Source enumeration method by combining diagonal loading andconstructing second-order statistics

A source enumeration method based on diagonal loading of eigenvalues and constructing second-order statistics is proposed, for the case that the antenna array observed signals are overlapped with spatial colored noise, and the number of antennas compared with the number of snapshots meet the requirement of general asymptotic regime. Firstly, the sample covariance matrix of the observed signals is obtained, the eigenvalues of the sample covariance matrix can be acquired by eigenvalue decompositio...     

Signal waveform estimation in the presence of uncertainties about the steering vector

We consider the problem of signal waveform estimation using an array of sensors where there exist uncertainties about the steering vector of interest. This problem occurs in many situations, including arrays undergoing deformations, uncalibrated arrays, scattering around the source, etc. In this paper, we assume that some statistical knowledge about the variations of the steering vector is available. Within this framework, two approaches are proposed, depending on whether the signal is assumed to be deterministic or random. In the former case, the maximum likelihood (ML) estimator is derived. It is shown that it amounts to a beamforming-like processing of the observations, and an iterative algorithm is presented to obtain the ML weight vector. For random signals, a Bayesian approach is advocated, and we successively derive an (approximate) minimum mean-square error estimator and maximum a posteriori estimators. Numerical examples are provided to illustrate the performances of the estimators.     

Robust Adaptive Beamforming Under Quadratic Constraint with Recursive Method Implementation

When adaptive arrays are applied to practical problems, the performances of the conventional adaptive beamforming algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal. Similar types of performance degradation can occur because of data nonstationarity and small training sample size, when the signal steering vector is known exactly. In this paper, to account for mismatches, we propose robust adaptive beamforming algorithm for implementing a quadratic inequality constraint with recursive method updating, which is based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix. We show that the proposed algorithm belongs to the class of diagonal loading approaches, but diagonal loading terms can be precisely calculated based on the given level of uncertainties in the signal array response and data covariance matrix. The variable diagonal loading term is added at each recursive step, which leads to a simpler closed-form algorithm. Our proposed robust recursive algorithm improves the overall robustness against the signal steering vector mismatches and small training sample size, enhances the array system performance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. Moreover, the proposed robust adaptive beamforming can be efficiently computed at a low complexity cost compared with the conventional adaptive beamforming algorithms. Computer simulation results demonstrate excellent performance of our proposed algorithm as compared with the existing adaptive beamforming algorithms.     

Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem

Adaptive beamforming methods are known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated. In particular, if the desired signal is present in training snapshots, the adaptive array performance may be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors (spatial signatures). Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration, distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance. It turns out that the natural formulation of this adaptive beamforming problem involves minimization of a quadratic function subject to infinitely many nonconvex quadratic constraints. We show that this (originally intractable) problem can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently (in polynomial time) using the well-established interior point method. It is also shown that the proposed technique can be interpreted in terms of diagonal loading where the optimal value of the diagonal loading factor is computed based on the known level of uncertainty of the signal steering vector. Computer simulations with several frequently encountered types of signal steering vector mismatches show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms.     

多输入多输出衰落信道的最小互信息盲均衡

提出了多输入多输出衰落信道的基于广义高斯分布近似的最小互信息盲均衡器.采用输出信号的广义高斯分布近似,基于互信息最小化目标函数自适应调整均衡器的系数.比较了基于广义高斯分布近似和非线性变换的两种最小互信息盲均衡算法.仿真实验表明基于广义高斯分布近似的方法比非线性变换方法有更大的星座图距离,更快的收敛速率和更好的误码性能.     

一种加载量迭代搜索的稳健波束形成

当阵列的导向矢量并不精确已知时,自适应波束形成有较大的性能损失.为提高波束形成的稳健性,对角加载成为一种常用的方式.但困扰这类方法的核心问题是合适的加载量如何确定.粗估导向矢量经对角加载后得到修正的导向矢量,如果加载量合适,则修正后的导向矢量接近真实导向矢量,即与噪声子空间的正交性变好.基于以上分析,构造修正导向矢量向信号子空间和噪声子空间投影的加权代价函数来评价加载量的合适与否,进而提出一种迭代搜索合适加载量的方法.计算机仿真验证了方法的有效性,与同类方法对比显示其优越性.     

Asymptotically optimum estimation of signal waveform in the presence of uncertainties about the steering vector

The problem of signal waveform estimation using an antenna array in case of uncertainties about the steering vector is considered. New asymptotically (in sample size) optimum estimators are derived. In contrast to the known optimal solutions, the employed method of synthesis yields non-iterative direct-form estimators. Simulation results are provided to evaluate the performance of the synthesized estimators. It is shown that the proposed asymptotic estimators perform as well as the iterative optimal estimators and they outperform the MVDR estimator in a wide range of input signal-to-noise and uncertainty ratios.     

On robust Capon beamforming and diagonal loading

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.     

A diagonal growth curve model and some signal-processing applications

We consider a variation of the growth-curve (GC) model, referred to as the diagonal growth-curve (DGC) model, where the steering vectors and waveforms are both known and the complex amplitude matrix is constrained to be diagonal. A closed-form approximate maximum likelihood (AML) estimator for this model is derived based on the maximum likelihood principle. We analyze the statistical properties of this method theoretically and show that the AML estimate is unbiased and asymptotically statistically efficient for a large snapshot number. Via several numerical examples in array signal processing and spectral analysis, we also show that the proposed AML estimator can achieve better estimation accuracy and exhibit greater robustness than the best existing methods.     

