Asymptotic performance analysis of ESPRIT, higher order ESPRIT, andvirtual ESPRIT algorithms

In this paper, we present an asymptotic performance analysis of three subspace-based methods for direction of arrival (DOA) estimation-the ESPRIT algorithm using second order statistics, the higher order ESPRIT algorithm using fourth-order cumulants, and the virtual ESPRIT (VESPA) algorithm using fourth-order cumulants. We examine the least-squares version of these algorithms, derive the expressions for the asymptotic variance of the estimated DOAs, and use specific examples to compare the relative performance of the algorithms. Finally, we present Monte Carlo simulations to validate the theoretical analysis     

空间高阶时频分布及虚拟时频ESPRIT算法

基于L-Wignrer分布(LWD),定义了一种全新的空间高阶累积量L-Wigner分布,并利用虚拟时频ESPRIT算法与阵列扩展,提出了一种多个多项式相位信号(PPS)的DOA估计算法.该方法利用平滑的伪WVD分布以实现PPS信号的LWD分布极大地抑制了其中的交叉项并提高了信号时频聚集性.同时,将时频分析与高阶累积量结合,使算法具有虚拟阵列扩展的特点,高分辨高精度的估计了PPS信号的DOA.理论分析和计算机仿真表明该方法具有很好的参数估计性能.     

空间任意阵的多宽带信源定位算法性能研究

针对宽带信号非平稳特性,以及常用宽带DOA估计算法要求信源个数是已知的情况,提出一种新的基于空间任意阵的非平稳信号DOA估计算法。首先,通过短时傅里叶变换将信号转为频域表示,然后构造阵列频域数据模型,最后利用短时功率谱矩阵的联合对角化特性实现宽带信号的波达方向估计。本文对提出的算法进行了理论分析,并在常见阵型（如线阵、十字阵）上进行了仿真和性能分析,仿真结果表明该算法可高分辨率地估计出DOA,并且估计误差小。相对于已有的MUSIC谱估计方法,该算法无需进行信源个数估计,更具实用性。      

Performance analysis of the total least squares ESPRIT algorithm

The asymptotic distribution of the estimation error for the total least squares (TLS) version of ESPRIT is derived. The application to a uniform linear array is treated in some detail, and a generalization of ESPRIT to include row weighting is discussed. The Cramer-Rao bound (CRB) for the ESPRIT problem formulation is derived and found to coincide with the asymptotic variance of the TLS ESPRIT estimates through numerical examples. A comparison of this method to least squares ESPRIT, MUSIC, and Root-MUSIC as well as to the CRB for a calibrated array is also presented. TLS ESPRIT is found to be competitive with the other methods, and the performance is close to the calibrated CRB for many cases of practical interest. For highly correlated signals, however, the performance deviates significantly from the calibrated CRB. Simulations are included to illustrate the applicability of the theoretical results to a finite number of data     

Matrix-based higher order spectral analysis for three-wave couplingprocesses

Composite linear and quadratic systems produce three-wave coupling when stimulated by random phase input sinusoids. Due to the nonlinearity of the system, the output frequencies are arithmetically related to the input. Using third-order cumulant statistics and their associated bispectrum, techniques are devised based on phase-insensitive matrix structures for detection and frequency estimation of coupling frequencies. The separation of the third-order cumulant series into symmetric and skew-symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation. After symmetrization, biphases can be easily extracted as coefficients of the cumulant sequence. Using a generalized eigenvector representation, one can relate symmetric and skew-symmetric bases by a subspace rotation algorithm. Biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew-symmetric matrices. The dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum. The Radon transform procedure is related to bispectral processing through an isotropic radial-slice Volterra filter. The compact third-order Kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation. Simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series     

Distributed source localization using ESPRIT algorithm

A new algorithm based on ESPRIT is proposed for the estimation of the central angle and angular extension of distributed sources. The central angles are estimated using TLS-ESPRIT for both incoherently distributed (ID) and coherently distributed (CD) sources. For CD sources, the extension width is estimated by constructing a one-dimensional (1-D) distributed source parameter estimator (DSPE) spectrum for each source. For ID sources, the extension widths are estimated using the central moments of the distribution. The algorithm can be used for sources with different angular distributions     

On the behavior of current second and higher order blind sourceseparation methods for cyclostationary sources

Most of the second-order (SO) and higher order (HO) blind source separation methods developed in the 1990s aim at blindly separating statistically independent sources that are assumed zero-mean, stationary, and ergodic. Nevertheless, in many situations of practical interest, such as in radiocommunication contexts, the sources are nonstationary and very often (quasi)-cyclostationary (digital modulations). In these conditions, it becomes important to wonder whether the performance of these current SO and HO blind source separation methods, which have been developed for stationary sources, may be affected by the potential nonstationarity of the latter. Limiting the analysis to the SO and fourth-order (FO) cumulant-based blind source separation methods, the purpose of this paper is to bring some answers to this important question through the behavior analysis of the empirical SO and FO cumulants estimator in the presence of zero-mean (quasi)-cyclostationary sources     

