Radar HRRP Statistical Recognition: Parametric Model and Model Selection

Statistical modeling for radar high-resolution range profile (HRRP) is a challenging task in radar HRRP statistical recognition. Theoretical analysis and experimental results show that elements in an HRRP sample are statistically correlated and non-Gaussian distributed. First, this paper introduces three joint-Gaussian models, i.e., subspace approximation model, probability principal components analysis (PPCA) model and factor analysis (FA) model, into radar HRRP statistical recognition. Due to the experimental results, we can have the conclusion that the jointly non-Gaussian distributed HRRP samples approximately follow the joint-Gaussian distribution described by FA model. Therefore, we can apply FA model to radar HRRP statistical recognition rather than a joint-Gaussian mixture model, e.g., PPCA mixture model or FA mixture model, which is a more accurate choice for modeling non-Gaussian distributed correlations in multidimensional data but with high learning complexity and large computation burden, and the difficulty in the statistical modeling for HRRP samples is largely reduced. Second, this paper concerns model selection of FA model in radar HRRP statistical recognition, in which there are two issues, i.e., the partition of target-aspect frames and the determination of the number of factors in each frame. Based on the Akaike information criterion (AIC) and the Bayes' information criterion (BIC), an iterated algorithm for model selection is proposed in this paper, which can automatically give the optimal aspect-frame boundaries and determine the optimal number of factors in each aspect-frame. The recognition experiments based on measured data show that the proposed adaptive partition approach can further improve the recognition performance with higher recognition efficiency.     

CRLB for DOA Estimation in Gaussian and Non-Gaussian Mixed Environments

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of Direction-of-arrival (DOA) estimation is a very important issue. Several CRLBs on DOA estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper derives the deterministic CRLB for Gaussian and non-Gaussian mixed environments. Since non-parametric kernel method is used to build the probability density function (PDF) of non-Gaussian noise, the CRLB derived is suitable for various noise distributions with or without symmetric PDF. The relationship between the CRLB for Gaussian noise and the proposed CRLB is also investigated. Theoretical analysis shows that the proposed CRLB provides a unified representation for both the cases of Gaussian and mixed environments. Computer simulations are included to verify the derived CRLB in different noise environments.     

Intersymbol interference and error probability

Using a criterion of minimum average error probability we derive a method for specifying an optimum linear, time invariant receiving filter for a digital data transmission system. The transmitted data are binary and coded into pulses of shapepm s(t). The linear transmission medium introduces intersymbol interference and additive Gaussian noise. Because the intersymbol interference is not Gaussian and can be correlated with the binary digit being detected, our problem is one of deciding which of two waveforms is present in a special type of correlated, non-Gaussian noise. For signal-to-noise ratios in a range of practical interest, the optimum filter is found to be representable as a matched filter followed by a tapped delay line--the same form as that of the least mean square estimator of the pulse amplitude. The performance (error probability vs.S/N) of the optimum filter is compared with that of a matched-filter receiver in an example.     

Cumulant-based method for bearing estimation in the presence ofnonGaussian noise

Bearing estimation algorithms based on the cumulants of array data have been developed to suppress additive spatially correlated Gaussian noises. In practice, however, the noises encountered in signal processing environments are often non-Gaussian, and the applications of those cumulant-based algorithms designed for Gaussian noise to non-Gaussian environments may severely degrade the estimation performance. The authors propose a new cumulant-based method to solve this problem. This approach is based on the fourth-order cumulants of the array data transformed by DFT, and relies on the statistical central limit theorem to show that the fourth-order cumulants of the additive non-Gaussian noises approach zero in each DFT cell. Simulation results are presented to demonstrate that the proposed method can effectively estimate the bearings in both Gaussian and non-Gaussian noise environments     

