Robust detection in digital communications

This paper deals with the problem of communicating through unspecified noise. Detectors, robust against variations in the probability density function of the noise, are developed and discussed. The paper covers three issues. First, the relation between a distance measuring receiver and a correlating receiver in a general case is shown. Second, a theoretical method for the computation of an upper limit for the probability of symbol error is presented. This computation fits into the ordinary framework for computation of the error probability by changing the inverted noise density 2/N₀ to efficacy, ϵ. Efficacy is defined in the paper. Third, detectors based on M-, i.e., maximum likelihood type, and R-, i.e., rank, statistics are tested and compared for GMSK and π/4-shifted DQPSK. From numerical comparisons of the upper bounds and their simulated estimates for robust detectors, it is concluded that the loss in Gaussian noise is very small compared to the optimum quadratic detector. The gain, compared to a nonrobust receiver optimized to Gaussian noise, is around 0.5 to 2 dB for large SNR and around 2 to 4 dB for low SNR in impulsive noise. This offers new methods of significantly improving communication when the noise is unknown     

Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis

Recently, a new adaptive scheme [Conte (1995), Gini (1997)] has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non-Gaussian noise. This latter has been modeled by compound-Gaussian noise, which is the product c of the square root of a positive unknown variable tau (deterministic or random) and an independent Gaussian vector x, c=radictaux. Because of the implicit algebraic structure of the equation to solve, we called the corresponding solution, the fixed point (FP) estimate. When tau is assumed deterministic and unknown, the FP is the exact maximum-likelihood (ML) estimate of the noise covariance structure, while when tau is a positive random variable, the FP is an approximate maximum likelihood (AML). This estimate has been already used for its excellent statistical properties without proofs of its existence and uniqueness. The major contribution of this paper is to fill these gaps. Our derivation is based on some likelihood functions general properties like homogeneity and can be easily adapted to other recursive contexts. Moreover, the corresponding iterative algorithm used for the FP estimate practical determination is also analyzed and we show the convergence of this recursive scheme, ensured whatever the initialization.     

非均匀非高斯杂波的协方差矩阵估计

在雷达目标检测中,杂波的协方差矩阵估计利用了待检测单元附近的杂波数据。本文考虑一种非均匀环境中,非高斯杂波下的杂波协方差矩阵估计问题,即假定待检测单元与参考单元的杂波协方差矩阵之间满足某种统计关系,并假定杂波数据满足复合高斯统计分布模型。在这种场景下,常规的杂波协方差矩阵估计方法会导致信号检测性能的下降。采用共轭先验分布作为非均匀非高斯场景的统计分布模型,利用贝叶斯方法,本文给出了基于Gibbs抽样的杂波协方差最小均方误差估计方法。计算机仿真结果表明,与常规的杂波协方差矩阵估计方法相比较,本文所给出的杂波协方差矩阵的估计算法能够在参考数据较少,累积脉冲个数较少时,非均匀场景中获得较好的检测性能。本文还分析了先验分布模型参数误差对检测性能的影响。      

一种基于分数低阶协方差矩阵的波束形成新方法

利用稳定分布对具有脉冲特性的噪声进行建模，提出了一种新的分数低阶协方差概念，推导了一种基于分数低阶协方差矩阵的波束形成方法，并分析了其旁瓣特性。模拟表明新方法具有更高的信号干扰噪声比及更强的波束形成与旁瓣抑制能力。新算法在高斯和分数低阶稳定分布环境下比传统的算法具有更好的韧性。     

一种非均匀场景复合高斯杂波下的自适应检测器

该文考虑一种非均匀环境中,复合高斯杂波下的目标检测问题,即待检测单元杂波协方差矩阵与参考单元杂波协方差矩阵之间并不相等,且杂波数据满足复合高斯统计分布模型。利用已知的先验信息,选择合适的先验分布,基于贝叶斯方法,该文给出了杂波协方差矩阵的最小均方误差估计,并将其应用于正则化匹配滤波器检验。计算机仿真结果表明,采用该文提出的杂波协方差估计算法,能够在参考数据较少的情况下,获得较好的检测性能。     

基于协方差匹配技术的互耦和幅相误差联合校正算法

 提出了基于协方差匹配技术的均匀线阵互耦和幅相误差联合校正算法.首先,根据协方差匹配技术中的目标函数和均匀线阵的误差模型,设计了一种交替迭代算法用以实现各种参数的优化计算.接着,为了避免该算法中的每轮循环迭代都需要进行波达方向估计这一复杂环节,利用理想条件均匀线阵协方差阵的Toeplitz性,给出了另一种改进型交替迭代算法用以减少计算复杂度.与基于子空间技术的阵列误差校正方法相比,文中的两种新算法可直接利用信源的统计特性,并且适用于不同的高斯噪声模型(例如噪声功率不一致),仿真实验验证了新算法的有效性和优越性.     

