Space-time fading channel estimation and symbol detection inunknown spatially correlated noise

We present maximum likelihood (ML) methods for space-time fading channel estimation with an antenna array in spatially correlated noise having unknown covariance; the results are applied to symbol detection. The received signal is modeled as a linear combination of multipath-delayed and Doppler-shifted copies of the transmitted waveform. We consider structured and unstructured array response models and derive the Cramer-Rao bound (CRB) for the unknown directions of arrival, time delays, and Doppler shifts. We also develop methods for spatial and temporal interference suppression. Finally, we propose coherent matched-filter and concentrated-likelihood receivers that account for the spatial noise covariance and analyze their performance     

Two-dimensional noisy autoregressive estimation with application to joint frequency and direction of arrival estimation

The present study addresses the problem of two-dimensional autoregressive estimation in the presence of additive white noise. The estimation method is based on combining the low-order and high-order Yule-Walker equations. The noise-compensated YW equations are solved using an iterative algorithm. The proposed method is also applied to joint frequency and direction of arrival estimation in uniform linear arrays. Using simulation study, the performance of the proposed algorithm is evaluated and compared with other methods.     

Two-dimensional direction of arrival estimation in the presence of uncorrelated and coherent signals

In this paper, a novel two-dimensional direction of arrival (2-D DOA) estimation method is proposed based on a new array configuration when uncorrelated and coherent signals coexist. The DOAs of uncorrelated signals are estimated using the non-zero eigenvalues and corresponding eigenvectors of the DOA matrix (DOAM) combined with our proposed criterion. Meanwhile, we can form a new matrix without the information of uncorrelated signals. Then the coherent signals are resolved with the redefined DOAM that is constructed by the smoothed matrices of the new matrix. Simulation results demonstrate the effectiveness and efficiency of the proposed method. Other arrays that contain multiple identical central-symmetric subarrays (e.g. uniform rectangular arrays) can also be applied with our method.     

Adaptive beamspace focusing for direction of arrival estimation of wideband signals

In this paper, we present an adaptive beamspace focusing technique for the direction of arrival (DOA) estimation of wideband signals. The proposed focusing scheme can perform coherent signal subspace transformation in the beamspace domain without preliminary DOA estimation or iteration. It can maintain low focusing error over a predefined sector-of-interest in the field-of-view (FOV) of the array while adaptively suppressing out-of-sector sources. The beamspace gain outside the sector-of-interest is controlled via additional constraints that provide robustness against moving or suddenly appearing out-of-sector sources. We formulate the adaptive beamspace design problem as a second-order cone program (SOCP) that can be solved efficiently using interior point methods. Numerical simulations are presented showing the superior performance of our approach compared to classical non-adaptive beamspace focusing techniques.     

A subspace method for direction of arrival estimation ofuncorrelated emitter signals

A novel eigenstructure-based method for direction estimation is presented. The method assumes that the emitter signals are uncorrelated. Ideas from subspace and covariance matching methods are combined to yield a noniterative estimation algorithm when a uniform linear array is employed. The large sample performance of the estimator is analyzed. It is shown that the asymptotic variance of the direction estimates coincides with the relevant Cramer-Rao lower bound (CRB). A compact expression for the CRB is derived for the ease when it is known that the signals are uncorrelated, and it is lower than the CRB that is usually used in the array processing literature (assuming no particular structure for the signal covariance matrix). The difference between the two CRBs can be large in difficult scenarios. This implies that in such scenarios, the proposed methods has significantly better performance than existing subspace methods such as, for example, WSF, MUSIC, and ESPRIT. Numerical examples are provided to illustrate the obtained results     

HOS-based direction of arrival estimation

A new technique for estimating the direction of arrival of multiple non-Gaussian signals using higher order statistics is reported. A set of new algorithms based on a new class of performance criteria related to the bispectral power of the array data is presented. Computer simulations show that the proposed algorithms outperform conventional array processing techniques     