基于分数低阶本征滤波的雷达目标检测方法

在非高斯相关杂波背景下,通常杂波分布的概率密度函数结构复杂甚至无闭式表达,难以建立统计检测模型。针对此问题,以α稳定分布为背景,基于分数低阶统计量和最佳滤波器理论,以滤波器输出分数低阶信杂比最大为准则,给出了一种分数低阶本征滤波(FLOEF)模型。该模型利用杂波的分数低阶协方差矩阵对非高斯相关杂波进行白化,可显著改善信杂比,实现非高斯相关杂波背景下雷达目标的有效检测。通过仿真和实测数据给出了FLOEF在不同条件下的检测性能,并同传统基于二阶统计量的本征滤波进行了比较,结果验证了FLOEF的优越性。     

Evaluation of beat noise in OCDMA system with non-Gaussian approximated method

With the development of phase encoding technologies, beat noise becomes one of the most predominant limitations of optical code division multiaccess (OCDMA) systems. In order to analyze beat noises' impact more accurately, a non-Gaussian analysis with consideration of a decision variable's moment generation function is first introduced in this paper to evaluate both the multiaccess interference and the beat noises simultaneously, where prime, secondary, and partial coherent beat noises are discussed in detail. In this paper, the saddle-point approximation (SPA) method is first utilized to investigate beat noise's impact on an OCDMA system. Comparison of probability density functions as well as bit error rates between the proposed method and the traditional Gaussian approximation method is given here. The resultant achievement shows the outstanding performance of SPA on this occasion, which proves the necessity of such a moment generation function-based non-Gaussian analysis.     

Nonparametric trellis equalization in the presence of non-Gaussian interference

We consider the problem of trellis equalization of the intersymbol interference channel in the presence of thermal noise and cochannel interference (CCI). Conventional maximum-likelihood sequence estimation (MLSE) and maximum a posteriori probability (MAP) trellis equalizers treat the sum of noise and interference as additive white Gaussian noise, while CCI is generally a colored non-Gaussian process. We propose a novel nonparametric approach based on the estimation of the probability density function of the noise-plus-interference. Given the availability of a limited volume of data, the density is estimated by kernel-smoothing techniques. The use of a whitening filter in the presence of temporally colored disturbance is also addressed. Simulation results are provided for the global system for mobile communications (GSM), showing a significant performance improvement with respect to the equalizer based on the Gaussian assumption. Major advantages of the proposed strategy are its intrinsic robustness and general applicability to those cases where accurate modeling of the interference is difficult or a model is not available.     

一种MIMO雷达非高斯杂波中的信号分离方法

针对传统匹配滤波方法对非高斯相关杂波下MIMO雷达信号分离性能下降的问题,本文基于线性约束最小功率波束形成器原理,给出了一种适用于非高斯相关杂波条件下的MIMO雷达自适应信号分离算法。该方法将需要分离的发射信号以外的信号和相关杂波作为干扰,利用接收信号的分数低阶统计量在线性约束最小功率准则下导出了滤波器权系数,实现了非高斯相关杂波中对信号实时有效的分离。最后采用本文方法在SG-Alpha稳定分布杂波背景下进行了仿真实验,结果表明,本文方法可有效实现非高斯相关杂波中的MIMO雷达信号分离。      

Robust adaptive array for wireless communications

In the application of a receiver antenna array to wireless communications, a known signal preamble is used for estimating the propagation vector at the beginning of each data frame. The estimated propagation vector is then used in linear combining of array inputs for interference suppression and demodulation of a desired user's information data stream. Since the training preamble is usually very short, conventional training methods, which estimate the propagation vector based solely on the training preamble, may incur large estimation errors. In many wireless channels, the ambient noise is known to be decidedly non-Gaussian, due to impulsive phenomena. The conventional training methods may suffer further from such impulsive noise. Moreover, performance of linear combining techniques can degrade substantially in the presence of impulsive noise. We first propose a new technique for propagation vector estimation which exploits the whole frame of the received signal. It is shown that as the length of the signal frame tends to infinity, in the absence of noise, this method can recover the propagation vector of the desired user exactly, given a small number of training symbols for that user. We then develop robust techniques for propagation vector estimation and array combining in the presence of impulsive noise. These techniques are nonlinear in nature and are based on the M-estimation method. It is seen that the proposed robust methods offer performance improvement over linear techniques in non-Gaussian noise, with little attendant increase in computational complexity. Finally, we address the extension of the proposed techniques to dispersive channels with intersymbol interference     

