Time-domain Matrix Research Articles

Orthogonal Time Frequency Space Detection via Low-Complexity Expectation Propagation

Orthogonal time frequency space (OTFS) can provide better error performance than orthogonal frequency division modulation in the high-speed scenario. However, the two-dimensional convolution between the information-bearing symbols and the channel response in the delay-Doppler domain induces high-complexity detection, which hinders the implementation of the OTFS. In this paper, expectation propagation (EP) is introduced in the OTFS system to improve the reliability compared to the message passing approaches. The low-complexity EP detection with a log-linear order is proposed by observing the sparsity and the block quasi-banded matrix structure of the time-domain matrix. The exploitation of the lower-upper factorization for the banded matrix, the forward or the back substitution algorithm for the lower or the upper triangular matrices reduces the complexity of the large-scale matrix inversion involved in the EP detection from a cubic order to a linear order. The error performance of the proposed scheme is further analyzed by utilizing the state evolution and discussed under the different frame sizes. Moreover, the proposed low-complexity detector is then explored together with the likelihood decoder in an iterative manner to further improve the reliability of the proposed receiver. Finally, the better error performance and the lower computational complexity of the proposed receiver are validated by the numerical results.

A high-precision harmonic distortion measurement algorithm and its system design based on time-domain matrix operations

In this paper, a harmonic distortion measurement algorithm and its system design based on time-domain matrix operations are proposed, which can quickly calculate the harmonic amplitudes, phases and total harmonic distortion of a signal. To realize the calculation of harmonic signal parameters in the time domain, we proposed a method to convert the nonlinear function representing the signal into a linear function, constructed a matrix equation, and solved the equation by the row transformation method, which significantly reduced the complexity of the algorithm. Finally, based on the proposed algorithm, a system design was implemented by the digital signal processing theory, and the measurements showed that the system achieves an amplitude error of nearly 1% and a THD error of less than 0.3% when measuring the generated 10 kHz fundamental with 5-order harmonics. The system can be used to measure and calculate the amplitudes and THD of harmonic distortion signals with high precision.

MuSpel-Fi: Multipath Subspace Projection and ELM-Based Fingerprint Localization

This letter proposes a multipath subspace projection and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extreme learning machine</i> (ELM)-based indoor fingerprint localization algorithm called MuSpel-Fi, where the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">channel state information</i> (CSI) is utilized as the raw data to establish fingerprints. In this algorithm, the CSI is firstly organized into a time-domain matrix and then is projected into a subspace. This processing not only preserves the channel multipath information as much as possible, but also reduces the data dimension. Based on the reduced dimension projected data, the ELM network is exploited to implement the fingerprint localization. Considering the limited performance of a single ELM network, multiple ELM networks are jointly optimized to improve the localization performance. The experimental results demonstrate that the proposed MuSpel-Fi algorithm has higher positioning accuracy than traditional ones.

Time‐domain analysis of parameters in the fitting of multiport frequency‐dependent system through matrix pencil method

AbstractIn this letter, in this process of using matrix pencil method (MPM) to perform the equivalent of the multiport frequency‐dependent system, a modified MPM is proposed to realize the solutions of common poles and residue matrix in time domain. In this technique, the frequency domain data of all ports are transformed into the time domain matrix vectors by IFFT. Then, the time domain matrix vectors are superimposed into a single vector, which is analyzed by the MPM to generate a common set of poles. The residue matrix is obtained by using the least square method to solve the equation consisting of the common poles and the time domain matrix vectors. The fast evaluation of the frequency domain data of the multiport frequency‐dependent system can be thus completed by the common poles and residue matrix. Finally, the correctness of the proposed method is verified by a three‐conductor transmission lines system.

