DOA estimation of mixed coherent and uncorrelated targets exploiting coprime MIMO radar

We propose a new scheme to estimate the directions-of-arrival (DOAs) of mixed coherent and uncorrelated targets exploiting a collocated multiple-input multiple-output (MIMO) radar with transmit/receive coprime arrays. In the proposed scheme, the DOAs of the uncorrelated targets are first estimated using subspace-based methods, whereas those of the coherent targets are resolved using Bayesian compressive sensing. Compared with the previous works, the proposed approach achieves improved DOA estimation accuracy with a flexible coprime array configuration and may resolve more targets than the number of coarray elements. Theoretical analysis and simulation results validate the effectiveness of the proposed technique.     

DOA estimation based on the difference and sum coarray for coprime arrays

In this paper, we construct a novel coarray named as the difference and sum (diff–sum) coarray by exploiting an improved Conjugate Augmented MUSIC (CAM) estimator, which utilizes both the temporal information and the spatial information. The diff–sum coarray is the union of the difference coarray and the sum coarray. When taking the coprime array as the array model, we find that the elements of the sum coarray can fill up all the holes in the difference coarray. Besides, the sum coarray contains bonus uniform linear array (ULA) segments which extend the consecutive range of the difference coarray. As a result, the consecutive lags of the diff–sum coarray are much more than those of the difference coarray. For analysis, we derive the hole locations and consecutive ranges of the difference set and the sum set, discuss the complementarity of the two sets, and provide the analytical expression of the diff–sum virtual aperture. Simulations verify the effectivity of the improved method and show the high DOF of the diff–sum coarray.     

A modular neural network for direction-of-arrival estimation of two sources

This work addresses the problem of estimating the direction-of-arrival (DOA) of two sources using an array of sensors. This problem is mostly useful in radar applications, where we have few targets at each range bin. Super-resolution algorithms, such as maximum likelihood (ML) estimation and multiple signal classification (MUSIC), have been applied to this problem, but the former involves high computation efforts, while the later has poor estimation performance for coherent sources. In this work, we propose a DOA estimation network, named RBF-AML, which combines the approximated ML (AML) estimator and a radial basis function (RBF) neural network (NN). In the proposed RBF-AML network, the entire two dimensional DOA space is divided into multiple sectors covered by RBF experts. The AML function is then used as a mediator among the experts and selects the most suitable one as the final output of the system. The performance of the RBF-AML network for a two coherent sources case in a Y shape array configuration is evaluated. We show that the performance of the RBF-AML network is similar to the performance of the classical AML DOA estimation for various signal-to-noise ratios (SNRs), phase of the correlation coefficient and signal-to-interference ratios (SIRs). Furthermore, the RBF-AML network requires fewer computational efforts than the classical AML DOA estimation and therefore is an attractive choice for real-time applications.     

基于互质阵的循环平稳信号低复杂度欠定DOA估计算法

针对现有大多数循环平稳信号DOA估计算法复杂度较高、估计精度低无法实现对有用信号的欠定估计问题,提出了一种基于互质阵的循环平稳信号低复杂度、欠定DOA估计算法.算法的主要思想是利用互质阵良好的稀疏特性,通过矢量化处理构造虚拟阵列模型,扩展阵列孔径,实现阵列自由度的提升.首先,算法构造了互质阵输出的循环自相关矩阵,然后进行矢量化处理得到最大连续虚拟阵元部分,给出其谱峰搜索的表达式.最后,为降低计算复杂度,对算法进行改进,应用多项式求根的方法直接求解DOA估计值.仿真结果表明,所提算法能实现对有用信号的欠定估计,计算复杂度较低,且相比于大多数的循环平稳信号DOA估计算法,所提算法估计自由度和估计精度有了进一步的提升.     

