非均匀噪声背景下混合信号DOA估计算法

针对非均匀噪声背景下非相关信源与相干信源并存时波达方向(DOA)估计问题，提出了基于迭代最小二乘和空间差分平滑的混合信号DOA估计算法。首先，该算法利用迭代最小二乘方法得到噪声协方差矩阵估计，然后对数据协方差矩阵进行“去噪”处理，利用子空间旋转不变技术实现非相关信源DOA估计；其次，基于空间差分法消除非相关信号并构造新矩阵进行前后向空间平滑，利用求根MUSIC算法估计相干信源DOA。相比于传统算法，该算法能估计更多的信源数，在低信噪比情况下DOA估计性能更优越。仿真实验结果验证了该算法的有效性。      

Computationally efficient maximum likelihood estimation ofstructured covariance matrices

By invoking the extended invariance principle (EXIP), we present herein a computationally efficient method that provides asymptotic (for large samples) maximum likelihood (AML) estimation for structured covariance matrices and is referred to as the AML algorithm. A closed-form formula for estimating the Hermitian Toeplitz covariance matrices that makes AML computationally simpler than most existing Hermitian Toeplitz matrix estimation algorithms is derived. Although the AML covariance matrix estimator can be used in a variety of applications, we focus on array processing. Our simulation study shows that AML enhances the performance of angle estimation algorithms, such as MUSIC, by making them very close to the corresponding Cramer-Rao bound (CRB) for uncorrelated signals. Numerical comparisons with several structured and unstructured covariance matrix estimators are also presented     

Performance comparison of subspace rotation and MUSIC methods fordirection estimation

The statistical performance of subspace rotation (SR) methods (such as the Toeplitz approximation method and a variant of ESPRIT) for direction estimation using arrays composed of matched sensor doublets is studied. The distributional properties of these methods are established, and a compact explicit formula for the covariance matrix of their estimation error is provided. Next, using this formula and a similar formula for MUSIC covariance matrix, it is shown that the SR methods are statistically less efficient than MUSIC, at least for a sufficiently large number of snapshots. The difference in statistical performance between the commonly used SR method and MUSIC may be substantial if the number of sensors in the array is large. An optimally weighted SR method which may approach the MUSIC level of statistical performance for one direction parameter (specified by the user) is introduced     

一种信源个数与波达方向联合估计的新算法

针对多级维纳滤波器(MSWF)用于子空间估计时信号特征矢量泄漏到噪声子空间的问题,提出了一种新的信号子空间估计算法,该算法不需要训练信号和信源个数的先验知识.随后,给出了一种信源个数的后判断方法,最终完成信源个数及方向的同时估计.整个算法不需要协方差矩阵的计算和特征值的分解,具有较低的计算复杂度.在均匀线阵且信号互不相关情况下,改进后的算法用于波达方向估计时拥有与基于特征分解方法近似的性能.仿真结果验证了该方法的有效性.     

Computationally efficient angle estimation for signals with knownwaveforms

This paper presents a large sample decoupled maximum likelihood (DEML) angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise. The DEML estimator decouples the multidimensional problem of the exact ML estimator to a set of 1-D problems and, hence, is computationally efficient. We shall derive the asymptotic statistical performance of the DEML estimator and compare the performance with its Cramer-Rao bound (CRB), i.e., the best possible performance for the class of asymptotically unbiased estimators. We will show that the DEML estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms. We will also show that for moderately correlated signals with known waveforms, the DEML estimator is no longer a large sample maximum likelihood (ML) estimator, but the DEML estimator may still be used for angle estimation, and the performance degradation relative to the CRB is small. We shall show that the DEML estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix. Finally, several numerical examples showing the performance of the DEML estimator are presented in this paper     

Subspace Smoothing for Direction of Arrival Estimation in DS-CDMA Systems

In this paper a subspace processing method is introduced that can be used for direction of arrival estimation of coherent signals in an asynchronous DS-CDMA system. Conventional methods of direction of arrival estimation are not directly applicable to the case of multiple coherent signals that impinge on an antenna array from different directions. Some preprocessing is essential prior to estimation in this case. The proposed method exploits the spreading code and the path delays of the desired user to eliminate the contribution of undesired paths in the signal subspace. To this end, the signal subspace is mapped to a new subspace which contains the spatial-temporal signature of the desired signal. Once the desired subspace is created, conventional methods such as MUSIC and ESPRIT can be employed to estimate the desired directions of arrival. It is proved that the obtained direction of arrival estimator, based on the proposed method, is consistent. Also, the estimation performance is evaluated by comparing the proposed method with conventional estimation methods.     