Threshold detection in correlated non-Gaussian noise fields

Classical threshold detection theory for arbitrary noise and signals, based on independent noise samples, i.e., using only the first-order probability density of the noise, is generalized to include the critical additional statistical information contained in the (first-order) covariances of the noise. This is accomplished by replacing the actual, generalized noise by a “quasi-equivalent” (QE-)model employing both the first-order PDF and covariance. The result is a “near-optimum” approach, which is the best available to date incorporating these fundamental statistical data. Space-time noise and signal fields are specifically considered throughout. Even with additive white Gaussian noise (AWGN) worthwhile processing gains per sample (Γ^(c)) are attainable, often O(10-20 dB), over the usual independent sampling procedures, with corresponding reductions in the minimum detectable signal. The earlier moving average (MA) noise model, while not realistic, is included because it reduces in the Gaussian noise cases to the threshold optimum results of previous analyses, while the QE-model remains suboptimum here because of the necessary constraints imposed in combining the PDF and covariance information into the detector structure. Full space-time formulation is provided in general, with the important special cases of adaptive and preformed beams in reception. The needed (first-order) PDF here is given by the canonical Class A and Class B noise models. The general analysis, including the canonical threshold algorithms, correlation gain factors Γ^(c), detection parameters for the QE-model, along with some representative numerical results for both coherent and incoherent detection, based on four representative Toeplitz covariance models is presented     

A robust past algorithm for subspace tracking in impulsive noise

The PAST algorithm is an effective and low complexity method for adaptive subspace tracking. However, due to the use of the recursive least squares (RLS) algorithm in estimating the conventional correlation matrix, like other RLS algorithms, it is very sensitive to impulsive noise and the performance can be degraded substantially. To overcome this problem, a new robust correlation matrix estimate, based on robust statistics concept, is proposed in this paper. It is derived from the maximum-likelihood (ML) estimate of a multivariate Gaussian process in contaminated Gaussian noise (CG) similar to the M-estimates in robust statistics. This new estimator is incorporated into the PAST algorithm for robust subspace tracking in impulsive noise. Furthermore, a new restoring mechanism is proposed to combat the hostile effect of long burst of impulses, which sporadically occur in communications systems. The convergence of this new algorithm is analyzed by extending a previous ordinary differential equation (ODE)-based method for PAST. Both theoretical and simulation results show that the proposed algorithm offers improved robustness against impulsive noise over the PAST algorithm. The performance of the new algorithm in nominal Gaussian noise is very close to that of the PAST algorithm.     

The Cost of Uncorrelation and Noncooperation in MIMO Channels

We investigate the capacity loss for using uncorrelated Gaussian input over a multiple-input multiple-output (MIMO) linear additive-noise channel. We upper-bound the capacity loss by a universal constant C* which is independent of the channel matrix and the noise distribution. For a single-user MIMO channel with n_t inputs and n_r outputs C* = min [ 1/2, n_r/n_t log₂ (1+n_t/n_r) ] bit per input dimension (or 2C* bit per transmit antenna per second per hertz), under both total and per-input power constraints. If we restrict attention to (colored) Gaussian noise, then the capacity loss is upper-bounded by a smaller constant C_G = n_r/2n_r log₂ (n_t/n_r) for n_r ges n_t/e, and C_G = 0.265 otherwise, and this bound is tight for certain cases of channel matrix and noise covariance. We also derive similar bounds for the sum-capacity loss in multiuser MIMO channels. This includes in particular uncorrelated Gaussian transmission in a MIMO multiple-access channel (MAC), and "flat" Gaussian dirty-paper coding (DPC) in a MIMO broadcast channel. In the context of wireless communication, our results imply that the benefit of beamforming and spatial water-filling over simple isotropic transmission is limited. Moreover, the excess capacity of a point-to-point MIMO channel over the same MIMO channel in a multiuser configuration is bounded by a universal constant.     