Two-step reliability test based unitary root-MUSIC for direction-of-arrival estimation

A two-step reliability test (TSRT) based unitary root-MUSIC algorithm for direction-of-arrival (DOA) estimation is proposed in this paper. We combine the conventional beamforming and unitary root-MUSIC to compute the DOA estimates and employ the pseudo-noise resampling (PR) technique to construct a DOA estimator bank. Unlike the standard reliability test, we devise the TSRT which retains the successful DOA estimates of a given DOA estimator separately to construct a DOA estimate set that is used to determine the final DOA estimates. Compared to the existing PR based DOA estimation methods, our solution can achieve better threshold performance by using fewer PR runs. Furthermore, the TSRT can be easily applied to other DOA estimation methods. Simulations verify the effectiveness of the proposed scheme.     

Joint direction of arrival estimation and array calibration for coprime MIMO radar

Compared to large-scale MIMO radar, coprime MIMO radar can achieve approximate estimation performance with reduced antenna number. In this paper, joint direction of arrival (DOA) estimation and array calibration for coprime multiple-input multiple-output (MIMO) radar is considered, and an iterative method for the estimations of DOA and array gain-phase errors is proposed. Based on the received data structure of coprime MIMO radar, trilinear decomposition is firstly adopted to obtain the estimations of transmit and receive direction matrices, which are perturbated by the gain-phase errors. Through equation transformation, the un-perturbated direction matrices and gain-phase errors can be iteratively updated based on Least squares (LS). Finally, the unique DOA estimation is determined from the intersection of transmit and receive direction matrices. The proposed algorithm achieves better DOA estimation and array calibration performance than other methods including estimation of signal parameters via rotational invariance techniques (ESPRIT)-like algorithm, multiple signal classification (MUSIC)-like algorithm and joint angle and array gain-phase error estimation (JAAGE) method, and it performs close to the method with ideal arrays. Multiple simulation results verify the algorithmic effectiveness of the proposed method.     

Efficient source enumeration for accurate direction-of-arrival estimation in threshold region

Estimation of the number of signals impinging on an array of sensors, also known as source enumeration, is usually required prior to direction-of-arrival (DOA) estimation. In challenging scenarios such as the presence of closely-spaced sources and/or high level of noise, using the true source number for nonlinear parameter estimation leads to the threshold effect which is characterized by an abnormally large mean square error (MSE). In cases that sources have distinct powers and/or are closely spaced, the error distribution among parameter estimates of different sources is unbalanced. In other words, some estimates have small errors while others may be quite inaccurate with large errors. In practice, we will be only interested in the former and have no concern on the latter. To formulate this idea, the concept of effective source number (ESN) is proposed in the context of joint source enumeration and DOA estimation. The ESN refers to the actual number of sources that are visible at a given noise level by a parameter estimator. Given the numbers of sensors and snapshots, number of sources, source parameters and noise level, a Monte Carlo method is designed to determine the ESN, which is the maximum number of available accurate estimates. The ESN has a theoretical value in that it is useful for judging what makes a good source enumerator in the threshold region and can be employed as a performance benchmark of various source enumerators. Since the number of sources is often unknown, its estimate by a source enumerator is used for DOA estimation. In an effort to automatically remove inaccurate estimates while keeping as many accurate estimates as possible, we define the matched source number (MSN) as the one which in conjunction with a parameter estimator results in the smallest MSE of the parameter estimates. We also heuristically devise a detection scheme that attains the MSN for ESPRIT based on the combination of state-of-the-art source enumerators.     

Spatial smoothing based methods for direction-of-arrival estimation of coherent signals in nonuniform noise

Spatial smoothing techniques have been widely used to estimate the directions-of-arrival (DOAs) of coherent signals. However, in general these techniques are derived under the condition of uniform white noise and, therefore, their performance may be significantly deteriorated when nonuniform noise occurs. This motivates us to develop new methods for DOA estimation of coherent signals in nonuniform noise in this paper. In our methods, the noise covariance matrix is first directly or iteratively calculated from the array covariance matrix. Then, the noise component in the array covariance matrix is eliminated to achieve a noise-free array covariance matrix. By mitigating the effect of noise nonuniformity, conventional spatial smoothing techniques developed for uniform white noise can thus be employed to reconstruct a full-rank signal covariance matrix, which enables us to apply the subspace-based DOA estimation methods effectively. Simulation results demonstrate the effectiveness of the proposed methods.     