零陷展宽对角载入算法

提出了零陷展宽对角载入算法,该算法既解决了干扰在快速运动时,干扰零陷过窄的问题,又解决了协方差矩阵误差和导向矢量误差存在时,算法稳定性变差的问题。同时,通过对角载入因子和采样协方差矩阵间的关系确定了对角载入算法载入因子的值。计算机仿真结果表明该算法有很好的稳健性,以及较宽的零陷。     

Robust multiple classification of known signals in additivenoise-an asymptotic weak signal approach

The problem of extracting one out of a finite number of possible signals of known form given observations in an additive noise model is considered. Two approaches are studied: either the signal with shortest distance to the observed data or the signal having maximal correlation with some transformation of the observed data is chosen. With a weak signal approach, the limiting error probability is a monotone function of the Pitman efficacy and it is the same for both the distance-based and correlation-based detectors. Using the minimax theory of Huber, it is possible to derive robust choices of distance/correlation when the limiting error probability is used as performance criterion. This generalizes previous work in the area, from two signals to an arbitrary number of signals. Considered are M-type and R-type distances and also one-dimensional and two-dimensional signals. Some Monte Carlo simulations are performed to compare the finite sample size error probabilities with the asymptotic error probabilities     

Sequential scalar quantization of vectors: an analysis

Proposes an efficient vector quantization (VQ) technique called sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit intercomponent correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, the authors appeal to asymptotic quantization theory, where the codebook size is assumed to be large. Closed-form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. The authors also demonstrate the use of asymptotic theory in designing SSQ for a practical application (color image quantization), where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE.     

Covariance Matrix Estimation With Heterogeneous Samples

We consider the problem of estimating the covariance matrix M_p of an observation vector, using heterogeneous training samples, i.e., samples whose covariance matrices are not exactly M_p. More precisely, we assume that the training samples can be clustered into K groups, each one containing L_k, snapshots sharing the same covariance matrix M_k. Furthermore, a Bayesian approach is proposed in which the matrices M_k. are assumed to be random with some prior distribution. We consider two different assumptions for M_p. In a fully Bayesian framework, M_p is assumed to be random with a given prior distribution. Under this assumption, we derive the minimum mean-square error (MMSE) estimator of M_p which is implemented using a Gibbs-sampling strategy. Moreover, a simpler scheme based on a weighted sample covariance matrix (SCM) is also considered. The weights minimizing the mean square error (MSE) of the estimated covariance matrix are derived. Furthermore, we consider estimators based on colored or diagonal loading of the weighted SCM, and we determine theoretically the optimal level of loading. Finally, in order to relax the a priori assumptions about the covariance matrix M_p, the second part of the paper assumes that this matrix is deterministic and derives its maximum-likelihood estimator. Numerical simulations are presented to illustrate the performance of the different estimation schemes.     

基于可变对角载入的鲁棒自适应波束形成算法

针对传统算法对方向向量偏差敏感的缺点,提出了一种基于可变对角载入的鲁棒自适应波束形成算法.为了提高算法的鲁棒性,采用非线性约束条件下的最优化阵列输出功率对信号方向向量进行优化求解,且优化解中的参量能够准确求出.为了减少计算量,采用递推算法求逆矩阵并利用泰勒级数展开,推导出基于可变对角载入的权重向量公式.该算法可有效地抑制方向向量偏差所带来的影响,降低了计算量易于实时实现,提高了系统的鲁棒性,改善了阵列输出的信干噪比,使其更接近最优值.仿真结果表明,该算法相对传统算法可以获得更好的性能.     

频率不变约束的角加载稳健宽带波束形成算法

应用角加载技术能够提高波束形成算法稳健性,但是角加载量确定却是一个难解决问题。文中提出了一种基于频率不变约束的可变角加载最优稳健波束形成算法(Frequency Invariance Constraints-Variable Diagonal Loading,FIC-VDL)。该算法基于宽带波束形成的时域模型,根据多频点约束下导向矢量的不确定范围,利用频率不变约束因子将多频点变为参考频点约束来求解最优角加载量,并推导出真实的导向矢量。该方法能够改善宽带波束形成器在期望方向的频率不变特性,同时降低系统计算复杂度。计算机仿真结果验证了所提算法的稳健性。     

Optimum detection of a weak signal with minimal knowledge of dependency

The optimum nonlinearity is defined for detection of a weak signal when minimal knowledge of the dependency structure of the observations is available. Specifically, it is assumed that the observations form a one-dependent strictly stationary sequence of random variables and that only a finite number of moments of the marginal density and the correlation coefficient between consecutive observations are known. It is assumed that the bivariate densities involved can be represented as diagonal series, using orthonormal polynomials. Using efficacy as a performance measure, the optimum nonlinearity is required to satisfy a saddle-point condition over this class of bivariate densities.     

基于最差性能最优的稳健STAP算法

导向矢量失配和协方差矩阵失配是影响空时自适应处理(STAP)性能的两大主要因素,基于在最差情况下的性能最优,提出了一种稳健的STAP算法.通过对原始问题的数学描述,建立了基于最差性能最优的稳健STAP算法模型,并将原始模型进行等价转换成可以处理的加载样本矩阵求逆(LSMI)算法,得到了加权矢量的具体表达式,通过对Lagrange乘数λ的准确计算,从而给出了LSMI算法中准确的加载量,解决了对角加载技术中加载量估计的难题.仿真分析表明了该算法的正确性和有效性.     

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