Maximum-likelihood synchronization of a single user forcode-division multiple-access communication systems

Code-division multiple access (CDMA) has emerged as an access protocol well-suited for voice and data transmission. One significant limitation of the conventional CDMA system is the near-far problem where strong signals interfere with the detection of a weak signal. Multiuser detectors assume knowledge of all of the modulation waveforms and channel parameters, and exploit this information to eliminate multiple-access interference (MAI) and to achieve near-far resistance. A major problem in practical application of multiuser detection is the estimation of the signal and channel parameters in a near-far limited system. We consider maximum-likelihood estimation of users delay, amplitude, and phase in a CDMA communication system. We present an approach for decomposing this multiuser estimation problem into a series of single-user problems. In this method the interfering users are treated as colored non-Gaussian noise. The observation vectors are preprocessed to be able to apply a Gaussian model for the MAI. The maximum-likelihood estimate (MLE) of each user's parameters based on the processed observation vectors becomes tractable. The estimator includes a whitening filter derived from the sample covariance matrix which is used to suppress the MAI, thus yielding a near-far resistant estimator     

Performance evaluation of optical fiber transmission systems

A method is presented for evaluating of error probability for optical-fiber communication systems in the present of intersymbol interference and additive noise. It is based on deriving a best approximation, in a minimax sense, for the cumulative distribution function of the additive noise. The method takes into account the avalanche photodetector's non-Gaussian shot noise statistics. The additive noise is also not constrained to be Gaussian. Examples are presented for comparison to previously published techniques     

A new statistical model for Markovian classification of urban areas in high-resolution SAR images

We propose a classification method suitable for high-resolution synthetic aperture radar (SAR) images over urban areas. When processing SAR images, there is a strong need for statistical models of scattering to take into account multiplicative noise and high dynamics. For instance, the classification process needs to be based on the use of statistics. Our main contribution is the choice of an accurate model for high-resolution SAR images over urban areas and its use in a Markovian classification algorithm. Clutter in SAR images becomes non-Gaussian when the resolution is high or when the area is man-made. Many models have been proposed to fit with non-Gaussian scattering statistics (K, Weibull, Log-normal, Nakagami-Rice, etc.), but none of them is flexible enough to model all kinds of surfaces in our context. As a consequence, we use a mathematical model that relies on the Fisher distribution and the log-moment estimation and which is relevant for one-look data. This estimation method is based on the second-kind statistics, which are detailed in the paper. We also prove its accuracy for urban areas at high resolution. The quality of the classification that is obtained by mixing this model and a Markovian segmentation is high and enables us to distinguish between ground, buildings, and vegetation.     

贝塔混合模型的变分贝叶斯学习及应用

贝塔混合模型（Beta Mixture Model,BMM）是一种重要的非高斯概率模型,常用于有界数据的统计分析.但是由于其表达式复杂,BMM的参数估计比较困难.针对该问题,本文提出一种高效的变分贝叶斯学习方法进行参数估计.该方法采用形式简单的自由分布,通过不断最大化初始变分目标函数的下界,迭代逼近得到真实的贝叶斯后验分布.在合成数据集与实际数据集上进行实验,实验结果证明了所提出算法的有效性和可行性.     