Computationally efficient DOA estimation for coprime linear array: a successive signal subspace fitting algorithm

ABSTRACT

In this paper, direction of arrival (DOA) estimation of multiple signals with coprime array is investigated and signal subspace fitting (SSF) method is linked to the coprime array, which achieves a better DOA estimation performance than the traditional uniform array. While the SSF method requires expensive computational cost in the case of multiple signals due to the multidimensional global angular searching, we propose a successive SSF (S-SSF) algorithm from a computationally efficient perspective. In the proposed algorithm, we employ rotational invariance and coprime property to obtain the initial estimates. Then, via a successive scheme, we transform the traditional multidimensional global angular searching problem into one-dimensional partial angular searching one. Consequently, the computational complexity has been significantly reduced. Specifically, the proposed S-SSF algorithm can obtain almost the same DOA estimation performance as SSF but with remarkably lower complexity. Finally, Cramer-Rao Bound (CRB) is provided and numerical simulations demonstrate the effectiveness of the proposed algorithm.     

A novel wideband DOA estimator based on Khatri-Rao subspace approach

A novel DOA estimation method for uncorrelated wideband sources named focusing Khatri-Rao subspace method (FKR) is proposed based on coherent signal-subspace method (CSM) and Khatri-Rao (KR) subspace. Compared with the conventional CSM that simply averages the covariance matrices of different frequency bins after focusing, FKR transforms the covariance matrices into a higher dimensional matrix through KR product. This method has three major advantages: (1) it achieves a higher resolution than CSM, (2) the root mean square error of DOA estimation from FKR is smaller than that of CSM when the initial angles are inaccurate and (3) it performs well even when the number of sensors is reduced to about half of the sources. The performance of the FKR method is demonstrated and analyzed through the computer simulations.     

混合信号情况下信源数与DOA联合估计算法

针对非相关信源与相干信源共存情况,提出了一种基于矩阵重构的信源数与波达方向（direction of arrival,DOA）联合估计算法.该算法首先利用特征值的二阶统计量（second order statistic of eigenvalues,SORTE）法和子空间旋转不变技术（estimated signal parameter via rotational invariance techniques,ESPRIT）实现非相关信源数与DOA估计;然后基于空间差分法消除非相关信号并构造新矩阵,利用构造矩阵进行前向空间平滑,实现对相干信源解相干;最后利用SORTE法检测相干信源数,结合求根多重信号分类（multiple signal classification,MUSIC）算法估计相干信源DOA.与传统的差分平滑方法相比,该算法在可估计信源数与低信噪比情况下DOA估计性能等方面优于传统算法.数值仿真实验结果验证了该算法的有效性.     

Optimal Utilization of Signal-Free Samples for Array Processing in Unknown Colored Noise Fields

Many algorithms for direction-of-arrival (DOA) estimation require the noise covariance matrix to be known or to possess a known structure. In many cases, the noise covariance is, in fact, estimated from separate measurements. This paper addresses the combined effects of finite sample sizes, both in the estimated noise covariance matrix and in the data with signals present. It is assumed that a batch of signal-free samples is available in addition to the signal-containing samples. No assumption is made on the structure of the noise covariance. In this paper, the asymptotic covariance of the weighted subspace fitting (WSF) algorithm is derived for the case in which the data are whitened using an estimated noise covariance. The expression obtained suggests an optimal weighting that improves performance compared to the standard choice. In addition, a new method based on covariance matching is proposed. Both methods are asymptotically statistically efficient. The CramÉr–Rao lower bound (CRB) on the covariance of the estimate for the data model is also derived. Monte Carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results.     

