Autocorrelation Matrix Research Articles

Subspace Averaging of Auditory Evoked Potentials.

The auditory evoked potential (AEP) is an electric potential generated in the brain in response to auditory stimuli. It has clinical importance in the detection of newborn infant hearing loss, among other applications. The signal-to-noise ratio (SNR) of the AEP is low, so signal averaging is typically employed to estimate it. Often, thousands of trials must be averaged before a sufficiently high SNR estimate is obtained. In this research, we have developed an AEP averaging method called subspace averaging. The subspace averaging method projects onto the signal subspace: the span of the principal eigenvectors of the signal autocorrelation matrix. The signal subspace has low dimensionality and captures the key features of the signal. Also, we introduce a new SNR estimator for AEP trials. Using our estimator, we compare SNR estimates of conventional averaging and subspace averaging. The subspace average has higher SNR compared to the conventional average.

Reduced order model analysis method via proper orthogonal decomposition for nonlinear transient heat conductionproblems

A reduced order analysis method is proposed to solve the nonlinear transient heat conduction problems with temperature-dependent conductivity of material by using the proper orthogonal decomposition (POD) model reduction method and the finite element method. Firstly, the POD basis vectors are developed by calculating eigenvectors of an autocorrelation matrix composed of snapshots, which clustered by the given results of obtained from experiments or numerical methods for the linear transient heat transfer problem. Secondly, the finite element discrete scheme of the nonlinear transient heat conduction problem is reduced the order by using the POD basis vectors of the linear problem, and a lower order ordinary differential equation system of the reduced order model of the nonlinear transient heat conduction problem is obtained. Finally, the value of temperature field at each time is obtained by solving the reduced-order ordinary differential equations. Several numerical examples are given to verify the effectiveness of the proposed method. The results show that the proposed method has a good accuracy and the computational efficiency can be improved by 1–2 orders of magnitude.

An Analysis and Implementation of the Harris Corner Detector

In this work, we present an implementation and thorough study of the Harris corner detector. This feature detector relies on the analysis of the eigenvalues of the autocorrelation matrix. The algorithm comprises seven steps, including several measures for the classification of corners, a generic non-maximum suppression method for selecting interest points, and the possibility to obtain the corners position with subpixel accuracy. We study each step in detail and propose several alternatives for improving the precision and speed. The experiments analyze the repeatability rate of the detector using different types of transformations.

Stress correlations in glasses.

We rigorously establish that, in disordered three-dimensional isotropic solids, the stress autocorrelation function presents anisotropic terms that decay as 1/r3 at long-range, with r being the distance, as soon as local stress fluctuations are normal, by which we mean that the fluctuations of stress, as averaged over spherical domains, decay as the inverse domain volume. Since this property is required for macroscopic stress to be self-averaging, it is expected to hold generically in all glasses and we thus conclude that the presence of 1/r3 stress correlation tails is the rule in these systems. Our proof follows from the observation that, in an infinite medium, when both material isotropy and mechanical balance hold, (i) the stress autocorrelation matrix is completely fixed by just two radial functions: the pressure autocorrelation and the trace of the autocorrelation of stress deviators; furthermore, these two functions (ii) fix the decay of the fluctuations of sphere-averaged pressure and deviatoric stresses with the increasing sphere volume. Our conclusion is reached because, in view of (ii), the normal decay of stress fluctuations is only compatible with both the pressure autocorrelation and the trace of the autocorrelation of stress deviators being integrable; in turn, due to the precise analytic relation (i) fixed by isotropy and mechanical balance, this condition demands the spatially anisotropic stress correlation terms to decay as 1/r3 at long-range.

3D Target Localization of Modified 3D MUSIC for a Triple-Channel K-Band Radar.

In this paper, a modified 3D multiple signal classification (MUSIC) algorithm is proposed for joint estimation of range, azimuth, and elevation angles of K-band radar with a small 2 × 2 horn antenna array. Three channels of the 2 × 2 horn antenna array are utilized as receiving channels, and the other one is a transmitting antenna. The proposed modified 3D MUSIC is designed to make use of a stacked autocorrelation matrix, whose element matrices are related to each other in the spatial domain. An augmented 2D steering vector based on the stacked autocorrelation matrix is proposed for the modified 3D MUSIC, instead of the conventional 3D steering vector. The effectiveness of the proposed modified 3D MUSIC is verified through implementation with a K-band frequency-modulated continuous-wave (FMCW) radar with the 2 × 2 horn antenna array through a variety of experiments in a chamber.