Design of Flat Defects’ Band in One-Dimensional Coupled-Cavity Photonic Crystal Waveguides for Transmitting Ultrashort Pulses

In the present study, the transmission characteristics of ultrashort pulses through coupled-cavity waveguides in one-dimensional photonic crystals were investigated theoretically, using finite-difference time-domain and transfer matrix methods. By controlling the configuration of the waveguides, a flat defects’ band can be obtained in the transmission spectra, which can be used for passing ultrashort pulses. The conditions for achieving a flat defects’ band are derived by optimization geometrical parameters of the waveguides. The optimized structure is able to transmit ultrashort pulses, up to 30 fs, with negligible distortion and attenuation. Unlike the previously designed waveguides with the same application, we designed our system without using graded index materials or many thin film layers.

PERFORMANCE EVALUATION OF SINGLE CARRIER FREQUENCY DOMAIN EQUILIZER (SC-FDE) OVER IMPULSIVE NOISE CHANNEL

Impulsive noise is considered as one of the major source of disturbance in the state-of-the-art multicarrier (MC) communication systems. Therefore, several techniques are being constantly proposed to eliminate the effect of such noise. In this work, a time domain matrix interleaved is compiled with a single carrier frequency domain equalizer (SC-FDE) is proposed to reduce the deleterious effects of impulsive noise. A mathematical model for the proposed scheme is also presented in this paper. Simulation results show that the proposed technique superiors the interleaved multicarrier system where the proposed scheme can completely avoid the error floors not only at high signal-to-noise ratio (SNR) but also at heavily distributed impulsive noise. The bit-error-rate (BER) of the alternative proposed scheme decreases as the signal-to-noise ratio (SNR) increases whereas the BER of the standard system suffers from error-floors with a constant BER at about 10-3 for about 8 dB SNR for medium and heavily impulsive noise.

A Spatial Multi-Bit Sub-1-V Time-Domain Matrix Multiplier Interface for Approximate Computing in 65-nm CMOS

Large-scale parallel implementation of matrix multiply and accumulate (MAC) core poses significant energy and area constraints in analog voltage domain under reduced supply voltage. A spatial multi-bit sub-1-V time-domain matrix multiplier interface is presented using multi-bit back-gate-driven delay elements as a scalable alternative for various approximate computing applications. A single-chip solution is demonstrated for two application modes: a high-throughput digitally driven mode for acceleration and a low-energy analog front-end mode for sensing. In accelerate mode, the system achieves an aggregate throughput of 21.6 GMAC/s with 9 TOPS/W energy efficiency. In sense mode, the system exhibits an energy efficiency of 55.3 TOPS/W for classification purpose. The proposed architecture utilizes 16-parallel 6-bit input vectors to perform matrix MAC computations using time-domain signal processing with 3-bit resistive weights at a sub-1-V supply of 0.7 V. An integrated speculative time-to-digital converter (is employed for 6-bit time-domain quantization with an on-chip mismatch calibration scheme. The prototype is fabricated in 65-nm CMOS technology and occupies an active area of 0.04 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The system performs image recognition of handwritten digits using a machine learning scheme and demonstrates an average classification accuracy of 84.3% on the MNIST dataset. The resultant energy per MAC computation in the proposed spatial architecture is about 15× lower than a digital CMOS combinational logic-based parallel-tree MAC.

Application of an optimal class of antisymmetric wavelet filter banks for obstructive sleep apnea diagnosis using ECG signals

Obstructive sleep apnea (OSA) is a sleep disorder caused due to interruption of breathing resulting in insufficient oxygen to the human body and brain. If the OSA is detected and treated at an early stage the possibility of severe health impairment can be mitigated. Therefore, an accurate automated OSA detection system is indispensable. Generally, OSA based computer-aided diagnosis (CAD) system employs multi-channel, multi-signal physiological signals. However, there is a great need for single-channel bio-signal based low-power, a portable OSA-CAD system which can be used at home. In this study, we propose single-channel electrocardiogram (ECG) based OSA-CAD system using a new class of optimal biorthogonal antisymmetric wavelet filter bank (BAWFB). In this class of filter bank, all filters are of even length. The filter bank design problem is transformed into a constrained optimization problem wherein the objective is to minimize either frequency-spread for the given time-spread or time-spread for the given frequency-spread. The optimization problem is formulated as a semi-definite programming (SDP) problem. In the SDP problem, the objective function (time-spread or frequency-spread), constraints of perfect reconstruction (PR) and zero moment (ZM) are incorporated in their time domain matrix formulations. The global solution for SDP is obtained using interior point algorithm. The newly designed BAWFB is used for the classification of OSA using ECG signals taken from the physionet's Apnea-ECG database. The ECG segments of 1 min duration are decomposed into six wavelet subbands (WSBs) by employing the proposed BAWFB. Then, the fuzzy entropy (FE) and log-energy (LE) features are computed from all six WSBs. The FE and LE features are classified into normal and OSA groups using least squares support vector machine (LS-SVM) with 35-fold cross-validation strategy. The proposed OSA detection model achieved the average classification accuracy, sensitivity, specificity and F-score of 90.11%, 90.87% 88.88% and 0.92, respectively. The performance of the model is found to be better than the existing works in detecting OSA using the same database. Thus, the proposed automated OSA detection system is accurate, cost-effective and ready to be tested with a huge database.