波达方向估计中的宽带信号个数检测新方法

在进行波达方向估计时,往往要对信号个数进行判断,传统的宽带信号个数检测方法需要在每个频点上进行多次采样,否则无法正确完成测向.针对此问题,提出了一种基于Bootstrap准则实现的宽带信号个数检测新方法.将宽带信号划分为若干个互不重叠的子带部分,之后对每个子带信号进行特征分解,利用特征值对相应的特征向量进行加权,再通过Bootstrap准则构造新的信号重采样矩阵,用聚类的方法判断出该子带上的信号个数,最后将各个子带上的结果进行综合判断出宽带信号个数.所提方法回避了聚焦的过程,且在非高斯噪声背景下也有较高的估计成功概率,尤其是在小快拍数下有着较好的估计性能,仿真结果证明了该方法的性能.     

Spectrum blind reconstruction and direction of arrival estimation of multi-band signals at sub-Nyquist sampling rates

In this paper we consider the problem of spectrum blind reconstruction (SBR) and direction of arrival (DOA) estimation of constituent sources of a disjoint multi-band signal (MBS) at sub-Nyquist sampling rates. Transformation of the problem into frequency domain indicates that the steering vector is a function of both the carrier frequency and its corresponding DOA. Employing the existing two dimensional frequency-DOA search algorithms suffers from the drawbacks of increased computational complexity and ambiguity issues. To overcome these drawbacks, in this paper we propose a simple modification to the receiver architecture by introducing an additional delay channel at every sensor. Estimation algorithms based on ESPRIT is then employed to estimate the carrier frequencies, while MUSIC algorithm is employed to estimate their corresponding DOAs. Using the knowledge of both these parameters, the MBS spectrum is then reconstructed. A two-dimensional iterative grid refinement algorithm is also described to further improve the estimation accuracy in the presence of noise. Identifiability issues are addressed and the conditions for unique identifiability are discussed. Furthermore, by assuming a two dimensional uniform array the advantages of the proposed approach in terms of identifiability is also provided. We further show that an \(M \ge N+1\) sensors and an overall sampling rate of at least \(2(N+1)B\) would be sufficient to achieve SBR and DOA estimation of an MBS comprising of N disjoint bands each of maximal bandwidth B. Numerical simulations are finally presented which verifies the validity of the proposed approach and compares the performance against appropriate bounds.     

基于虚拟旋转不变技术的宽带信号二维到达角估计

在相关信号子空间方法的基础上,本文提出了一种阵列宽带信号二维角度的估计方法。该方法首先利用虚拟互相关计算方法得到阵列输出的协方差矩阵,并构造出两个子阵(实际子阵和虚拟子阵);然后采用投影算子来形成聚焦矩阵,最后对聚焦后的协方差矩阵采用ESPRIT方法估计出宽带信号的二维到达角。这种方法能抑制非高斯噪声对算法的影响,并能扩展阵列孔径,且不需要进行角度预估计;估计出的二维角度能自动配对,提高了算法的实现速度。计算机仿真试验证实了该算法的有效性。     

一种分布式目标波达方向估计方法

本文提出一种在多径情况下,利用广义阵列流形的特点,通过求解矩阵的广义特征值分解,不用进行谱峰搜索或多维参数搜索,直接由广义特征值得到分布式目标波达方向（DOA）估计的方法。该方法的估计性能对信号源的分布特性优于MUSIC方法。     

Multiple wavelet threshold estimation by generalized crossvalidation for images with correlated noise

Denoising algorithms based on wavelet thresholding replace small wavelet coefficients by zero and keep or shrink the coefficients with absolute value above the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. To estimate this optimal threshold, we use generalized cross validation. This procedure does not require an estimation for the noise energy. Originally, this method assumes uncorrelated noise. In this paper, we describe how we can extend it to images with correlated noise.     