Super-resolution Doppler beam sharpening method using fast iterative adaptive approach-based spectral estimation

Doppler beam sharpening (DBS) is a critical technology for airborne radar ground mapping in forward-squint region. In conventional DBS technology, the narrow-band Doppler filter groups formed by fast Fourier transform (FFT) method suffer from low spectral resolution and high side lobe levels. The iterative adaptive approach (IAA), based on the weighted least squares (WLS), is applied to the DBS imaging applications, forming narrower Doppler filter groups than the FFT with lower side lobe levels. Regrettably, the IAA is iterative, and requires matrix multiplication and inverse operation when forming the covariance matrix, its inverse and traversing the WLS estimate for each sampling point, resulting in a notably high computational complexity for cubic time. We propose a fast IAA (FIAA)-based super-resolution DBS imaging method, taking advantage of the rich matrix structures of the classical narrow-band filtering. First, we formulate the covariance matrix via the FFT instead of the conventional matrix multiplication operation, based on the typical Fourier structure of the steering matrix. Then, by exploiting the Gohberg–Semencul representation, the inverse of the Toeplitz covariance matrix is computed by the celebrated Levinson–Durbin (LD) and Toeplitz-vector algorithm. Finally, the FFT and fast Toeplitz-vector algorithm are further used to traverse the WLS estimates based on the data-dependent trigonometric polynomials. The method uses the Hermitian feature of the echo autocorrelation matrix R to achieve its fast solution and uses the Toeplitz structure of R to realize its fast inversion. The proposed method enjoys a lower computational complexity without performance loss compared with the conventional IAA-based super-resolution DBS imaging method. The results based on simulations and measured data verify the imaging performance and the operational efficiency.

Frequency-Domain Joint Channel Estimation and Decoding for Faster-Than-Nyquist Signaling

Faster-than-Nyquist (FTN) signaling has attracted a lot of attentions for the fifth-generation (5G) cellular communication systems. However, low-complexity receiver design for FTN signaling becomes challenging. In this paper, we develop frequency-domain joint channel estimation and decoding methods for FTN signaling transmitting systems over frequency-selective fading channels. To deal with the colored noise inherent in FTN signaling, we propose to approximate the corresponding autocorrelation matrix by a circulant matrix, the special eigenvalue decomposition of which facilitates an efficient fast Fourier transform operation and decoupling the noise in frequency domain. Through a specific partition of the received symbols, many independent estimates are obtained and combined to further improve the accuracy of the channel estimation and data detection. Moreover, instead of assuming the data symbols to be Gaussian random variables, a generalized approximated message passing-based equalization is developed and embedded in the turbo iterations between the channel estimation and the soft-in soft-out decoder. Simulation results show that the proposed algorithm outperforms the cyclic prefix-based and overlap-based frequency-domain equalization methods. With the proposed algorithms, FTN signaling reaches up to 67% higher transmission rate compared to the Nyquist counterpart without substantially consuming more transmitter energy per bit, and the overall complexities grow logarithmically with the length of the observations.

A Divergence Median-based Geometric Detector with A Weighted Averaging Filter

To overcome the performance degradation of the classical fast Fourier transform (FFT)-based constant false alarm rate detector with the limited sample data, a divergence median-based geometric detector on the Riemannian manifold of Heimitian positive definite matrices is proposed in this paper. In particular, an autocorrelation matrix is used to model the correlation of sample data. This method of the modeling can avoid the poor Doppler resolution as well as the energy spread of the Doppler filter banks result from the FFT. Moreover, a weighted averaging filter, conceived from the philosophy of the bilateral filtering in image denoising, is proposed and combined within the geometric detection framework. As the weighted averaging filter acts as the clutter suppression, the performance of the geometric detector is improved. Numerical experiments are given to validate the effectiveness of our proposed method.

The Proposed Quantile Regression Model For Longitudinal Data

The observed data are often from subjects measured repeatedly over time. This kind of data with repeated responses is known as longitudinal data. Such data are from the subjects measured repeatedly over time and correlation may arise between measurements from the same topical subject. One of the advantages of the longitudinal data is that one can be able to specify the individual patterns of change for each subject. In this thesis, we develop a more general linear quantile regression model by extending the generalized quasi-likelihood method under mean regression to the quantile regression. Because the usage of the general stationary auto-correlation matrix, we do not need to specify any particular working correlation structure between repeated measurements. We can prove that parameter estimators obtained by our proposed method are consistent and asymptotically normal. By applying the induced smoothing method, we can introduce several methods to estimate quantile regression models built on longitudinal datasets.