Highly scalable intelligent sensory application and time domain matrix for safety-critical system design

The designs of highly scalable intelligent sensory application—Ethernet-based communication architectures—are moving toward the integration of a fault recovery and fault-detection algorithm on the automotive industry. In particular, each port on the same network interface card design is required to provide highly scalable and low-latency communication. In this article, we present a study of intelligent sensory application for the Ethernet-based communication architecture and performance of multi-port configuration which is mainly used in safety-enhanced application such as automotive, military, finance, and aerospace, in other words, safety-critical applications. Our contributions and observations on the highly scalable intelligent behavior: (1) proposed network interface card board design scheme and architecture with multi-port configuration are a stable network configuration; (2) timing matrix is defined for fault detection and recovery time; (3) experimental and related verification methods by cyclic redundancy check between client–server and testing platform provide comparable results to each port configurations; and (4) application program interface–level algorithm is defined to make network interface card ready for fault detection.

Superposition Modulation-Based Cooperation for Oversampled OFDM Signals

This paper proposes an iterative detector for uncoded OFDM signals in cooperative networks, where the information symbols are simply partitioned through a time-domain matrix at the OFDM transmitter. We analytically show that our proposed iterative detector at the partner node converges and can completely recover the user’s data from its partitioned version, if sufficient redundancy is inserted in the user’s data. For efficient use of the redundancy in the user’s data, a coded cooperative transmission based on superposition modulation is proposed. Additionally, a closed-form input–output relationship for the partitioning and reconstruction algorithm in the proposed cooperative scenario is derived. We also obtain closed-form expressions for symbol error rate performance of the proposed coded cooperative scenario over Rayleigh frequency-selective fading channels. Numerical comparisons shed light on the relative merits of the proposed coded cooperation under various inter-user and uplink channel conditions.

Pathloss Calculation Using the Transmission Line Matrix and Finite Difference Time Domain Methods With Coarse Grids

Numerical simulations of the wave equation that are intended to provide accurate time domain solutions require a computational mesh with grid points separated by a distance less than the wavelength of the source term and initial data. However, calculations of radio signal pathloss generally do not require accurate time domain solutions. This paper describes an approach for calculating pathloss by using the finite difference time domain and transmission line matrix models of wave propagation on a grid with points separated by distances much greater than the signal wavelength. The calculated pathloss can be kept close to the true value for freespace propagation with an appropriate selection of initial conditions. This method can also simulate diffraction with an error governed by the ratio of the signal wavelength to the grid spacing.

Local Time-Step TLM Unstructured Block Meshing for Electromagnetic and Bio-Thermal Applications

Many practical problems are of multiscale nature. This issue appears when relatively small regions inside the computational domain have a large impact on the overall behavior of the structure. This requires using small mesh size in these regions of interest for adequately representing their geometrical details. Using uniform fine grid everywhere is computationally very exhaustive. The use of irregular structured grids may lead to some memory cost reduction as compared to uniform fine mesh. However, it imposes a smaller time step and yields higher dispersion as cell aspect ratio deviates from unity. The alternate approach is to use block meshing which allows fine discretization in regions with fine details and larger mesh size in quasi homogenous regions. The main disadvantage of this technique is that a global time step corresponding to the Courant–Friedrichs–Lewy (CFL) limit in the smallest cells should be used to avoid long-term instability. In this paper, we present a time-domain transmission-line matrix (TLM) algorithm for interfacing block regions that allows the use of local time steps. Hence, cubic cells can be optimally used in all regions with substantial coarseness error reduction. Applied to both electromagnetic and heat transfer TLM models, simulation experiments are presented to show the behavior and performances of the algorithm.