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     

阵元失效条件下的高精度DOA估计方法

为解决波达方向（Direction Of Arrival,DOA）估计方法在阵元失效条件下性能下降甚至失效的问题,本文提出一种基于Toeplitz协方差矩阵重构的DOA估计方法.首先,提出了一种失效阵元检测方法,并根据阵列的鲁棒性将失效阵元分为冗余阵元失效和非冗余阵元失效两种情况.然后,分别针对两种失效场景提出相应DOA估计方法：一是冗余阵元失效,利用阵列冗余度,结合差联合阵列对失效阵元进行填充;二是非冗余阵元失效,利用阵列冗余度进行填充后仍存在空洞,结合矩阵填充理论,用迹范数代替秩范数进行凸松弛以恢复协方差矩阵,进而实现对虚拟阵元空洞的填充,恢复阵列自由度.相对于稀疏类算法,有效消除了模型失配的影响.最后,基于子空间方法进行DOA估计.理论和仿真结果表明,相对于现有方法,本文方法有效避免了阵元失效的影响,提高了估计精度.     

一种新的互耦条件下宽带信号DOA估计算法

基于一致聚焦和Khatri-Rao子空间的思想,提出了一种新的互耦条件下宽带信号DOA 估计算法。首先,通过在阵列两端设置辅助阵元来补偿各个频率处的互耦效应;接着,对补偿后的协方差矩阵进行一致聚焦操作,并重排成一个高维矩阵;最后,通过搜索Khatri鄄Rao 子空间谱估计出宽带信号的DOA。算法适用于互耦未知的场合,对宽带信号频率谱是否平坦没有要求,且在互耦自由度较小时能够分辨多于阵元数的宽带信号。计算机仿真结果证明了算法的有效性。     

DOA Estimation in Mobile Communications System using Subspace Tracking Methods

The radio environments in mobile communications are complicated and time-varing in general; therefore, we need high resolution DoA (direction of arrival) estimation methods that can follow quickly the change of radio environments. High resolution DoA estimation methods have been proposed which are based on the eigen decomposition of the correlation (covariance) matrix of an array input. MUSIC (Multiple Signal Classification) is one of a typical of such methods. However, these methods must normally repeat high-load computation involving the eigen decomposition of a correlation matrix every time a snapshot is taken. Therefore, it takes a very long time to obtain the estimated DoA when the number of array elements is too large. In addition, it is quite inefficient in the case that the DoA estimation is carried out continuously. To solve the above problems, Bi-SVD (Bi-Iteration Singular Value Decomposition) and PAST (Projection Approximation Subspace Tracking) have been proposed and investigated, which are typical methods of successively updating (tracking) eigenvectors in the signal subspace of correlation matrix. The radio environments in mobile communications are complicated and time-varing in general; therefore, we need high resolution DoA (direction of arrival) estimation methods that can follow quickly the change of radio environments. High resolution DoA estimation methods have been proposed which are based on the eigen decomposition of the correlation (covariance) matrix of an array input. MUSIC (Multiple Signal Classification) is one of a typical of such methods. However, these methods must normally repeat high-load computation involving the eigen decomposition of a correlation matrix every time a snapshot is taken. Therefore, it takes a very long time to obtain the estimated DoA when the number of array elements is too large. In addition, it is quite inefficient in the case that the DoA estimation is carried out continuously. To solve the above problems, Bi-SV     

一种低复杂度的信号子空间拟合的新方法

提出一种低复杂度的信号子空间拟合的新方法.证明了多级维纳滤波器的匹配滤波器(或降维矩阵的列矢量)可以张成一个压缩信号子空间.利用其与Krylov子空间等效这一特点,推导出信号子空间拟合一个新的基本公式,进而建立信号子空间拟合一个新的准则函数.分析表明,压缩信号子空间可以由降维矩阵的列矢量有效地张成,而且计算降维矩阵只需要多级维纳滤波器的若干步前向递推,所以本文方法的运算量和复杂度均较小.最后,计算机仿真验证了本文方法的有效性.     

