Robust Least Squares Constant Modulus Algorithm to Signal Steering Vector Mismatches

The linearly constrained least squares constant modulus algorithm (LSCMA) may suffer significant performance degradation and lack robustness in the presence of the slight mismatches between the actual and assumed signal steering vectors, which can cause the serious problem of desired signal cancellation. To account for the mismatches, we propose a doubly constrained robust LSCMA based on explicit modeling of uncertainty in the desired signal array response and data covariance matrix, which provides robustness against pointing errors and random perturbations in detector parameters. Our algorithm optimizes the worst-case performance by minimizing the output SINR while maintaining a distortionless response for the worst-case signal steering vector. The weight vector can be optimized by the partial Taylor-series expansion and Lagrange multiplier method, and the optimal value of the Lagrange multiplier is iteratively derived based on the known level of uncertainty in the signal DOA. The proposed implementation based on iterative minimization eliminates the covariance matrix inversion estimation at a comparable cost with that of the existing LSCMA. We present a theoretical analysis of our proposed algorithm in terms of convergence, SINR performance, array beampattern gain, and complexity cost in the presence of random steering vector mismatches. In contrast to the linearly constrained LSCMA, the proposed algorithm provides excellent robustness against the signal steering vector mismatches, yields improved signal capture performance, has superior performance on SINR improvement, and enhances the array system performance under random perturbations in sensor parameters. The on-line implementation and significant SINR enhancement support the practicability of the proposed algorithm. The numerical experiments have been carried out to demonstrate the superiority of the proposed algorithm on beampattern control and output SINR enhancement compared with linearly constrained LSCMA.     

DOA estimation for sparse nested MIMO radar with velocity receive sensor array

Direction of arrival (DOA) estimation for sparse nested MIMO radar with velocity receive sensor array is studied, and an algorithm based on extended unitary root multiple signal classification (MUSIC) is proposed. The nested MIMO radar utilizes sparse transmit array and velocity receive array with nested inter-element distances, which can make the final virtual array to be a long and sparse velocity sensor array. After exploiting unitary transformation to transform the data into real-valued one, an extended root MUSIC based method is developed to decompose the angle estimation into high-resolution but ambiguous and low-resolution but unambiguous DOA estimations, which are automatically paired. Thereafter, the ambiguous estimation is used to recover all possible DOAs, and the unambiguous DOA estimation is used as a reference to resolve the estimation ambiguity problem. Compared to conventional methods, the proposed algorithm requires no peak search, maintains larger aperture and achieves better DOA estimation performance. The simulation results verify the effectiveness of our approach.     

迭代自适应收缩加权融合的波束形成方法

自适应数字波束形成是通过对阵列接收数据进行加权处理来获得最大的输出信干噪比,对采样协方差矩阵的依赖性较大。针对小样本条件下采样协方差矩阵求逆算法性能下降问题,提出迭代自适应加权融合样本协方差矩阵与先验协方差矩阵的波束形成算法。在估计协方差矩阵时,依据最小均方误差准则计算加权系数,并采用迭代自适应的方式更新先验协方差矩阵。仿真结果表明,所提方法能显著提高小样本条件下的协方差矩阵估计精度,能获得更大的输出信干噪比。      

Minimax MSE-ratio estimation with signal covariance uncertainties

In continuation to an earlier work, we further consider the problem of robust estimation of a random vector (or signal), with an uncertain covariance matrix, that is observed through a known linear transformation and corrupted by additive noise with a known covariance matrix. While, in the earlier work, we developed and proposed a competitive minimax approach of minimizing the worst-case mean-squared error (MSE) difference regret criterion, here, we study, in the same spirit, the minimum worst-case MSE ratio regret criterion, namely, the worst-case ratio (rather than difference) between the MSE attainable using a linear estimator, ignorant of the exact signal covariance, and the minimum MSE (MMSE) attainable by optimum linear estimation with a known signal covariance. We present the optimal linear estimator, under this criterion, in two ways: The first is as a solution to a certain semidefinite programming (SDP) problem, and the second is as an expression that is of closed form up to a single parameter whose value can be found by a simple line search procedure. We then show that the linear minimax ratio regret estimator can also be interpreted as the MMSE estimator that minimizes the MSE for a certain choice of signal covariance that depends on the uncertainty region. We demonstrate that in applications, the proposed minimax MSE ratio regret approach may outperform the well-known minimax MSE approach, the minimax MSE difference regret approach, and the "plug-in" approach, where in the latter, one uses the MMSE estimator with an estimated covariance matrix replacing the true unknown covariance.     