Gaussian Cramer-Rao bound for direction estimation of noncircular signals in unknown noise fields

This paper focuses on the stochastic Cramer-Rao bound (CRB) on direction of arrival (DOA) estimation accuracy for noncircular Gaussian sources in the general case of an arbitrary unknown Gaussian noise field parameterized by a vector of unknowns. Explicit closed-form expressions of the stochastic CRB for DOA parameters alone are obtained directly from the Slepian-Bangs formula for general noncircular complex Gaussian distributions. As a special case, the CRB under the nonuniform white noise assumption is derived. Our expressions can be viewed as extensions of the well-known results by Stoica and Nehorai, Ottersten et al., Weiss and Friedlander, Pesavento and Gershman, and Gershman et al. Some properties of these CRBs are proved and finally, these bounds are numerically compared with the conventional CRBs under the circular complex Gaussian distribution for different unknown noise field models.     

High-precision estimation of the time of arrival of radio signals

An interpolation algorithm of high-precision estimation of the time of arrival of radio signals has been proposed. Analytical expressions were obtained for specifications of the algorithm that were corroborated by the results of computer simulation. It was shown that with due regard for the complexity adequate to a receiver of the maximum likelihood estimation of the temporal position with quantized output, the proposed interpolation algorithm ensures the noise immunity close to potentially attainable. The performed analysis makes it possible to select parameters of the estimation algorithm in a reasonable way depending on the requirements to its accuracy and complexity of realization.     

Time delays and angles of arrival estimation using known signals

Channel estimation in a multipath mobile communication system is addressed in this paper, and a novel approach based on the linear prediction in frequency domain and the singular value decomposition technique is presented for joint estimation of the angles of arrival and the time delays of multiple reflections of a known signal. Simulation results illustrating the performance of the proposed algorithm are included, and the results show that the proposed method is close in accuracy when compared to the iterative maximum-likelihood method. However, when the two methods are compared in computational complexity, it is demonstrated that the proposed method reduces the complexity to nearly half of that of the maximum-likelihood method. The Cramer–Rao bounds are computed for comparison.     

Application of natural computing algorithms to maximum likelihood estimation of direction of arrival

This work presents a study of the performance of populational meta-heuristics belonging to the field of natural computing when applied to the problem of direction of arrival (DOA) estimation, as well as an overview of the literature about the use of such techniques in this problem. These heuristics offer a promising alternative to the conventional approaches in DOA estimation, as they search for the global optima of the maximum likelihood (ML) function in a framework characterized by an elegant balance between global exploration and local improvement, which are interesting features in the context of multimodal optimization, to which the ML-DOA estimation problem belongs. Thus, we shall analyze whether these algorithms are capable of implementing the ML estimator, i.e., finding the global optima of the ML function. In this work, we selected three representative natural computing algorithms to perform DOA estimation: differential evolution, clonal selection algorithm, and the particle swarm. Simulation results involving different scenarios confirm that these methods can reach the performance of the ML estimator, regardless of the number of sources and/or their nature. Moreover, the number of points evaluated by such methods is quite inferior to that associated with a grid search, which gives support to their application.     

基于多用户去相关的波达方向估计新方法

以直接序列码分多址(DS/CDMA)系统中的天线阵为背景,讨论了一种在多径慢衰落信道环境下的波达方向(DOA)估计新方法.该方法在基站对各用户各路径同步信息的基础上,根据扩频序列表现出的周期性和非完全正交的性质,利用用户多径与多址干扰表现出的信息,相关处理后再去相关,实现对各用户各路径的DOA及幅值估计.它不是简单地忽略掉解扩后残留的多径与多址干扰,或仅将其当作噪声处理,而是通过去相关的方法消除它们的影响.理论推导与仿真实验表明,该方法提高了DOA的估计性能,很好地实现了多径信道的空间分离,为后面进一步的空时处理提供了可能.     