Optimal duration-bandwidth localized antisymmetric biorthogonal wavelet filters

We present a design of a new class of compactly supported antisymmetric biorthogonal wavelet filter banks which have the analysis as well as the synthesis filters of even-length. Here, the analysis and the synthesis filters are designed to have minimum joint duration-bandwidth localization (JDBL). The design of filters has been formulated as a direct time-domain linearly constrained eigenvalue problem that does not involve any parametrization and iterations. The optimal analysis and synthesis filters have been obtained as the eigenvectors of the positive definite matrices. The closed form analytic expression for the objective function has been presented. The perfect reconstruction and regularity conditions have been incorporated in the design by employing time-domain matrix characterization. The method can control duration and bandwidth localizations of the analysis and synthesis filters, independently. A few design examples have been presented and compared with previous works. The performance of the optimal filter banks designed by employing the proposed method has been evaluated in image coding and signal denoising applications.

Construction of Minirhizotron Facilities for Investigating Root Zone Processes

Core Ideas Horizontal straight holes for rhizotube installation were bored by a homemade system. Dynamics of root growth and soil moisture could be described by rhizotron facilities. Soil moisture could be monitored by TDR and GPR approaches in rhizotron facilities. Minimally invasive monitoring of root development and soil states (soil moisture, temperature) in undisturbed soils during a crop growing cycle is a challenging task. Minirhizotron (MR) tubes offer the possibility to view root development in situ with time. Two MR facilities were constructed in two different soils, stony vs. silty, to monitor root growth, root zone processes, and their dependence on soil water availability. To obtain a representative image of the root distribution, 7‐m‐long tubes were installed horizontally at 10‐, 20‐, 40‐, 60‐, 80‐, and 120‐cm depths. A homemade system was developed to install MR tubes in the silty soil in horizontally drilled straight holes. For the stony soil, the soil rhizotubes were installed in an excavated and subsequently backfilled pit. In both facilities, three subplots were established with different water treatments: rain sheltered, rainfed, and irrigated. To monitor soil moisture, water potential, and soil temperature, time domain reflectometer probes, tensiometers, and matrix water potential sensors were installed. Soil water content profiles in space and time were obtained between two MR tubes using cross‐hole ground‐penetrating radar along the tubes at different depths. Results from the first growing season of winter wheat (Triticum aestivum L.) after installation demonstrate that differences in root development, soil water, and temperature dynamics can be observed among the different soil types and water treatments. When combined with additional measurements of crop development and transpiration, these data provide key information that is essential to validate and parameterize root development and water uptake models in soil–vegetation–atmosphere transfer models.

An on-Line Electrochemical Parameter Estimation Study on Lithium-Ion Batteries Using Neural Network (NN)