Modified linear prediction method for directions of arrivalestimation of narrow-band plane waves

A modified linear prediction (MLP) method is proposed in which the reference sensor is optimally located on the extended line of the array. The criterion of optimality is the minimization of the prediction error power, where the prediction error is defined as the difference between the reference sensor and the weighted array outputs. It is shown that the L₂-norm of the least-squares array weights attains a minimum value for the optimum spacing of the reference sensor, subject to some soft constraint on signal-to-noise ratio (SNR). How this minimum norm property can be used for finding the optimum spacing of the reference sensor is described. The performance of the MLP method is studied and compared with that of the linear prediction (LP) method using resolution, detection bias, and variance as the performance measures. The study reveals that the MLP method performs much better than the LP technique     

Simple and Efficient Nonparametric Method for Estimating the Number of Signals Without Eigendecomposition

Inspired by the computational simplicity and numerical stability of QR decomposition, a nonparametric method for estimating the number of signals without eigendecomposition (MENSE) is proposed for the coherent narrowband signals impinging on a uniform linear array (ULA). By exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging, the number of signals is revealed in the rank of the QR upper-trapezoidal factor of the autoproduct of a combined Hankel matrix formed from the cross correlations between some sensor data. Since the infection of additive noise is defused, signal detection capability is improved. A new detection criterion is then formulated in terms of the row elements of the QR upper-triangular factor when finite array data are available, and the number of signals is determined as a value of the running index for which this ratio criterion is maximized, where the QR decomposition with column pivoting is also used to improve detection performance. The statistical analysis clarifies that the MENSE detection criterion is asymptotically consistent. Furthermore, the proposed MENSE algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model. The effectiveness of the MENSE is verified through numerical examples, and the simulation results show that the MENSE is superior in detecting closely spaced signals with a small number of snapshots and/or at relatively low signal-to-noise ratio (SNR)     

Design of broadband beamformers robust against gain and phase errors in the microphone array characteristics

Fixed broadband beamformers using small-size microphone arrays are known to be highly sensitive to errors in the microphone array characteristics. The paper describes two design procedures for designing broadband beamformers with an arbitrary spatial directivity pattern, which are robust against gain and phase errors in the microphone array characteristics. The first design procedure optimizes the mean performance of the broadband beamformer and requires knowledge of the gain and the phase probability density functions, whereas the second design procedure optimizes the worst-case performance by using a minimax criterion. Simulations with a small-size microphone array show the performance improvement that can be obtained by using a robust broadband beamformer design procedure.     

Sensor Allocation for Source Localization With Decoupled Range and Bearing Estimation

The source localization accuracy is known to be affected by the placement of sensors. This paper addresses the problem of optimum sensor allocation for decoupled range and bearing estimation, as well as position estimation of an emitting source, under the constraint that all sensors must be confined within a certain area. The source is assumed to be distant and has a curved wavefront when arriving at the sensors. The optimization criterion is the minimum estimation variance defined by the Cramer–Rao lower bound that is derived under Gaussian noise model. A geometric approach is employed to arrive at the optimum geometries and no complicated optimization technique is required. The optimum sensor allocations for time difference of arrival (TDOA), angle of arrival (AOA), and time of arrival (TOA) positionings are derived and their estimation accuracies are contrasted. The optimum geometries belong to the generic structure of a ring array plus some sensors at the center. TDOA and TOA are found to have identical optimum geometries for bearing estimation and yield the same accuracy, although the position localization accuracy of TDOA is known to be worse than that of TOA. Simulations are included to confirm the theoretical development and illustrate the improvement of using an optimum array compared to a random sensor placement array.      

一种新的基于 EEF 准则的空间声源个数估计算法

针对指数嵌入族（ Exponentially Embedded Families ,EEF）准则在快拍数小于阵元数情况下无法估计声源个数的问题,本文提出一种新的空间声源个数估计算法。首先通过球麦克风阵列采集空间声场高阶信息,建立球阵列信号模型,将声源个数估计扩展到三维空间。继而将观测信号空间分解为信号子空间和噪声子空间,利用最小均方差（ Minimum Mean-Squared Error ,MMSE）方法估计观测信号空间及噪声子空间的协方差矩阵,确保矩阵估计的一致性和准确性。在此基础上改进似然比函数,同时引入新的自由度计算,使得算法在快拍数小于阵元数的情况下能有效估计声源个数。仿真结果表明,在进行空间声源个数估计时,相对于EEF准则,新的算法不仅适用于快拍数小于阵元数情况,同时提高了估计准确率。     

用信号子空间法校准天线阵各通道增益和相位的不一致性

基于阵列协方差矩阵特征分解的测向技术,在天线阵各通道特性不一致时,其性能会急剧下降。本文提出了一种校准非线性阵列各通道增益和相位不一致性的新方法,即利用两个未知精确方向校准信号源的信号,分别作特征分解处理,然后通过用迭代算法求解非线性方程组以估计各通道的增益和相位因子。模拟结果表明,本文的方法是成功的。     

阵列通道复增益盲估计

在阵列接收机各通道增益和相位不一致时,基于模型的超分辨波达方向估计性能大大下降。在已知２个信号的波达方向差的条件下,提出一种基于四阶累量进行盲信号处理的新算法。在方法中首先求出阵列流形,然后利用搜索法估计阵列通道复增益矩阵。     

