PERFORMANCE ANALYSIS OF THE MUSIC ALGORITHM IN THE PRESENCE OF AMPLITUDE AND PHASE ERROR

This paper presents the performance analysis of the MUSIC algorithm in the presence of channel amplitude and phase Error. Theoretical expression for the error of DOA estimating with MUSIC algorithm and Cramer-Rao bound are derived. It is compared with simulations performed for some representative cases. The results of theoretical expression and simulation show that existence of these errors will increase the error of DOA estimating and degrade its performance.     

有限采样影响下秩减估计器的波达方向估计性能分析

首先从理论上分析有限采样影响下秩减估计器的波达方向估计性能,然后基于信号(或噪声)子空间的正交投影矩阵扰动定理,分别推导秩减估计器方位估计偏差的一阶和二阶闭式表达式,在此基础上给出其方位估计均方误差、偏置以及测向成功概率的理论计算公式,最后针对若干重要的秩减估计器给出数值实验,实验结果验证了所提理论推导的有效性。     

Array interpolation and DOA MSE reduction

Interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. In an earlier companion paper , a first-order condition for zero DOA bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the DOA estimate bias. This bias-minimizing theory is now extended to minimize not only bias, but also to consider finite sample effects due to noise and reduce the DOA mean-square error (MSE). An analytical first-order expression for mapped DOA MSE is derived, and a design algorithm for the transformation matrix that minimizes this MSE is proposed. Generally, DOA MSE is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the DOA estimator criterion function. The analytical MSE expression and the design algorithm are supported by simulations that show not only conspicuous MSE improvements in relevant scenarios, but also a more robust preprocessing for low signal-to-noise ratios (SNRs) as compared with the pure bias-minimizing design developed in the previous paper.     

Performance analysis of spatial smoothing with interpolated arrays

The interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival (DOAs) of signals, some of which may be perfectly correlated. It extends the spatial smoothing method to arbitrary array geometries. A statistical performance analysis of the algorithm is presented. Closed-form expressions for the covariance matrix of the DOA estimation errors are derived using a perturbation analysis. Evaluating these expressions for specific cases and comparing them to the Cramer-Rao lower bound for the DOA estimates provides insight into the statistical efficiency of this algorithm. The formulas for the error covariance are quite general and can be specialized to provide results for other DOA estimation algorithms as well     

On 2-D Direction-of-Arrival Estimation Performance for Rank Reduction Estimator in Presence of Unexpected Modeling Errors

The rank reduction estimator (RARE) is one kind of autocalibration method used in the presence of sensor errors. It demonstrates high accuracy of direction-of-arrival (DOA) estimation in the absence of multidimensional search or iteration. However, its estimation performance is affected by “unexpected modeling errors.” There is a lack of research regarding the performance of 2-D RARE estimation, although 2-D RARE estimation is extensively employed in applications. This paper presents a theoretical derivation for the closed-form expression of the mean square error (MSE) of 2-D RARE estimation under the influence of small unexpected modeling errors in the first order analysis. First, three definitions of 2-D joint direction-finding success are introduced, in order to establish the criterion for estimate performance. Then corresponding theoretical formulas for three probabilities of direction-finding success are given with the circularly Gaussian assumption of unexpected modeling errors, and their relations are discussed. Finally, the results of simulations utilizing our analysis method are demonstrated, verifying the effectiveness of the MSE expression and the formulas for probabilities of success. Therefore, our first order approximation provides a good prediction of the necessary calibration accuracy in the presence of unexpected modeling errors in order to help RARE meet an expected performance specification.     

天线方向性误差对DOA估计影响及其校正

天线阵元的方向性误差会导致基于特征值分解的DOA估计算法性能的下降,因此有必要对阵元方向性误差进行校正.首先建立了存在方向性误差情况下DOA估计的数学分析模型,提出利用空间平滑法和改进空间平滑法对方向性误差进行校正.仿真实验表明,方向性误差对DOA估计的影响主要表现在谱峰峰值的降低.空间平滑法和改进空间平滑法均可以有效地对方向性误差进行校正.     

