Cyclic Matrix Research Articles

Asynchronous Implementation of Distributed Coordination Algorithms: Conditions Using Partially Scrambling and Essentially Cyclic Matrices

Given a distributed coordination algorithm (DCA) for agents coupled by a network, which can be characterized by a stochastic matrix, we say that the DCA can be asynchronously implemented if the consensus property is preserved when the agents are activated to update their states according to their own clocks. This paper focuses on two central problems in asynchronous implementation of DCA: which class of DCA can be asynchronously implemented, and which other cannot. We identify two types of stochastic matrices, called partially scrambling and essentially cyclic matrices, for which we prove that DCA associated with a partially scrambling matrix can be asynchronously implemented, and there exists at least one asynchronous implementation sequence, which fails to realize consensus for DCA associated with an essentially cyclic matrix.

Encryption and Decryption Using Cycle Square Matrix

A novel approach to encrypt and decrypt the message using key with the help of cyclic square matrix provides the approach applicable for any number of words having more number of characters and longest word. The proposed algorithm is simple but difficult to break the process.

A new method for constructing parity check matrix of QC-LDPC codes based on shortening RS codes for wireless sensor networks

In this paper, a new method to construct parity check matrix of QC-LDPC codes based on shortening RS codes for wireless sensor networks (WSNs) is proposed. The proposed method constructs a basic matrix based on shortening RS codes with two information symbols, then expands the basic matrix optimally utilizing cyclic permutation matrix, so as to obtain the check matrix of quasi-cyclic regular LDPC codes in which the girth is 8 at least, and constructed LDPC codes have good minimum distances. Especially, the basic matrix and its expansion are both fully structured, so it is convenient for hardware implementation. The simulation results show that the QC-LDPC codes constructed by the proposed method have good BER performance and convenient for the hardware design and implementation. Moreover, the simulation results show that WSNs using the constructed QC-LDPC codes have good energy efficiency.

Development of block loading spectrum for car powertrain rig test correlated with customers’ usage

To establish the loading spectrum for rig test of a car powertrain, non-contact torque telemeter is adopted to measure the testing data, including target vehicle transmission shaft torque, rotation speed, and engine rotation speed, under the typical cases of customers’ actual usage. Then, the Process Builder module in Tecware is used to establish the gear split batch-processing model and process the customer data into target rotating rainflow counting cyclic matrix and eliminate the small cyclic loads which have relatively smaller influence on the fatigue life. Next, based on the road percentage and data collected in actual customer survey, the total cumulative damage of 90% customer is calculated according to the Weibull distribution equation, and powertrain damage calculation model for fatigue cumulative damage and its probability distribution function is examined by Kolmogorov–Smirnov. Finally, the customer data are compressed into block loading spectrum which can be identified by the rig test based on the fatigue damage equivalent principle, thus achieving the powertrain rig assembly testing life equivalent to the customers’ usage life. The car powertrain rig test can replace the full-vehicle road test, which efficiently lowers the testing cost and shortens the testing period.

An efficient numerical algorithm for the determinant of a cyclic pentadiagonal Toeplitz matrix

In the past few years, a number of numerical and symbolic algorithms for evaluating the determinants of cyclic pentadiagonal matrices have been developed. In this paper, we present a fast numerical algorithm for the determinant of an n-by-n cyclic pentadiagonal matrix with Toeplitz structure. The algorithm is based upon a certain type of matrix reordering and partitioning, and linear transformation. Some numerical examples are provided, and the results are compared with the ones obtained via Matlab built-in function and two existing algorithms. All of the numerical experiments are performed on a computer with the aid of programs written in Matlab.

A Fundamental LOD-FDTD Method in Cylindrical Coordinates

An efficient implicit finite-difference time-domain (FDTD) algorithm in cylindrical coordinates is developed on the basis of a fundamental locally 1-D scheme. The Sherman–Morrison formula is introduced to treat a cyclic matrix and the image theory is utilized to impose the perfect electric conductor boundary condition. The effectiveness of the present method is investigated through the analysis of a metal disc-type terahertz surface wave splitter. The computation time is found to be reduced to less than half that of the explicit FDTD method, while maintaining a comparable accuracy.

A Novel Complex-Coefficient In-Band Interference Suppression Algorithm for Cognitive Ultra-Wide Band Wireless Sensors Networks.