Fast converging adaptive detection of Doppler-shifted,range-distributed targets

A generalized likelihood ratio test (GLRT) for the adaptive detection of a target or targets that are Doppler-shifted and distributed in range is derived. The unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference, which is assumed to be characterized as complex zero-mean correlated Gaussian random variables. The target's or targets' complex amplitudes are assumed to be distributed across the entire input data block (sensor × range). The unknown covariance matrix is constrained to have the reasonable form of the identity matrix (the internal noise contribution) plus an unknown positive semidefinite (psdh) matrix (the external interference contribution). It is shown via simulation for a variety of interference scenarios that the new detector has the characteristic of having a bounded constant false alarm rate (CFAR), i.e., for our problem, the probability of false alarm P_F for a given detection threshold is bounded by the P_F that results when no external interference is present. It is also shown via simulation that the new detector converges relatively fast with respect to the number of sample vectors K necessary in order to achieve a given probability of detection P_D     

Performance analysis of QAM systems under class A impulsive noiseenvironment

This paper describes the performance of QAM (quadrature amplitude modulation) systems under impulsive noise environment. In the analysis, we employ, as a model of the impulsive noise, Middleton's (1977) model labeled class A. First, the statistical characteristics of the in-phase and quadrature components of the impulsive noise are investigated, and it is proved that, in contrast to Gaussian noise, these components are dependent especially for the impulsive noise with small impulsive indices. Next, with consideration of the dependence between the in-phase and quadrature components of the noise, the performance of QAM systems with the conventional receiver designed for Gaussian noise is analyzed. The numerical results show that the performance is much worse than that achieved under Gaussian noise. Moreover, we show the design of the maximum likelihood receiver for class A impulsive noise and the great performance improvement by this receiver is confirmed     

Maximum likelihood DOA estimation and asymptotic Cramer-Rao boundsfor additive unknown colored noise

This paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise. With the spatial noise covariance modeled as a function of certain unknown parameters, e.g., an autoregressive (AR) model, a direct and systematic way is developed to find the exact maximum likelihood (ML) estimates of all parameters associated with the direction finding problem, including the direction-of-arrival (DOA) angles Θ, the noise parameters α, the signal covariance Φ_s, and the noise power σ². We show that the estimates of the linear part of the parameter set Φ_s and σ² can be separated from the nonlinear parts Θ and α. Thus, the estimates of Φ_s and σ² become explicit functions of Θ and α. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of Θ and α, and compact formulas are obtained for the Cramer-Rao bounds (CRB's). Finally, a Newton-type algorithm is designed to solve the nonlinear optimization problem, and simulations show that the asymptotic CRB agrees well with the results from Monte Carlo trials, even for small numbers of snapshots     

Two-dimensional spectrum estimation using noncausal autoregressive models

Two-dimensional (2-D) spectrum estimation from raw data is of interest in signal and image processing. A parametric technique for spectrum estimation using 2-D noncausal autoregressive (NCAR) models is given. The NCAR models characterize the statistical dependency of the observation at location s on its neighbors in all directions. This modeling assumption reduces the spectrum estimation problem to two subproblems: the choice of appropriate structure of the NCAR model and the estimation of parameters in NCAR models. By assuming that the true structure of the NCAR model is known, we first analyze the existence and uniqueness of Gaussian maximum likelihood (GML) estimates of NCAR model parameters. Due to the noncausal nature of the models, the computation of GML estimates is burdensome. By assuming specific boundary conditions, computationally tractable expressions are obtained for the likelihood function. Expressions for the asymptotic covariance matrix of the GML estimates as well as the simultaneous confidence bands for the estimated spectrum using GML estimates are derived. Finally, the usefulness of the method is illustrated by computer simulation results.     

Optimal speckle reduction for the product model in multilookpolarimetric SAR imagery and the Wishart distribution

Several optimal techniques exist to reduce speckle effects on polarimetric data, e.g. the Linear Minimum Mean Square Error (LMMSE) vector filter for multilook detected data or optimum summations such as the Polarimetric Whitening Filter (PWF) for one look complex data. Among other drawbacks, these standard methods do not preserve full polarimetric data, or they do not use the a priori texture distribution, or they are restricted to one look data. In the simplified case of data satisfying the so-called “product model”, new optimal techniques are described in this paper that are able to reduce speckle effects on multilook data, while preserving fully polarimetric information and texture variations. This “product model” is valid when the scene texture has a large scale of variation and is polarization independent, for instance in K-distributed clutter. Under this assumption, the measured covariance matrix (multilook data) is the product of a scalar random variable μ (the texture) and the covariance matrix C_zh of an equivalent Gaussian homogeneous surface. C_zh is the mean covariance matrix and contains the polarimetric information. A PWF for multilook complex data (MPWF) is proposed and is shown to be related to optimal statistical estimators of the texture (Maximum Likelihood, Maximum A Posteriori, MMSE…) when the complex Wishart distribution is used. The ML estimation of C _zh for textured areas is given and the adaptive filters based on these new tools are described. The results indicate a large speckle reduction. Moreover, the mean values of polarimetric features such as the magnitude and the phase of the HH-VV complex degree of coherence are preserved     