Efficient 2D DOA estimation of coherent signals in spatially correlated noise using electromagnetic vector sensors

This paper considers a new azimuth-elevation DOA estimation algorithm for multiple signals using electromagnetic vector sensor array. We firstly exploit the planar-plus-an-isolated sensor array geometry (Li et al. in IEE Proc Radar Sonar Navig 143(5):295–299, 1996) to define a full rank cross-covariance matrix. Then we develop an efficient ESPRIT-like algorithm using the so-called propagator to estimate the steering vectors of electromagnetic vector sensor, without performing eigen-decomposition into signal subspaces. Finally, we compute the vector cross product to obtain the closed-form azimuth-elevation angle estimates. The new algorithm does not require 2D iterative searching, and is applicable to coherent (fully correlated) signals and spatially correlated noise. In addition, the proposed algorithm offers enhanced estimation precision by sparse array aperture extension, but suffers no DOA cyclical ambiguity. Monte-Carlo simulations are presented to verify the effectiveness of the proposed algorithm.     

Direction of arrival estimation for more correlated sources than active sensors

In this paper, a new direction of arrival (DOA) estimation method for more correlated sources than active receiving antennas is proposed. The trick to solve this problem using only second-order statistics is to consider a periodic scanning of an underlying uniform array, where a single scanning period contains several time slots and in different time slots different sets of antennas are activated leading to a dynamic non-uniform array with possibly less active antennas than sources in each time slot. We collect the spatial correlation matrices of the active antenna arrays for all time slots and are able to present them as a linear function of the spatial correlation matrix of the underlying array. We provide a necessary and sufficient condition for this system of equations to be full column-rank, which allows for a least squares (LS) reconstruction of the spatial correlation matrix of the underlying array. Some practical greedy algorithms are presented to design dynamic arrays satisfying this condition. In a second step, we use the resulting spatial correlation matrix of the underlying array to estimate the DOAs of the possibly correlated sources by spatial smoothing and MUSIC. Alternatively, we can express this matrix as a linear function of the correlation matrix of the sources (incoming signals) at a grid of investigated angles, and solve this system of equations using either LS or sparsity-regularized LS (possibly assisted by additional constraints), depending on the grid resolution compared to the number of antennas of the underlying array.     

RKHS approach to detection and estimation problems--I: Deterministic signals in Gaussian noise

First it is shown how the Karhunen-Loève approach to the detection of a deterministic signal can be given a coordinate-free and geometric interpretation in a particular Hilbert space of functions that is uniquely determined by the covariance function of the additive Gaussian noise. This Hilbert space, which is called a reproducing-kernel Hilbert space (RKHS), has many special properties that appear to make it a natural space of functions to associate with a second-order random process. A mapping between the RKHS and the linear Hilbert space of random variables generated by the random process is studied in some detail. This mapping enables one to give a geometric treatment of the detection problem. The relations to the usual integral-equation approach to this problem are also discussed. Some of the special properties of the RKHS are developed and then used to study the singularity and stability of the detection problem and also to suggest simple means of approximating the detectability of the signal. The RKHS for several multidimensional and multivariable processes is presented; by going to the RKHS of functionals rather than functions it is also shown how generalized random processes, including white noise and stationary processes whose spectra grow at infinity, are treated.     

相干信源波达方向估计的加权空间平滑算法

提出了一种用于空间相干源DOA估计的加权空间平滑算法(WSS，weighted spatial smoothing)。常规的空间平滑算法没有利用子阵输出的互相关信息，而且对相干信源的分辨力较差。WSS算法充分利用了子阵输出的自相关信息和互相关信息，将主阵协方差矩阵的所有子阵阵元数阶的子矩阵进行加权平均，以期提高常规空间平滑算法的分辨性能。文中以加权平滑后等效的信源协方差矩阵的对角化为约束条件，推导了加权矩阵的理论表达式。计算机仿真结果表明，WSS算法与常规空间平滑算法相比具有更高的分辨性能和更低的信噪比门限。特别是在于阵划分较多时其优越性更加明显。