With the rapid development of wireless communication systems and electronic techniques, the limited frequency spectrum resources are shared with various wireless devices, leading to a crowded and challenging coexistence circumstance. Cognitive radio (CR) and ultra-wide band (UWB), as sophisticated wireless techniques, have been considered as significant solutions to solve the harmonious coexistence issues. UWB wireless sensors can share the spectrum with primary user (PU) systems without harmful interference. The in-band interference of UWB systems should be considered because such interference can severely affect the transmissions of UWB wireless systems. In order to solve the in-band interference issues for UWB wireless sensor networks (WSN), a novel in-band narrow band interferences (NBIs) elimination scheme is proposed in this paper. The proposed narrow band interferences suppression scheme is based on a novel complex-coefficient adaptive notch filter unit with a single constrained zero-pole pair. Moreover, in order to reduce the computation complexity of the proposed scheme, an adaptive complex-coefficient iterative method based on two-order Taylor series is designed. To cope with multiple narrow band interferences, a linear cascaded high order adaptive filter and a cyclic cascaded high order matrix adaptive filter (CCHOMAF) interference suppression algorithm based on the basic adaptive notch filter unit are also presented. The theoretical analysis and numerical simulation results indicate that the proposed CCHOMAF algorithm can achieve better performance in terms of average bit error rate for UWB WSNs. The proposed in-band NBIs elimination scheme can significantly improve the reception performance of low-cost and low-power UWB wireless systems.

Decomposition of Multi-Channel Intramuscular EMG Signals by Cyclostationary-Based Blind Source Separation.

We propose a novel decomposition method for electromyographic signals based on blind source separation. Using the cyclostationary properties of motor unit action potential trains (MUAPt), it is shown that the MUAPt can be decomposed by joint diagonalization of the cyclic spatial correlation matrix of the observations. After modeling the source signals, we provide the proof of orthogonality of the sources and of their delayed versions in a cyclostationary context. We tested the proposed method on simulated signals and showed that it can decompose up to six sources with a probability of correct detection and classification >95%, using only eight recording sites. Moreover, we tested the method on experimental multi-channel signals recorded with thin-film intramuscular electrodes, with a total of 32 recording sites. The rate of agreement of the decomposed MUAPt with those obtained by an expert using a validated tool for decomposition was >93%.

DOA Estimation With Enhanced DOFs by Exploiting Cyclostationarity

Many modulated signals exhibit a cyclostationarity property, which has been applied in direction of arrival estimation due to its immunity to interference and noise. In this paper, we focus on how this cyclostationarity can be effectively integrated with the spatial dimension to enhance both the degrees of freedom and the accuracy of DOA estimation. First, for narrowband signal case, by vectorizing the second-order cyclic correlation matrix (instead of the conventional zero-lag covariance matrix), one can directly generate an augmented virtual array with sensors at positions defined by the difference coarray of the physical array. Then for wideband signal case, two additional fractional factors are introduced so that the vectorized cyclic correlation matrix can be viewed as a single snapshot received signal from an array with sensors at positions defined by the fractional weighted difference coarray. Due to the fact that cyclic correlation matrices, as special second-order statistics, allow us to obtain more degrees of freedom, the proposed two virtual array models can resolve $O(N^2)$ sources by using a sparse linear array consisting of only $N$ physical sensors (e.g., nested/coprime array). Furthermore, a scheme of multipseudosampling is proposed in order to reduce the sensitivity to noise and parameter. The proposed models can be considered as an extension of difference coarray perspective via the combination of cyclic frequency and temporal lag. In the end, numerical simulation results validate the effectiveness of the proposed models.

NUMERICAL RESEARCH ON THE THREE-DIMENSIONAL FIBER ORIENTATION DISTRIBUTION IN PLANAR SUSPENSION FLOWS

Abstract - To describe flow-induced fiber orientation, the Fokker-Planck equation is widely applied in the processing of composites and fiber suspensions. The analytical solution only exists when the Peclet number is infinite. So developing a numerical method covering a full range of Peclet number is of great significance. To accurately solve the Fokker-Planck equation, a numerical scheme based on the finite volume method is developed. Using spherical symmetry, the boundary is discretized and formulated into a cyclic tridiagonal matrix which is further solved by the CTDMA algorithm. To examine its validity, benchmark tests over a wide range of Peclet number are performed in a simple shear flow. For Pe=∞, the results agree well with the analytical solutions. For the other Pe numbers, the results are compared to results available in the literature. The tests show that this algorithm is accurate, stable, and globally conservative. Furthermore, this algorithm can be extended and used to predict the three-dimensional orientation distribution of complex suspension flows.

