approach. The results show the capability of the UML estimator for estimating the DOA when the angular separation is taken into account as a critical parameter. These results are consistent in both low SNR and multiple‐source scenarios.     

2D DOA Estimator for Multiple Coherently Distributed Sources Using Modified Propagator

In this paper, we propose a new algorithm for estimating the two-dimensional (2D) nominal direction-of-arrivals (DOAs) of multiple coherently distributed (CD) sources by utilizing three parallel uniform linear arrays (ULAs). The proposed algorithm firstly shows that some rotational eigenstructures exist approximately for three pair of shifted ULAs. And then a modified propagator method is used to estimate three rotational invariance matrices which denote the rotational eigenstructures. Finally, the nominal angular parameters of CD sources are obtained from the eigenvalues of the rotational invariance matrices. Without spectrum searching, the estimation and eigendecomposition of the sample covariance matrix, our approach is computationally more attractive compared with the earlier algorithms. In addition, it can be applied to the scenario with multiple sources that may have different angular distribution shapes. Simulation results illustrate the performance of the algorithm.     

Joint azimuth, elevation, and time of arrival estimation of diffuse sources

In this paper, we estimate the azimuth, the elevation, and the time of arrival of diffuse sources using the covariance matching estimator (COMET) algorithm. Previous works dealt with azimuth estimation of diffuse sources or azimuth and time of arrival estimation of point sources. However, in realistic situations, a tridimensional diffuse source localization is needed, which is the main objective of this paper. We show that the dimensionality of the COMET algorithm can be reduced by separating the estimation of the different source powers and the noise variance from that of the remaining parameters, namely the azimuth, the elevation, the time of arrival, and the corresponding angular and temporal spreads. As COMET still involves a multidimensional nonlinear optimization, we choose, in this purpose, the alternating projection algorithm to alleviate the corresponding complexity. The multiple signal classification (MUSIC) algorithm is processed to initialize the so-resulted algorithm. Simulations of the proposed algorithm are carried in different contexts and compared to the Cramér-Rao Bound, MUSIC algorithm, and dispersed signal parametric estimation simulation results.     

一种低复杂度的ESPRIT新算法

该文提出了一种基于QR分解的Power-ESPRIT (以下简称QP-ESPRIT算法) 新算法。首先使用采样数据协方差矩阵的幂(Power)获得噪声子空间的估计,然后对噪声子空间进行QR分解并使用R矩阵估计信源个数,提出了无特征分解的信源个数检测算法SDWED算法。进而,信号子空间的特征向量就可以由Q矩阵确定,从而应用ESPRIT算法获得信源波达方向的估计。该算法不需要预先知道信源个数的先验知识以及分离信号与噪声特征值的门限。在确定信源个数和子空间估计的同时,本文算法与传统的基于奇异值分解算法相比,具有近似性能时却拥有较低的计算复杂度。仿真结果证明了该方法的有效性。     

A Stochastic Approximation Approach to the Power-Control Problem

This paper proposes and analyzes a new distributed power-control algorithm based on the theory of stochastic approximation. The power-control problem is first converted into a stochastic approximation problem in which the zero point of a specific function is determined. A distributed power-control algorithm is then derived and its convergence properties are analyzed using standard techniques. In the distributed algorithm, each user iteratively updates its power level by using estimates of the inverse of the signal-to-interference ratio (SIR) of its channel. No knowledge of the channel gains or state information of other users is required. Moreover, the algorithm is robust in the sense that it can handle errors in the bit-error rate estimates, and hence, can be used in practical scenarios. Convergence of the algorithm is analyzed in the almost-sure sense     

一种新的相干信源DOA估计算法: 加权空间平滑协方差矩阵的Toeplitz矩阵拟合

文献[1]提出的最优加权空间平滑技术可以使相干源存在时的信源协方差矩阵恢复为对角阵.由于文献[1]中导出的最优权矩阵是空间信源方位的函数矩阵,本文利用最优加权空间平滑后阵列协方差矩阵的Toeplitz性,构造了一个全新的优化拟合的代价函数,并基于此提出了一种相干源方位估计的新算法.与文献[1]不同,算法的实现不需要方位估计的先验知识和协方差矩阵的去噪预处理.分辨性能的蒙特卡罗仿真实验表明,新算法对空间相干信源的分辨性能优于常规的空间平滑算法和最大似然算法,在小阵列和信源空间间隔较近时,算法的优越性尤为突出.     

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting any approximation about the observation statistics or the a priori distribution of the parameters. The proposed solution is obtained minimizing the estimator variance subject to some constraints on the estimator bias. The resulting optimal estimator is found to depend on the observation fourth-order moments that can be calculated analytically from the known signal model. Unfortunately, in most cases, the performance of this estimator is severely limited by the residual bias inherent to nonlinear estimation problems. To overcome this limitation, the second-order minimum variance unbiased estimator is deduced from the general solution by assuming accurate prior information on the vector of parameters. This small-error approximation is adopted to design iterative estimators or trackers. It is shown that the associated variance constitutes the lower bound for the variance of any unbiased estimator based on the sample covariance matrix. The paper formulation is then applied to track the angle-of-arrival (AoA) of multiple digitally-modulated sources by means of a uniform linear array. The optimal second-order tracker is compared with the classical maximum likelihood (ML) blind methods that are shown to be quadratic in the observed data as well. Simulations have confirmed that the discrete nature of the transmitted symbols can be exploited to improve considerably the discrimination of near sources in medium-to-high SNR scenarios.     