Propagator-based computationally efficient direction finding via low-dimensional equation rooting

Direction-of-arrival (DOA) estimation of multiple emitters with sensor arrays has been a hot topic in the area of signal processing during the past decades. Among the existing DOA estimation methods, the subspace-based ones have attracted a lot of research interest, mainly due to their satisfying performance in direction estimation precision and super-resolution of temporally overlapping signals. However, subspace-based DOA estimation methods usually contain procedures of covariance matrix decomposition and refined spatial searching, which are computationally much demanding and significantly deteriorate the computational efficiency of these methods. Such a drawback in heavy computational load of the subspace-based methods has further blocked the application of them in practical systems. In this paper, we follow the major process of the subspace-based methods to propose a new DOA estimation algorithm, and devote ourselves to reduce the computational load of the two procedures of covariance matrix decomposition and spatial searching, so as to improve the overall efficiency of the DOA estimation method. To achieve this goal, we first introduce the propagator method to realize fast estimation of the signal-subspace, and then establish a DOA-dependent characteristic polynomial equation (CPE) with its order equaling the number of incident signals (which is generally much smaller than that of array sensors) based on the signal-subspace estimate. The DOA estimates are finally obtained by solving the low-dimensional CPE. The computational loads of both the subspace estimation and DOA calculation procedures are thus largely reduced when compared with the corresponding procedures in traditional subspace-based DOA estimation methods, e.g., MUSIC. Theoretical analyses and numerical examples are carried out to demonstrate the predominance of the proposed method in both DOA estimation precision and computational efficiency over existing ones.     

An efficient DOA estimation method in multipath environment

An efficient direction of arrival (DOA) estimation method is proposed with uniform linear array (ULA) in multipath environment. By applying a transformation, we can convert a constructed complex matrix to a real one, and then utilize the real matrix combined with our proposed criterion to estimate the DOAs of uncorrelated signals. Afterwards, the contributions of uncorrelated signals are eliminated, and then several new matrices without the information of uncorrelated signals are constructed to resolve the remaining coherent signals. The proposed estimation method overcomes the shortcomings of the existing methods and has satisfactory performance. Simulation results confirm the theoretical analysis and show the effectiveness of the proposed method.     

On the achievable localization accuracy of multiple sources at highSNR

The Cramer-Rao bound (CRB) for the problem of localizing multiple signal sources by an arbitrary passive sensor array is analyzed for the general case where the array is not necessarily simultaneously sampled and where the signals may a priori be known to be uncorrelated. It is shown that unlike in the case where the number of samples grows, wherein the CRB for the localization error always converges to zero, in the case where the number of snapshots is kept fixed and the signal-to-noise ratio (SNR) grows, the CRB converges to zero only if the number of sensors simultaneously sampled exceeds the signal subspace dimension     

多径传播条件下宽带线性调频信号波达方向估计方法

针对信号出现多径传播情况时现有宽带信号波达方向（direction of arrival, DOA）估计方法性能下降的问题,提出了一种多径传播条件下宽带线性调频（chirp）信号波达方向估计方法,该方法将导向有效投影（steered effective projection, STEP）技术与宽带线性调频信号的时频特性相结合,对具有不同时频特性的信号分量进行分离,逐个处理,并以时频分布矩阵代替传统的协方差矩阵,从而构造有效噪声子空间,实现时域角度估计。本方法无需进行信号聚焦操作,因此理论上不受聚焦误差的影响。仿真结果验证了所提方法的有效性。      

基于均匀线阵的混合源波达方向估计方法

文中提出了一种基于均匀线阵的混合源波达方向DOA估计的改进方法。该方法首先利用传统MUSIC方法估计出非相干信号源的DOA,然后接收数据协方差矩阵进行差分消除不相关源和噪声的影响,对其进行特殊的空间平滑去相干,从而利用重建的数据协方差矩阵估计相干源的DOA。此方法的特点是分别估计不相关信号和相干信号的DOA。优点是算法在估计出多于阵元数信号的前提下具有较高的DOA估计精度和稳健性。仿真结果表明此方法的估计性能优于空间差分平滑算法。