Robust Cyclic MUSIC Algorithm for Finding Directions in Impulsive Noise Environment

This paper addresses the issue of direction finding of a cyclostationary signal under impulsive noise environments modeled byα-stable distribution. Sinceα-stable distribution does not have finite second-order statistics, the conventional cyclic correlation-based signal-selective direction finding algorithms do not work effectively. To resolve this problem, we define two robust cyclic correlation functions which are derived from robust statistics property of the correntropy and the nonlinear transformation, respectively. The MUSIC algorithm with the robust cyclic correlation matrix of the received signals of arrays is then used to estimate the direction of cyclostationary signal in the presence of impulsive noise. The computer simulation results demonstrate that the two proposed robust cyclic correlation-based algorithms outperform the conventional cyclic correlation and the fractional lower order cyclic correlation based methods.

On determinants of cyclic pentadiagonal matrices with Toeplitz structure

Cyclic pentadiagonal matrices with Toeplitz structure have received tremendous attention in recent years. In the current paper, we present a block upper triangular transformation of the cyclic pentadiagonal Toeplitz matrices. By using the transformation, the determinant of an n-by-n cyclic pentadiagonal Toeplitz matrix can be readily evaluated since one just needs to compute the determinant of a 4-by-4 matrix obtained from the transformation. In addition, an efficient numerical algorithm of O(n) is derived for computing nth order cyclic pentadiagonal Toeplitz determinants. Some numerical experiments are given to show the performance of the proposed algorithm.

An Energy-Preserving Wavelet Collocation Method for General Multi-Symplectic Formulations of Hamiltonian PDEs

AbstractIn this paper, we develop a novel energy-preserving wavelet collocation method for solving general multi-symplectic formulations of Hamiltonian PDEs. Based on the autocorrelation functions of Daubechies compactly supported scaling functions, the wavelet collocation method is conducted for spatial discretization. The obtained semi-discrete system is shown to be a finite-dimensional Hamiltonian system, which has an energy conservation law. Then, the average vector field method is used for time integration, which leads to an energy-preserving method for multi-symplectic Hamiltonian PDEs. The proposed method is illustrated by the nonlinear Schrödinger equation and the Camassa-Holm equation. Since differentiation matrix obtained by the wavelet collocation method is a cyclic matrix, we can apply Fast Fourier transform to solve equations in numerical calculation. Numerical experiments show the high accuracy, effectiveness and conservation properties of the proposed method.

Probing maximal zero textures with broken cyclic symmetry in inverse seesaw

Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry (Z3) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry invariant form of the constituent matrices. In the first one we consider explicit cyclic symmetry in the neutrino sector of the Lagrangian which dictates the emerged effective neutrino mass matrix (mν) to be symmetry invariant and hence leads to a degeneracy in masses. We then consider explicit breaking of the symmetry through a dimensionless parameter ϵ′ to remove the degeneracy. It is seen that the method doesn't support the current neutrino oscillation global fit data even after considering the correction from cyclic symmetry invariant charged lepton mass matrix (ml) unless the breaking parameter is too large. In the second method, we assume the same forms of the neutrino mass matrices, however, symmetry is broken in the charged lepton sector. All the structures of the mass matrices are now dictated by an effective residual symmetry of some larger symmetry group in the Lagrangian. For illustration, we exemplify a toy model based on softly broken A4 symmetry group which leads to one of the combinations of ml, mD, MRS and μ to generate effective mν. All the emerged mass matrices predict a constraint range of the CP violating phases and atmospheric mixing angle along with an inverted hierarchical structure of the neutrino masses. Further, significant predictions on ββ0ν decay parameter |m11| and the sum of the three light neutrino masses (Σimi) are also obtained.

Efficient Hardware Architecture for Cyclostationary Detector

Cognitive radio is one of the modern techniques which is evolved for utilising the unused spread spectrum effectively in wireless communication. In cognitive radio system the foremost concept is sensing the holes (spaces) in the frequency spectrum allotted and it facilitates a way that how effectively and efficiently the bandwidth is used by finding the spectrum holes in a designated spectrum. There are various methods available for sensing the spectrum and one such a sensing method is cyclostationary detection. The method of cyclostationary feature mainly focuses on detecting whether the primary user is present or absent. The threshold of a signal is calculated by cyclic cross-periodogram matrix of the corresponding signal to determine the presence of signal or noise. The difficulty in evaluating the targeted threshold is evaded by training an artificial neural network by extracted cyclostationary feature vectors which are obtained by FFT accumulation method. This paper proposes a hardware architecture for cyclostationary detection.