用于信号波达方向估计的共轭ESPRIT算法及其性能分析

针对阵列天线的波达方向估计问题,给出了一种新颖的ESPRIT算法--共轭ESPRIT算法(C-ESPRIT).此算法利用阵列单元输出信号的共轭信息,得到整个阵列输出的协方差矩阵,通过对此矩阵的特征分解,并构造运算矩阵,最终求得信号的波达方向.仿真实验表明,C-ESPRIT算法不仅克服了传统ESPRIT算法在阵列单元数与信源数相同时不能可靠测向的不足,并且对信号波达方向的分辨能力和测角精度也显著高于传统的ESPRIT算法,因此,C-ESPRIT算法具有更广泛的适应性和更优越的测向性能.     

Performance of blind equalization with higher order statistics inindoor radio environments

This paper analyzes the performance of blind equalization using the complex cepstrum of third-order moments applied to 4-QAM time division multiple access (TDMA) indoor radio communication systems. In particular, we have modeled a dispersive indoor channel with Rice statistics. We used the blind algorithms to estimate the channel-impulse response, and from this, we computed the equalizer coefficients using a classical minimum mean square error (MMSE) algorithm. In order to evaluate the system performance, we calculated the bit error rate (BER) of a decision feedback equalizer (DFE) that uses a tricepstrum algorithm to estimate the channel-impulse response. The results are compared with those obtained using a least sum of square errors (LSSE) algorithm as a channel estimator and considering the exact channel response. The results obtained show that this kind of blind equalizer performs better than the more classically trained equalizer when Rice channels with a strong direct path and signal-to-noise ratios (SNRs) lower than 20 dB are taken into account. However, some problems relating to the length of time needed for convergence must be solved     

Integral equation analysis for higher order modes and cutofffrequencies of arbitrary profiles

A semianalytical method of analysis for arbitrary weakly guiding circular and noncircular profiles, which has its fundamental basis in perturbation theory and incorporates Green's function and integral equation techniques in a powerful method of analysis possessing extremely high accuracy, is extended to the analysis of higher order modes and cutoff frequencies of arbitrary weakly guiding circular and noncircular profiles. Its accuracy is demonstrated by its application to several weakly guiding profiles, for which the method is found to be extremely accurate (<10^-5%). Furthermore, additional simplifications to the semianalytical method of analysis are presented, which dramatically reduce the number of calculations required for solution     

The new multidimensional time/multi-frequency transform for higher order spectral analysis

A new multidimensional time/multi-frequency higher order spectral(HOS) transform is proposed for transient signals with nonlinear polynomial variation of instantaneous frequency: the short time higher order chirp spectra (HOCS) based on the higher order chirp-Fourier transform and time-domain windowing technique. The proposed transform is compared with the classical multi-frequency HOS based on the Fourier transform. It is shown that the proposed transform is more effective for processing of transient processes in comparison with the classical transform.     

An extended UTD analysis for RCS computations involving higher order curved surfaces

An extended utd (eutd) solution is developed for the scattering and diffraction of high frequency em fields from higher order (polynomial and spline defined) curved surfaces. The new solution is computationally efficient and overcomes the difficulties of the classic go/gtd/utd solutions near ray caustics and caustic terminations. The approach for constructing the eutd solution is based on a spatial domain radiation integral representation for the scattered field which is then reduced using a uniform asymptotic procedure. Further heuristic modifications are also made and correct the go induced current assumption near the shadow boundaries. New uniform reflection, first order edge diffraction, and zero-curvature diffraction coefficients are then derived and involve higher order phase integrals as canonical functions. Numerical results involving third and fourth order polynomial strips are provided and compare favorably with reference moment method results. abs]Fr|Résumé Une théorie uniforme de la diffraction étendue (eutd) est développée pour la diffraction ? un champ électromagnétique à haute fréquence sur des surfaces de courbure complexe. La nouvelle résolution est intéressante du point de vue du temps de calcul et permet ? éviter les difficultés classiques des méthodes gtd/utd près de certaines caustiques. ? approche prise pour la construction de ? eutd est basée sur une représentation intégrate dans le domaine spatial du champ diffracté, réduite par une procédure asymptotique uniforme. Des modifications heuristiques sont faites qui corrigent le courant ? optique géométrique près de la frontière ? ombre. Des expressions uniformes sont alors déduites qui demandent le calcul ? intégrates de termes possédant une phase ? ordre élevé. Des résultats numériques sont donnés et comparés avec ceux obtenus par une méthode des moments.     