Fast Estimation Method of Space-Time Two-Dimensional Positioning Parameters Based on Hadamard Product

The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA) and direction of arrival (DOA) parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC) algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM) system, and the Cramer-Rao bound (CRB) is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and 2D matrix pencil (MP) algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.

Chaotic Nonlinear Encryption Scheme for CPAs Resistance and PAPR Reduction in OFDM-PON

In this letter, a chaos-based nonlinear encryption scheme is presented to enhance the physical layer security and reduce the peak-to-average power ratio (PAPR) in an orthogonal frequency division multiplexing passive optical network (OFDM-PON). A four-dimensional (4D) hyper chaotic system is utilized to generate the chaotic binary sequences and construct the nonlinear substitution boxes (S-boxes). With the help of these S-boxes, nonlinear transformation bit data are generated through a cyclic XOR operation with chaotic binary data to improve the resistance against chosen-plaintext attacks (CPAs). A specially designed chaotic constant amplitude zero autocorrelation matrix is used to reduce the PAPR and allow for encryption. We verify the resistance against CPAs with completely dynamic cipher texts in an ~10-Gb/s encrypted OFDM-PON transmission over a distance of 25 km. Compared with the standard OFDM-PON, our proposed scheme achieves ~2.8-dB PAPR reduction, which compensates for any sensitivity deterioration.

Robust adaptive beamforming of coherent signals in the presence of the unknown mutual coupling

A new method based on the matrices reconstruction is proposed to deal with coherent signals in the presence of the unknown mutual coupling. By using a novel expression of the spatial covariance matrix in the presence of mutual coupling, the interference-plus-noise covariance matrix and the desired signal covariance matrix can be reconstructed via estimating the autocorrelation matrix of the signal envelope with unknown mutual coupling in an iteration process. Based on the criterion of the maximum output signal-to-interference-plus-noise ratio, a subspace orthogonal to the interference subspace can be then found out by using these reconstructed matrices. Therefore, the desired signal and the noise can be let out by mapping this estimated subspace to the observed data. Finally, an optimal weight vector can be obtained by maximising the output power of the desired signal. The performance of the proposed method is quite close to the optimal beamforming. The simulations demonstrate the effectiveness of the proposed beamformer.

Novel subspace method for frequencies estimation of two sinusoids with applications to vital signals

This study proposes a novel subspace method to estimate frequencies of two sinusoids embedded in noise. The estimation process is basically composed of three main steps. Two principal eigenvectors of the autocorrelation matrix for the received vector are first found. Then, the authors use the elements of these eigenvectors to form a set of linear and non-linear equations to solve an ambiguous matrix linked two signal subspaces which contain the information of frequencies. With the product of the matrix formed from these two eigenvectors and the solved ambiguous matrix, they can finally find the frequencies. In addition, they also combine an interleaving technique with the proposed method to improve the estimation performance for two close sinusoidal frequencies. Simulation results for synthetic data and practical vital signals are used to demonstrate the performance of the proposed method. The demonstrated results show that the proposed method is feasible for frequencies estimation of two sinusoids, and it can be applied to the case of very close sinusoidal frequencies.

Inherent stress correlations in a quiescent two-dimensional liquid: Static analysis including finite-size effects.

After constructing a formalism to analyze spatial stress correlations in two-dimensional equilibrated liquids, we show that the sole conjunction of mechanical balance and material isotropy demands all anisotropic components of the inherent state (IS) stress autocorrelation matrix to decay at long range as 1/r^{2} in the large system size limit. Furthermore, analyzing numerical simulation data for an equilibrated supercooled liquid, we bring evidence that, in finite-sized periodic systems, the autocorrelations of pressure and shear stresses present uniform backgrounds of amplitudes proportional to the inverse cell area. These backgrounds bring relevant contributions to macroscopic IS stress fluctuations, with the consequence that the latter scale as inverse area, yet in an anomalous way, inconsistent with viewing an IS as equivalent, in the thermodynamic limit, to an ensemble of independent finite-sized subsystems. In that sense, ISs are not spatially ergodic.