鲁棒的四元数空间平滑算法

本文针对相干信号波达方向(DOA)估计问题,利用简化电磁矢量传感器阵列提出了一种基于四元数模型的空间平滑(Q-SS)算法。首先,根据四元数的正交特性能够很好地描述矢量传感器阵元内部信号分量之间的垂直关系这一特点,将每个阵元的两分量接收数据合成为一个四元数,建立了简化电磁矢量传感器阵列的四元数接收模型,该模型比传统的长矢量模型更适合于矢量传感器阵列的信号处理。在此基础上,利用本文提出的Q-SS算法对相干信号进行预处理,实现了解相干,并对解相干性能进行了分析,然后通过四元数域的ESPRIT算法估计出相干信号的DOA。理论分析表明Q-SS算法比传统的长矢量空间平滑(V-SS)方法有更高的DOA估计精度,具有对矢量传感器内部电场噪声分量解相关的能力,这是V-SS算法所不具备的优势。最后,通过计算机仿真实验比较和分析了所提算法的有效性。      

Direction finding in the presence of mutual coupling

An eigenstructure-based method for direction finding in the presence of sensor mutual coupling, gain, and phase uncertainties is presented. The method provides estimates of the directions-of-arrival (DOA) of all the radiating sources as well as calibration of the gain and phase of each sensor and the mutual coupling in the receiving array. The proposed algorithm is able to calibrate the array parameters without prior knowledge of the array manifold, using only signals of opportunity and avoiding the need for deploying auxiliary sources at known locations. The algorithm is described in detail, and its behavior is illustrated by numerical examples     

Adaptive minimum bit-error-rate filtering

Adaptive filtering has traditionally been developed based on the minimum mean square error (MMSE) principle and has found ever-increasing applications in communications. The paper develops adaptive filtering based on an alternative minimum bit error rate (MBER) criterion for communication applications. It is shown that the MBER filtering exploits the non-Gaussian distribution of filter output effectively and, consequently, can provide significant performance gain in terms of smaller bit error rate (BER) over the MMSE approach. Adopting the classical Parzen window or kernel density estimation for a probability density function (pdf), a block-data gradient adaptive MBER algorithm is derived. A stochastic gradient adaptive MBER algorithm is further developed for sample-by-sample adaptive implementation of the MBER filtering. Extension of the MBER approach to adaptive nonlinear filtering is also discussed.     

Generalizing MUSIC and MVDR for multiple noncoherent arrays

We examine the problem of source localization and spatial spectrum estimation using sensor arrays that are noncoherent collections of small, coherent subarrays. The covariance of the signal snapshots at each of the coherent subarrays are functions of, among other things, the signal source locations (or the spatial spectrum). Our approach is to derive functions of the subarray covariance matrices that are close approximations of the signal source locations (or the spatial spectrum). We also show how these functions may be considered generalizations of the multiple signal classification (MUSIC) algorithm and the minimum variance distortionless response (MVDR) criterion, respectively. We demonstrate via simulation that, using this approach and array architecture, it is possible to resolve directional ambiguities.     

一种新的阵元位置误差有源校正算法

阵列天线位置的不确定性会严重影响阵列天线的测向性能。文中基于子空间类测向方法,在远场情况下,提出了一种新的估计阵元位置误差的有源校正算法。该算法是以迭代的形式给出,其目标函数建立在信号子空间基本性质的基础上,适用于多个校正源同时存在的情况,并且可以应用于任意阵列形式。计算机仿真验证了文中的算法具有较快的收敛速度和较高的参数估计精度。     

一种阵列天线阵元幅相、位置误差校正方法

针对毫米波热辐射信号弱的问题,该文提出一种对存在阵元幅相、位置误差的线阵进行校正的方法。该文基于低信噪比(SNR)的阵列误差模型,利用单个校正源,其信源方向未精确已知,通过旋转天线阵列在多个校正方位测得校正数据,并估计出阵元幅相、位置误差参数,从而对阵列中的阵元幅相、位置误差进行联合校正。该方法运算复杂度低,具有较高的估计精度,校正性能良好。理论分析和计算机仿真结果表明了该文方法的有效性。     

Nested planar array: configuration design,optimal array and DOA estimation

Nested array enables to enhance localisation resolution and achieve under-determined direction of arrival (DOA) estimation. In this paper, we improve the traditional nested planar array to achieve more degrees of freedom (DOFs) and better angle estimation performance. The closed-form expressions for sensor positions of the improved array are given and the optimal array configuration for largest available DOFs is derived. Meanwhile, a computationally efficient DOA estimation algorithm is proposed. Specifically, we utilise two dimensional Discrete Fourier Transform (2D DFT) method to obtain the coarse DOA estimates; Subsequently, we achieve the fine DOA estimates by 2D spatial smoothing multiple signals classification (SS-MUSIC) algorithm. The proposed algorithm enjoys the same estimation accuracy as SS-MUSIC algorithm but with lower complexity because the coarse DOA estimates enable to shrink the range of spectral search. In addition, estimation of the number of signals is not required by 2D DFT method. Extensive simulation results testify the effectiveness of the proposed algorithm.     

通道增益的有源估计方法

在DOA估计中解决通道不一致性问题的关键是设法求得各通道的复增益。本文利用在天线阵列所在平面设置的一个校正源，运用信号空间对信号DOA和通道增益的约束关系对通道增益进行估计，在未知校正信号DOA时可通过迭代的方法获得二者的一致估计。仿真证明了此方法的有效性。