Performance of ESPRIT for Estimating Mixtures of Complex Exponentials Modulated by Polynomials

High-resolution (HR) methods are known to provide accurate frequency estimates for discrete spectra. The polynomial amplitude complex exponentials (PACE) model, also called quasi-polynomial model in the literature, was presented as the most general model tractable by HR methods. A subspace-based estimation scheme was recently proposed, derived from the classical ESPRIT algorithm. In this paper, we focus on the performance of this estimator. We first present some asymptotic expansions of the estimated parameters, obtained at the first order under the assumption of a high signal-to-noise ratio (SNR). Then the performance of the generalized ESPRIT algorithm for estimating the parameters of this model is analyzed in terms of bias and variance, and compared to the Cramer-Rao bounds (CRB). This performance is studied in an asymptotic context, and it is proved that the efficiency of undamped single poles estimators is close to the optimality. Moreover, our results show that the best performance is obtained for a proper dimensioning of the data. To illustrate the practical capabilities of the generalized ESPRIT algorithm, we finally propose an application to ARMA filter synthesis, in the context of system conversion from continuous time to discrete time.     

Performance analysis of clustering-based fingerprinting localization systems

Wireless Networks - Localization is highly required to develop the smart-phone based pervasive computing applications. Because of very poor signal strength of global positioning system in indoor...     

高阶曲线矢量有限元方法实现及关键问题

针对传统的直线型高阶矢量基函数对曲边界模拟不好的缺点,研究了基于四面体叠层矢量元的高阶曲线建模技术。系统而显式地分析了三维高阶曲线矢量元的实现过程,探讨了实现过程中的一些关键问题。通过分析一个球形谐振腔,系统比较了各种直线或曲线形式的高、低阶矢量元的性能（如计算精度、条件数等）,并将其用于分析不均匀腔体的谐振问题。计算结果表明：采用曲线元对曲线模型进行建模,在不影响计算效率的情况下,可极大地提高计算精度。     

Improved formulations for higher order absorbing boundaryconditions

New formulations for higher order ABCs are introduced. Third and fourth order ABCs are reduced to first and second order derivatives with each one having one additional integral term. Considerable reductions in computer storage and computational time are achieved     

A quantitative analysis approach for cardiac arrhythmia classification using higher order spectral techniques

Ventricular tachyarrhythmias, in particular ventricular fibrillation (VF), are the primary arrhythmic events in the majority of patients suffering from sudden cardiac death. Attention has focused upon these articular rhythms as it is recognized that prompt therapy can lead to a successful outcome. There has been considerable interest in analysis of the surface electrocardiogram (ECG) in VF centred on attempts to understand the pathophysiological processes occurring in sudden cardiac death, predicting the efficacy of therapy, and guiding the use of alternative or adjunct therapies to improve resuscitation success rates. Atrial fibrillation (AF) and ventricular tachycardia (VT) are other types of tachyarrhythmias that constitute a medical challenge. In this paper, a high order spectral analysis technique is suggested for quantitative analysis and classification of cardiac arrhythmias. The algorithm is based upon bispectral analysis techniques. The bispectrum is estimated using an autoregressive model, and the frequency support of the bispectrum is extracted as a quantitative measure to classify atrial and ventricular tachyarrhythmias. Results show a significant difference in the parameter values for different arrhythmias. Moreover, the bicoherency spectrum shows different bicoherency values for normal and tachycardia patients. In particular, the bicoherency indicates that phase coupling decreases as arrhythmia kicks in. The simplicity of the classification parameter and the obtained specificity and sensitivity of the classification scheme reveal the importance of higher order spectral analysis in the classification of life threatening arrhythmias. Further investigations and modification of the classification scheme could inherently improve the results of this technique and predict the instant of arrhythmia change.     

Modified higher order spectral analysis based TDE algorithm for CFAR signal detection problem

With the conditions of small data size and low Signal-to-Noise Ratio (SNR), the application of Higher Order Statistics (HOS) is restrained not only by its high estimation variance, but also by its low estimation precision. Therefore, a modified HOS based Time Delay Estimation (TDE) algorithm is proposed to overcome these problems. Comparing with the conventional TDE algorithms, the estimation variance is improved greatly. A typical simulation example is completed in order to test the performance of the algorithm proposed, which shows that the proposed algorithm has advantages over the traditional ones in both detection performance and computation efficiency.     

An analysis of the Wigner higher order spectra of multicomponent signals

The analysis of multicomponent signal representation by the Wigner higher order spectra is done. It is shown that the cross-terms can be removed only for an odd order, having equal number of conjugated and nonconjugated terms in the local multidimensional moment function. A method for higher order time-multifrequency analysis that eliminates cross-terms is proposed. This method turns out to be a dual definition of the L-Wigner distribution. The theory is illustrated by the numerical example.