Fast DOA estimation of incoherently distributed sources by novel propagator

A low-complexity algorithm is presented for the estimation of the nominal direction-of-arrivals (DOAs) of incoherently distributed (ID) sources. The presented algorithm estimates the nominal DOAs of ID sources by a novel propagator method which makes use of the approximate rotational invariance relationship between two closely spaced identical uniform linear arrays. Without any search and the eigendecomposition of the sample covariance matrix, our algorithm can provide lower computational complexity than other known methods. In addition, it can be applied to the multisource scenario with different angular distribution shapes. Simulation results prove the effectiveness of the presented algorithm.     

Sparse recovery method for far-field and near-field sources localization using oblique projection

In this paper, we propose a novel source localization method to estimate parameters of arbitrary field sources, which may lie in near-field region or far-field region of array aperture. The proposed method primarily constructs two special spatial-temporal covariance matrixes which can avoid the array aperture loss, and then estimates the frequencies of signals to obtain the oblique projection matrixes. By using the oblique projection technique, the covariance matrixes can be transformed into several data matrixes which only contain single source information, respectively. At last, based on the sparse signal recovery method, these data matrixes are utilized to solve the source localization problem. Compared with the existing typical source localization algorithms, the proposed method improves the estimation accuracy, and provides higher angle resolution for closely spaced sources scenario. Simulation results are given to demonstrate the performance of the proposed algorithm.     

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     

空间非平稳噪声下的宽带DOA估计算法

投影子空间正交性测试(TOPS)法是利用子空间的正交性实现宽带信号DOA估计,而在空间非平稳噪声环境下子空间的正交性条件不再满足,尤其是在低信噪比或低快拍条件下子空间估计将出现较大误差,TOPS算法性能将急剧下降。针对该问题,提出了一种空间非平稳噪声下宽带DOA估计算法。该算法首先通过构造特殊对角矩阵将噪声从数据协方差矩阵中剔除,从而克服非平稳噪声对DOA估计的影响;然后利用平方TOPS法实现宽带信号DOA估计,消除了传统TOPS算法中的伪峰。该算法适用于空间非平稳噪声背景及低信噪比环境,提高了对角度相近目标的分辨性能;仿真实验表明了该算法的有效性。     

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。     

Vector-sensor array processing for electromagnetic sourcelocalization

The authors present a new approach for localizing electromagnetic sources using sensors where the output of each is a vector consisting of the complete six electric and magnetic field components. Two types of source transmissions are considered: (1) single signal transmission (SST), and (2) dual signal transmission (DST). The model is given in terms of several parameters, including the wave direction of arrival (DOA) and state of polarization. A compact expression is derived for the Cramer-Rao bound (CRB) on the estimation errors of these parameters for the multi-source multi-vector-sensor model. Quality measures including mean-square angular error (MSAE) and covariance of vector angular error (CVAE) are introduced, and their lower bounds are derived. The advantage of using vector sensors is highlighted by explicit evaluation of the MSAE and CVAE bounds for source localization with a single vector sensor. A simple algorithm for estimating the source DOA with this sensor is presented along with its statistical performance analysis     

多源观测逆问题的多尺度分布式分层求解算法

针对多源观测逆问题求解时所需的计算量过大这问题,该文给出了多源观测逆问题的一种多尺度分布式分层求解算法。其基本思想是:首先,对各传感器上采集到的观测数据分别进行多尺度分解;其次,基于每个传感器的观测信息,得到目标信号的小波变换系数的局部最优估计值;然后,基于相对误差协方差矩阵提供的信息,在每个尺度上将目标信号的小波系数或最粗尺度系数的局部估计值进行融合;最后,做小波逆变换,得到目标信号基于全局信息的融合估计值。采用该算法求解多源观测逆问题既能得到与采用集中式求解算法相当的估计效果,又能有效地降低求解所需的计算量,进一步增强算法的可实施性。     

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。      

Fast Approximate Joint Diagonalization Incorporating Weight Matrices

We propose a new low-complexity approximate joint diagonalization (AJD) algorithm, which incorporates nontrivial block-diagonal weight matrices into a weighted least-squares (WLS) AJD criterion. Often in blind source separation (BSS), when the sources are nearly separated, the optimal weight matrix for WLS-based AJD takes a (nearly) block-diagonal form. Based on this observation, we show how the new algorithm can be utilized in an iteratively reweighted separation scheme, thereby giving rise to fast implementation of asymptotically optimal BSS algorithms in various scenarios. In particular, we consider three specific (yet common) scenarios, involving stationary or block-stationary Gaussian sources, for which the optimal weight matrices can be readily estimated from the sample covariance matrices (which are also the target-matrices for the AJD). Comparative simulation results demonstrate the advantages in both speed and accuracy, as well as compliance with the theoretically predicted asymptotic optimality of the resulting BSS algorithms based on the weighted AJD, both on large scale problems with matrices of the size 100$,times,$100.