Matrix spectral factorization for SA4 multiwavelet

In this paper, we investigate Bauer's method for the matrix spectral factorization of an r-channel matrix product filter which is a halfband autocorrelation matrix. We regularize the resulting matrix spectral factors by an averaging approach and by multiplication by a unitary matrix. This leads to the approximate and exact orthogonal SA4 multiscaling functions. We also find the corresponding orthogonal multiwavelet functions, based on the QR decomposition.

AVSF‐based control algorithm of DSTATCOM for distribution system

Recent trends have shown that the power quality has been adversely affected due to increased power electronics based devices at the utility grid in the distribution system. Suppression of harmonics and reactive power current compensation at point of common coupling (PCC) improve the power quality using distribution static compensator (DSTATCOM). The development of new control algorithm based on adaptive Volterra second-order filter (AVSF) for DSTATCOM to extract the fundamental power current components from the polluted load current of non-linear load in distribution system is presented in this study. The AVSF is a combination of linear and non-linear functions of the input signals. Both linear and quadratic functions optimise filter coefficients with fast convergence, which is quite important in the success of an adaptive solution. The proposed algorithm is also related to autocorrelation matrix and step size, which are used for rapid convergence. The performance of proposed algorithm for DSTATCOM is validated through experimental results for unity power factor of AC source and zero voltage regulation of the terminal voltage at PCC.

Time-frequency decomposition of multivariate multicomponent signals

A solution of the notoriously difficult problem of characterization and decomposition of multicomponent multivariate signals which partially overlap in the joint time-frequency domain is presented. This is achieved based on the eigenvectors of the signal autocorrelation matrix. The analysis shows that the multivariate signal components can be obtained as linear combinations of the eigenvectors that minimize the concentration measure in the time-frequency domain. A gradient-based iterative algorithm is used in the minimization process and for rigor, a particular emphasis is given to dealing with local minima associated with the gradient descent approach. Simulation results over illustrative case studies validate the proposed algorithm in the decomposition of multicomponent multivariate signals which overlap in the time-frequency domain.

Adaptive Noise Cancellation Using Noise Dependent Affine Projection Algorithm

In this paper, an improved adaptive noise cancellation approach is proposed for voice communication signals. The method is based on using noise dependent affine projection algorithm ND-APA. A conditionally variable projection order affine projection algorithm APA is developed and tested. The order of the algorithm is changed according to the change in the characteristics of the noise. The eigenvalue spread of the noise autocorrelation matrix is used as a criterion for projection order change. The order of the algorithm is made to vary from 4 to 32 according the value of the spread which changes from less than 5 for white noise to more than 15 for colored noise. The proposed method showed a superior performance as compared to the classical APA, LMS and RLS noise cancelation methods. The technique presented here can be very useful in removing environmental noise in fixed and mobile communication.

A New Turbo Equalizer Conditioned on Estimated Channel for MIMO MMSE Receiver

In this letter, we propose a new equalization scheme based on minimum mean-square error (MMSE) criteria with a channel estimation error. Different from the existing work on linear MMSE receivers, we consider both the a priori information and channel estimation error in the equalizer design, and re-derive the soft output extrinsic information used for the channel decoder. Conditioned on the estimated channel, we developed the new autocorrelation and covariance matrix of the received vector, which are used to derive the equalizer coefficients. One of our major contributions of this letter is a general expression of the MMSE-based turbo equalization to account for both the channel estimation error and the a priori information, which is not presented in the literature. Simulation results show that significant performance improvement can be achieved with the proposed turbo equalizer.

Normalised Spline Adaptive Filtering Algorithm for Nonlinear System Identification

This paper proposed a normalised spline adaptive filtering algorithm to improve the stability of spline adaptive filtering (SAF) algorithm against the eigenvalue spread of the autocorrelation matrix of the input signal. The new adaptive filtering algorithm is based on the normalised least mean square (NLMS) approach and the value range of the learning rate in this algorithm is specified. This algorithm is called SAF-NLMS. In this work, first the derivation of the SAF-NLMS algorithm is given. Second, detailed convergence and the computational complexity analyses are carried out. Finally, the performance of the proposed algorithm is tested according to artificial datasets and real datasets. The achieved results present actually good performance. So, in practical engineering, the algorithm can be used to solve the problem of modeling or identification of nonlinear systems.