Robust Huber adaptive filter

Classical filtering methods are not optimal when the statistics of the signals violate the underlying assumptions behind the theoretical development. Most of the classical filtering theory like least-squares filtering assumes Gaussianity as its underlying distribution. We present a new adaptive filter that is optimal in the presence of Gaussian noise and robust to outliers. This novel robust adaptive filter minimizes the Huber objective function. An estimator based on the Huber objective function behaves as an L₁ norm estimator for large residual errors and as an L₂ norm estimator for small residual errors. Simulation results show the improved performance of the Huber adaptive filter (configured as a line enhancer) over various nonlinear filters in the presence of impulsive noise and Gaussian noise     

Robust parameter estimation of a deterministic signal in impulsivenoise

This paper presents a robust class of estimators for the parameters of a deterministic signal in impulsive noise. The proposed technique has the structure of the maximum likelihood estimator (MLE) but has an extra degree of freedom: the choice of a nonlinear function (which is different from the score function suggested by the MLE) that can be adjusted to improve robustness. The effect of this nonlinear function is studied analytically via an asymptotic performance analysis. We investigate the covariance of the estimates and the loss of efficiency induced by nonoptimal choices of the nonlinear function, giving special attention to the case of α-stable noise. Finally, we apply the theoretical results to the problem of estimating the parameters of a sinusoidal signal in impulsive noise     

脉冲噪声环境下高斯稀疏信源贝叶斯压缩感知重构

 大多数现有的压缩感知重构算法对脉冲噪声不具有鲁棒性,在脉冲噪声环境下,重构性能急剧下降,使得整个重构系统崩溃.针对此问题,本文提出了一种脉冲噪声环境下的稀疏重构算法BINSR算法,其基于贝叶斯理论,可以有效地估计出信号的支撑集和脉冲噪声中脉冲的位置,并且根据压缩感知观测序列的democracy特性,利用最小均方误差MMSE估计量,有效地估计出原信号.在此基础上,本文结合鲁棒统计学,提出自适应的ABINSR算法,使其不再依赖于信号以及噪声的统计参数.实验结果表明,BINSR算法在脉冲噪声环境下可以有效地恢复出稀疏信号,很大程度上改善了脉冲噪声环境下算法的重构性能.ABINSR算法不仅对脉冲噪声具有鲁棒性,而且可以在高斯白噪声环境下实现有效的信号重构.     

Phase-difference distribution for a narrow-band non-Gaussian noiseand related statistics

A probability density function _Pm(R₁,R₂,Δ) is presented for a narrowband noise process in which R₁ and R₂ are two envelope samples and Δ is the phase difference. For m=1 the process is Gaussian, but for m=2,3, etc., it is non-Gaussian. New second-order statistical properties are identified for it as well as the density function for the resulting envelope when a signal is added to the noise. These results are given, though the major concern is with the density of the phase difference Δ and the density of &thetas;, the response of an FM detector fed with the noise     

MIMO Radar Detection in Non-Gaussian and Heterogeneous Clutter

In this paper, the generalized likelihood ratio test-linear quadratic (GLRT-LQ) has been extended to the multiple-input multiple-output (MIMO) case where all transmit–receive subarrays are considered jointly as a system such that only one detection threshold is used. The GLRT-LQ detector has been derived based on the Spherically Invariant Random Vector (SIRV) model and is constant false alarm rate (CFAR) with respect to the clutter power fluctuations (also known as the texture). The new MIMO detector is then shown to be texture-CFAR as well. The theoretical performance of this new detector is first analytically derived and then validated using Monte Carlo simulations. Its detection performance is then compared to that of the well-known Optimum Gaussian Detector (OGD) under Gaussian and non-Gaussian clutter. Next, the adaptive version of the detector is investigated. The covariance matrix is estimated using the Fixed Point (FP) algorithm which enables the detector to remain texture- and matrix-CFAR. The effects of the estimation of the covariance matrix on the detection performance are also investigated.      

冲击噪声背景下双基地MIMO 雷达目标角度估计方法

实际工作环境中雷达经常会受到琢稳态分布冲击噪声的影响,使得大量高斯噪声背景下基于二阶或更高阶累积量的角度估计算法性能急剧下降。文中提出了一种基于FLOM-ESPRIT算法的双基地MIMO雷达收发角度估计方法,算法通过利用匹配滤波后数据构造分数低阶协方差矩阵实现对冲击噪声的有效抑制,弥补了传统的二阶或四阶统计模型及相应的处理算法不适用于冲击噪声环境的缺陷,增强了信号子空间估计算法的稳健性,并且无需计算量繁杂的二维谱峰搜索。