基于DOA矩阵法的矢量传感器阵列二维波达方向估计

DOA矩阵法是一种二维波达方向估计方法,该方法具有分辩率较高、计算量较少的特点。该文将DOA矩阵法扩展至矢量传感器阵列的波达方向估计,推导出相应的计算公式,分析了算法计算复杂度。算法分析表明,相对于ESPRIT算法,DOA矩阵法计算复杂度大大降低。Monte Carlo仿真结果表明,与ESPRIT算法相比,DOA矩阵法估计的均方根偏差和均方根标准方差相对大一些,所需的最低快拍数也增加。     

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     

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     

阵列误差对四阶MUSIC算法到达角估计的影响

子空间算法用于窄带信号到达角估计时，通常认为阵列响应是已知的。然而，在实际中，阵列响应往往偏离正常值，成为角度估计误差的重要来源之一。文中讨论阵列误差对四阶MUSIC算法估计到达角的影响，并与传统二阶MUSIC算法进行比较。结果表明：相同阵列误差时，四阶MUSIC算法的角度估计误差小于二阶MUSIC算法。     

共形阵列天线信源方位与极化状态的联合估计算法

 针对共形天线阵列流形的特点,提出了共形阵列天线信源方位与极化状态的联合估计算法.算法的方位估计不需要信源极化状态的任何信息,估计精度高、分辨力强,在完成信源方位估计的同时,还可以精确的估计出信源的极化状态,不需要参数配对,实现了共形阵列天线信源方位与极化状态的联合估计.算法仅需要二维参数搜索,计算量比已有的联合估计算法小,且适用于任意共形载体,具有广泛的应用范围.对算法参数估计的理论性能进行了分析推导,给出了参数估计的CRB(Cramer-Rao Bound),并通过Monte-Carlo仿真实验验证了理论分析的正确性与算法的有效性.     

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     

Robustness of the coherently distributed MUSIC algorithm to the imperfect knowledge of the spatial distribution of the sources

The MUltiple SIgnal Classification (MUSIC) estimator has been widely studied for a long time for its high resolution capabilities in the domain of the directional of arrival (DOA) estimation, with the sources assumed to be point. However, when the actual sources are spatially distributed with angular dispersion, the performance of the conventional MUSIC is degraded. This paper deals with the sensitivity of MUSIC to modeling error due to coherently distributed (CD) sources. A performance analysis of an extended MUSIC taking into account a generalized steering vector based on a CD source model (CD-MUSIC) is first studied. We establish closed-form expressions of the DOA estimation bias and mean square error due to both the model error and the effects of a finite number of snapshots. The aim of this paper is also to determine when the point source assumption is acceptable for standard MUSIC. The analytical results are validated by numerical simulations and discussed in different configurations.     

基于子空间的幅相误差自校正算法

针对实际应用中普遍存在的阵列幅相误差扰动问题,结合子空间类波达方向估计算法,提出了一种幅相误差的自校正算法。先利用均匀线阵协方差矩阵的结构特点对幅相误差进行初步校正,再通过迭代方法得到更精确的估计值,自校正方法无需任何参数初始值,实现比较简单。仿真实验验证了算法具有良好的误差校正效果,能够比较准确的估计出方位角和幅相误差值。     

双基地分布式阵列MIMO雷达的DOA和DOD估计方法

结合分布式阵列和双基地多输入多输出(Multiple-Input Multiple-Output, MIMO)雷达的特点, 提出了一种新的双基地分布式阵列MIMO雷达的接收角(Direction of Arrival, DOA)和发射角(Direction of Departure, DOD)估计方法.根据发射阵列和接收阵列的空域旋转不变特性, 利用旋转不变估计技术(Estimation of Signal Parameters via Rotational Invariance Techniques, ESPRIT)获取无模糊DOA粗估计和高精度周期性模糊的DOA、DOD精估计; 再利用无模糊DOA粗估计、目标的双基地距离信息以及双基地MIMO雷达的几何特点, 解除DOA、DOD精估计的周期性模糊, 得到高精度且无模糊的DOA和DOD估计.最后, 根据ESPRIT算法原理和估计误差的概率统计特性进行算法的性能分析, 给出算法基线模糊门限的近似计算方法.该算法有效地放宽了发射阵列孔径扩展程度的限制, 从而提高了阵列在大孔径下的角度估计精度, 且能够实现DOA和DOD估计的自动配对.仿真结果验证了所提算法和性能分析方法的有效性.     