基于频差修正的余弦信号频率估计算法

针对余弦振动信号的频率高精度估计需求,提出了一种基于频差修正的频率估计算法.对连续时间信号进行采样后,使用Candan算法估计出频差,运用频差对信号的频率进行修正.对修正后的信号使用Liang算法再次进行频偏估计.最后将2次估计得到的频率值相加求得最终估计频率.通过频差修正,避免了Candan算法因插值方向错误和Liang算法自身特点导致估计精度降低的问题,虽然增加了计算量,但并不影响信号实时处理.仿真结果表明:在相对频偏为任意值的情况下,改进算法的频率估计均方误差接近克拉美罗下限(CRLB),性能优于现有频率估计算法.     

A sparse direction-of-arrival estimation algorithm for MIMO radar in the presence of gain-phase errors

In this paper, the problem of direction-of-arrival (DOA) estimation for monostatic multiple-input multiple-output (MIMO) radar with gain-phase errors is addressed, by using a sparse DOA estimation algorithm with fourth-order cumulants (FOC) based error matrix estimation. Useful cumulants are designed and extracted to estimate the gain and the phase errors in the transmit array and the receive array, thus a reliable error matrix is obtained. Then the proposed algorithm reduces the gain-phase error matrix to a low dimensional one. Finally, with the updated gain-phase error matrix, the FOC-based reweighted sparse representation framework is introduced to achieve accurate DOA estimation. Thanks to the fourth-order cumulants based gain-phase error matrix estimation, and the reweighted sparse representation framework, the proposed algorithm performs well for both white and colored Gaussian noises, and provides higher angular resolution and better angle estimation performance than reduced-dimension MUSIC (RD-MUSIC), adaptive sparse representation (adaptive-SR) and ESPRIT-based algorithms. Simulation results verify the effectiveness and advantages of the proposed method.     

基于算术傅里叶变换的离散Hartley变换的快速算法

离散Hartley变换是一种有用的实值正交变换。文中对其快速算法进行研究,首先介绍利用算术傅里叶变换（AFT）计算离散傅里叶变换（DFT）可使其乘法计算量仅为O（N）,然后文章根据这一特点,分析离散Hartley变换（DHT）的结构特征,通过DFT将AFT和DHT建立了直接联系,提出了一种新的快速DHT算法。算法的计算复杂度能够达到线性O（N）,且算法结构简单,公式统一且易于实现,并与其他快速算法进行了比较,分析可知在数据长度不是2的幂次方时,文中提出的算法的计算时间明显比其他算法的计算时间要小。实验结果也验证了文中算法的有效性,从而为DHT的快速计算开辟了新的思路和途径。     

A variational Bayesian strategy for solving the DOA estimation problem in sparse array

This paper reformulates the problem of direction-of-arrival (DOA) estimation for sparse array from a variational Bayesian perspective. In this context, we propose a hierarchical prior for the signal coefficients that amounts marginally to a sparsity-inducing penalty in maximum a posterior (MAP) estimation. Further, the specific hierarchy gives rise to a variational inference technique which operates in latent variable space iteratively. Our hierarchical formulation of the prior allow users to model the sparsity of the unknown signal with a high degree, and the corresponding Bayesian algorithm leads to sparse estimators reflecting posterior information beyond the mode. We provide experimental results with synthetic signals and compare with state-of-the-art DOA estimation algorithm, in order to demonstrate the superior performance of the proposed approach.     