Performance of RS-BCH Concatenated Codes and BCH Single-Stage Codes on an Interference Satellite Channel

In this correspondence, a model is analyzed that was designed to study interference on satellite channels. We developed this model to obtain performance results for a coherent phase-shift keyed (CPSK) system in which RS-BCH concatenated codes and BCH singlestage codes are applied to a satellite channel corrupted by cochannel interference. These results make use of earlier work on performance analysis of anm-phase CPSK system operating in the presence of random Gaussian noise and non-Gaussian interference. Earlier work on performance evaluation of concatenated codes on an equierror channel is also used. Our model incorporates features that account for the burst behavior of the interference sources. Results indicate that the use of RS-BCH concatenated coding provides significant performance improvement over no coding as well as single-stage BCH coding.     

Time-varying ARMA stable process estimation using sequential Monte Carlo

Various time series data in applications ranging from telecommunications to financial analysis and from geophysical signals to biological signals exhibit non-stationary and non-Gaussian characteristics. α-Stable distributions have been popular models for data with impulsive and non-symmetric characteristics. In this work, we present time-varying autoregressive moving-average α-stable processes as a potential model for a wide range of data, and we propose a method for tracking the time-varying parameters of the process with α-stable distribution. The technique is based on sequential Monte Carlo, which has assumed a wide popularity in various applications where the data or the system is non-stationary and non-Gaussian.     

Approaches to modelling FM video spectra for satellite signalinterference prediction

Three approaches to modelling FM video spectra which include energy dispersal are described. The first method is an analytical approach minimizing computer processing time. The second gives a more complete solution using numerical methods. In the third approach a statistical model is proposed with particular application to interference analysis. Each approach has both advantages and disadvantages, the most suitable method must be chosen depending on the application and availability of data. With limited data samples it is probable that one of the first two techniques can be used. The analytical approach minimizes computation time but is only effective around the carrier. The numerical analysis provides a more complete approach but requires substantial computer processing. Hence, for CCI (cochannel interference) analysis, the analytical method is acceptable. For an ACI (adjacent-channel interference) problem, the FFT (fast Fourier transform) approach is more realistic. The final method relies on the existence of the system to enable extensive data collection to be carried out     

New fractionally spaced recursive polynomials perceptron model for adaptive M-QAM digital mobile radio reception

A new fractionally spaced recursive polynomial perceptron (FSRPP) model for adaptive M-QAM digital mobile radio reception is described, which can adaptively equalise the multipath fading channels and reject non-Gaussian cochannel interference (CCI) simultaneously. Experimental results obtained are satisfactory, which shows that FSRPP with lower computational burden and faster convergence rate can perform more efficiently than polynomial perceptron (PP) and multilayer perceptron (MLP) in the presence of multipath fading of channels and non-Gaussian interference.<>     

基于盲源分离方法的工频干扰消除

生物医学信号检测和处理过程中,50Hz(或60Hz)工频干扰的消除一直非常重要的技术问题。本文提出了一种基于独立分量分析的工频干扰消除新方法。我们用该方法对模拟数据和实测脑电(EEG)信号中的工频干扰进行消除,并与自适应滤波工频干扰消除方法进行了比较。实验表明,本文所提出的方法在工频干扰消除上具有一定的优势。     

激光高度计接收脉冲回波信号分析器

激光高度计接收脉冲回波是叠加有噪声的多重非高斯波形,有效提取非高斯波形的统计参量对于反演目标高度和种类信息是十分关键的。基于接收脉冲回波信号的特点,利用广义高斯函数模型完成接收脉冲回波信号的数学建模。通过对接收脉冲回波的平滑滤波和初始参数获取,并采用非线性最小二乘算法,开发了一种提取接收脉冲回波统计参量的波形分析器。利用波形分析器对仿真的回波波形进行了处理,结果表明,对于15 dB的单个广义高斯波形,其统计参量的最大提取误差不超过1%。随着广义高斯分量个数的增加以及回波信噪比的降低,统计参量的提取误差有所增加。利用波形分析器能够有效地提取回波波形的统计参量,为反演目标信息提供数据依据。