Generating binary diffusion layers with maximum/high branch numbers and low search complexity

In this paper, we propose a new method to generate n × n binary matrices for n = ki¾ź2t where k and t are positive integers with a maximum/high of branch numbers and a minimum number of fixed points by using 2t×2t Hadamard almost maximum distance separable matrices and k × k cyclic binary matrix groups. By using the proposed method, we generate n × n for n = 6, 8, 12, 16, and 32 binary matrices with a maximum of branch numbers, which are efficient in software implementations. The proposed method is also applicable with m × m circulant matrices to generate n × nfor n = ki¾źm binary matrices with a maximum/high of branch numbers. For this case, some examples for 16 × 16, 48 × 48, and 64 × 64 binary matrices with branch numbers of 8, 15, and 18, respectively, are presented. Copyright © 2016 John Wiley & Sons, Ltd.

Efficient Hardware Architecture for Cyclostationary Detector

Objectives:Cognitive radio is evolved for utilising the unused spread spectrum effectively in wireless communication. The foremost concept is sensing the holes (white spaces) in the frequency spectrum allotted and it facilitates a way that how effectively and efficiently the bandwidth is used.Methods/Analysis:There are various methods available for sensing the spectrum and one such a sensing method is cyclostationary detection. The method of cyclostationary feature mainly focuses on detecting whether the primary user is present or absent. By using cyclic cross-periodogram matrix, the calculation of threshold of a signal is carried out to find the existence of noise or signal. Findings:The difficulty in evaluating the targeted threshold is evaded by training an artificial neural network by extracted cyclostationary feature vectors which are obtained by FFT accumulation method. Novelty /Improvement:This paper proposes hardware architecture for cyclostationary detection.

A blind signal‐to‐jamming‐plus‐noise ratio estimation based on second‐order cyclostationarity under typical tone‐jamming and its CRLB

SummaryIn this paper, a blind signal‐to‐jamming‐plus‐noise ratio (SJNR) estimation under typical tone‐jamming is proposed in a Rayleigh fading channel. Based on the differences among communication signal, jamming, and noise in cyclostationarity, the proposed algorithm obtained SJNR values by using different parts of the cyclic autocorrelation matrix of received signals and applying the minimum square error (MSE) method to estimate the communication signal power and jamming‐plus‐noise power, respectively. Through deriving the Cramer–Rao lower bound (CRLB) for the SJNR estimation, the normalized MSE performance is examined. Simulation results show that the proposed estimation performs better than the subspace‐based eigenvalue decomposition estimation on a normalized estimation bias, and its normalized MSE performance is also closer to CRLB. Copyright © 2016 John Wiley & Sons, Ltd.

Design of (4, 8) Binary Code with MDS and Zigzag-Decodable Property

Dedicated to network code structured distributed storage system, a novel (4, 8) storage code is designed. The code possesses the following properties: operation within binary field , maximum distance separable property, zigzag decodable, requiring symmetric storage overhead among multiple storage nodes, and requiring little storage overhead . In the design of such a storage code, we first let original packets shift to the right by several bits and then add them together within binary field in bitwise manner . We propose a smart design on a cyclic matrix that represents the number of bits shifted by those packet. Existing works do not hold these properties simultaneously , which have the drawback of high encoding and decoding complexity, large storage overhead, and complicated storage room allocation procedure, etc.

A comparative study of four low-Reynolds-number k-ε turbulence models for periodic fully developed duct flow and heat transfer

ABSTRACTIn this study, streamwise-periodic fully developed turbulent flow and heat transfer in a duct is investigated numerically. The governing equations are solved by using the finite-control-volume method together with nonuniform staggered grids. The velocity and pressure terms of the momentum equations are solved by the SIMPLE algorithm. A cyclic tri-diagonal matrix algorithm (TDMA) is applied in order to increase the convergence rate of the numerical solution. Four versions of the low-Reynolds-number k-ε model are used in the analysis: Launder-Sharma (1974), Lam-Bremhorst (1981), Chien (1982), and Abe-Kondoh-Nagano (1994). The results obtained using the models tested are analyzed comparatively against some experimental results given in the literature. It is discussed that all the models tested failed in the separated region just behind the ribs, where the turbulent stresses are underpredicted. The local Nusselt numbers are overpredicted by all the models considered. However, the Abe-Kondoh-Nagano low-Re k-ε model presents more realistic heat transfer predictions.