An iterative approach for sparse direction-of-arrival estimation in co-prime arrays with off-grid targets

This paper addresses the problem of direction of arrival (DOA) estimation by exploiting the sparsity enforced recovery technique for co-prime arrays, which can increase the degrees of freedom. To apply the sparsity based technique, the discretization of the potential DOA range is required and every target must fall on the predefined grid. Off-grid target can highly deteriorate the recovery performance. To the end, this paper takes the off-grid DOAs into account and reformulates the sparse recovery problem with unknown grid offset vector. By introducing a convex function majorizing the given objective function, an iterative approach is developed to gradually amend the offset vector to achieve final DOA estimation. Numerical simulations are provided to verify the effectiveness of the proposed method in terms of detection ability, resolution ability and root mean squared estimation error, as compared to the other state-of-the-art methods.     

基于FFT的多个空间信号波达方向的估计算法

本文提出了一种与传统算法完全不同的多个空间窄带信号波达方向的估计算法。该算法通过对阵列输出数据的快速傅立叶变换(FFT),建立了FFT频谱与波达方向角的关系;利用这一关系并通过对FFT谱峰的搜索,从而实现了对波达方向的快速估计。计算机模拟实验验证了算法的可行性。     

An eigenstructure-based 2D DOA estimation method using dual-size spatial invariance array

A sparse planar array vertically placed in y-z plane is proposed to improve the angle estimation accuracy of sources in low angle region with reflection multipath.With two sizes of spatial invariances along both dimensions,the array estimates the azimuth and elevation angles using unitary ESPRIT(estimation of signal parameters via rotational invariance techniques).The first spatial invariance with a displacement of half-wavelength yields unambiguous coarse estimates of high-variance,while the second spatial...     

基于迭代的多频频率估计方法

调频连续波（Frequency modulated continuous wave,FMCW）雷达中的频率测量精度直接决定了测距的精度,但实际应用中频率估计受到负频谱和多目标带来的多频信号的干扰,误差较大。本文基于常用的单频频率估计方法Orguner算法提出了一种新的多频频率估计方法,并利用迭代逐步消除负频谱和其他频率带来的干扰。该方法只需要对信号进行离散傅里叶变换（Discrete Fourier transform,DFT）,进而取各频率点附近的3个采样值实现精确的频率估计。仿真结果证明,本文提出的方法无论在无噪声条件下还是在高斯白噪声条件下均能带来频率估计精度的提升,且无需加窗处理,相比传统方法拥有更低的计算复杂度。     

改进的DFT插值频率估计算法及其DSP实现

在Quinn算法和插值迭代算法(A&M算法)的基础上 ,提出了一种改进的离散傅里叶变换(Discrete Fourier transform, DFT)插值频率估计算法。该算法首先通过Quinn算法估计出1个频率误差作为迭代估计算法的误差初值,然后用迭代算法精确估计频率误差。改进后的算法可以有效减少迭代次数,因此同时具有Quinn算法 的高效率和A&M插值迭代算法的高精度。为了提高算法在DSP处理器上的运行效率,本文还对算法在DSP上的实现提出了一种优化方法,有利于该算法的实时性应用。仿真结果表明该算法在频率估计精度、实时运算效率以及对噪声的抗干扰性能上均获得了提升。     

基于DFT的相位差估计精度与改进方法

相位差是传感器信号处理中重要的检测参数。针对相位差高精度估计要求,在阐述DFT相位差估计原理基础上,分析了影响估计精度的主要因素,推导出估计方差与信噪比、采样长度、频率偏差及对称窗型窗长的具体关系,并给出了满足精度要求的信噪比、采样长度和和频率偏差条件。提出一种校正谱泄漏的相位差估计方法,先通过比值法计算出频率偏差,然后考虑负频率泄漏影响进行相位差估计,校正了短程和长程两类谱泄漏影响,给出了加矩形窗或Hanning窗的估计式和方法步骤。实验结果验证了估计精度分析及本文方法性能,科氏流量计应用实验表明了方法的工程可行性和实用价值。