基于改进互耦系数估计算法的自适应波束形成

阵列信号在实际应用中,常常会面临噪声的干扰,低信噪比(signal noise ratio, SNR)时波束形成器性能会急剧下降.针对该问题,提出一种基于改进互耦系数估计的抗互耦算法的自适应波束形成,即研究信号在不同输入SNR以及不同干扰波达方向(direction of arrival,DOA)估计误差下的互耦系数估计误差;并通过误差分析修正原算法不同SNR下参与估计信号的数目.改进算法改进了导向矢量和期望信号,提高了低SNR下互耦系数估计的准确度,对比分析验证了其在低SNR情况下有更强的抗干扰能力,对互耦现象有着更好的稳健性.     

Joint estimation of TOA and DOA in IR-UWB system using a successive propagator method

Impulse radio ultra-wideband (IR-UWB) ranging and positioning require accurate estimation of time-of-arrival (TOA) and direction-of-arrival (DOA). With receiver of two antennas, both of the TOA and DOA parameters can be estimated via two-dimensional (2D) propagator method (PM), in which the 2D spectral peak searching, however, renders much higher computational complexity. This paper proposes a successive PM algorithm for joint TOA and DOA estimation in IR-UWB system to avoid 2D spectral peak searching. The proposed algorithm firstly gets the initial TOA estimates in the two antennas from the propagation matrix, then utilises successively one-dimensional (1D) local searches to achieve the estimation of TOAs in the two antennas, and finally obtains the DOA estimates via the difference in the TOAs between the two antennas. The proposed algorithm, which only requires 1D local searches, can avoid the high computational cost in 2D-PM algorithm. Furthermore, the proposed algorithm can obtain automatically paired parameters and has better joint TOA and DOA estimation performance than conventional PM algorithm, estimation of signal parameters via rotational invariance techniques algorithm and matrix pencil algorithm. Meanwhile, it has very close parameter estimation to that of 2D-PM algorithm. We have also derived the mean square error of TOA and DOA estimation of the proposed algorithm and the Cramer-Rao bound of TOA and DOA estimation in this paper. The simulation results verify the usefulness of the proposed algorithm.     

STC-OFDM系统中基于扩展贝叶斯滤波的鲁棒共信道干扰抑制算法研究

空时编码正交频分复用(STC-OFDM)系统易受共信道干扰(CCI)影响,利用波束成形可以抑制共信道干扰的影响。然而,目前存在的一些方法都是基于期望信号波达方向(DOA)的精确估计的。实际上,当期望信号的波达方向存在误差时,这些波束成形器的性能将明显下降。为此,该文提出了基于扩展贝叶斯滤波的鲁棒波束成形算法来提高当期望信号的波达方向存在误差时的系统性能。在这一算法中,每一个期望信号的波达方向被看成一个由若干离散样点组成的随机变量。利用贝叶斯公式对这些样点的后验概率进行估计,当有样点的后验概率低于一定的门限值时,对这些样点进行重采样,使有效样点的数目保持恒定。最后,波束成形器的最优权值由这些样点的后验概率加权获取。仿真结果表明,该文算法对抑制多径信道中STC-OFDM系统的共信道干扰具有很强的鲁棒性。     

一种解析的基于旋转矩阵估计的波达方向估计方法

本文提出了一种解析的基于旋转矩阵估计的高分辨波达方向估计算法.为了充分利用空时信息以提高算法的估计性能,利用传感器阵列接收数据相关矩阵构建既包含旋转矩阵信息又具有可对角化结构的目标矩阵组.通过一系列矩阵变换,将复数域普通目标矩阵组转化为实数域对称目标矩阵组,以利用ACDC算法实现目标矩阵组的联合对角化并求得对角矩阵,继而求取旋转矩阵并挖掘波达角度信息,实现了波达方向估计.仿真结果表明,与其他现存的经典算法相比,所提算法具有更强的分辨能力及更准确的估计性能.     

通道失配条件下的MUSIC算法性能分析

本文分析了通道失配对高分辨率谱估计算法(MUSIC)的影响.推导了通道失配与方向估计误差的关系表达式,给出了Cramer-Rao界和计算机模拟结果。理论和仿真结果表明:通道失配会增大方向估计误差,使其性能变坏。