Several studies have been devoted to the modeling of electrochemical lithium-ion (Li-ion) batteries. The success of all these models relies, among other things, on the precise knowledge of the electrochemical properties of the battery. Direct measurement of these properties is, however, a tedious task. It typically requires the dismantling of the battery. Also, the measured properties are dependent on the battery’s age and may vary according to the measurement technique. To overcome the difficulties of estimating the battery properties, inverse methods are proposed. These methods are based on optimization algorithms that aim at minimizing the discrepency between the predictions of a direct model (including estimated parameters) and experimental data. The major drawback of inverse methods is that they are computationally demanding. As a result, they cannot be retained for on-line control, monitoring or Battery Management Systems (BMSs). In this paper, for the first time, an inverse method resting on a trained neural network is presented for the on-line estimation of the following five electrochemical properties of a Li-ion battery: The diffusion coefficients of the electrodes (Dn & Dp), the intercalation/deintercalation reaction-rate constant for both electrodes (kn & kp) and the electrolyte resistance (Rcell). The black box model employs the 1C discharge curve of a Li-ion battery with a LiCoO2cathode material. Due to the complexity of Li-ion batteries, four different layers were chosen for the neural network: one input layer, two hidden layers and one output layer. The 1C discharge curve is fed to the model via a time domain matrix for the input layer. In order to reduce the training error, two different hidden layers comprising 50 and 75 neurons were employed. The output layer was composed of five signals which characterize the electrochemical properties. The data needed for the training of the neural network was generated with an improved Single Particle Model (SPM). The 1C discharge curves were first calculated for a reasonable range of the expected parameters. These data were then used to determine the values of the weights and functions of the neural network. The process was next implemented into two steps. First, the optimum number of training iterations was calculated. Seventy percent (70 %) of the generated data was randomly employed to train the network. The remaining data (30%) was used to test the performance of the network. Second, once the optimum value of the iteration number had been determined, the model was trained again by introducing the available data for the optimum iteration number. Finally, the trained neural network was used to estimate the electrochemical properties for different 1C discharge curves. The model was successfully validated with experimental data. Moreover, due to the matrix structure of the neural network, the parameter estimation process is adaptable and easy to implement. As a result, the proposed neural network model is suitable for real-time control and monitoring applications. Acknowledgements: The financial supports of Natural Sciences and Engineering Research Council of Canada (NSERC) and Hydro-Quebec are gratefully acknowledged. Figure 1

GLOBAL LAND COVER CLASSIFICATION USING MODIS SURFACE REFLECTANCE PROSUCTS

The objective of this study is to develop high accuracy land cover classification algorithm for Global scale by using multi-temporal MODIS land reflectance products. In this study, time-domain co-occurrence matrix was introduced as a classification feature which provides time-series signature of land covers. Further, the non-parametric minimum distance classifier was introduced for timedomain co-occurrence matrix, which performs multi-dimensional pattern matching for time-domain co-occurrence matrices of a classification target pixel and each classification classes. The global land cover classification experiments have been conducted by applying the proposed classification method using 46 multi-temporal(in one year) SR(Surface Reflectance) and NBAR(Nadir BRDF-Adjusted Reflectance) products, respectively. IGBP 17 land cover categories were used in our classification experiments. As the results, SR and NBAR products showed similar classification accuracy of 99%.

A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene

In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin time-domain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using an RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is first approximated by rational basis functions using the fast-relaxation vector-fitting (FRVF) method in the Laplace domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant–Friedrichs–Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references.

Solar absorbers using 1D and 2D periodic nanostructured nickel films

This paper presents results obtained from finite difference time domain and transfer matrix method modelling of nickel thin films. It is shown that by adding a periodic 1D grating to the surface of the nickel its optical absorption over the 300 nm–1000 nm spectral range can be dramatically increased. 2D gratings show excellent polarization independence making them ideally suited to high temperature solar thermal applications.

Tunable multiple all-optical switch based on multi-nanoresonator-coupled waveguide systems containing Kerr material

By using a 2-D finite difference time domain and transfer matrix method, we have theoretically and numerically analyzed the optical transmission characteristics of optical waveguide coupling to ring cavity array. The simulation results reveal that the dual-ring cavity waveguide configuration with Kerr nonlinear material can act as a double channel all-optical switch. The contrast ratio of the two switch channels is 16.6dB and 10.37dB, respectively. We also designed a bidirectional all-optical switch based on two parallel waveguides coupled to ring cavity structure. In addition, multi-channel optical switches are achieved by increasing the number of cavity. The designed all optical switching models will be helpful to dynamic control of light in photonic circuits.

Efficient Evaluation of Double Surface Integrals in Time-Domain Integral Equation Formulations

A new integration approach is presented for accurately calculating time-domain EFIE, MFIE, and CFIE matrix elements over triangular domains. It mainly consists of a radial integration scheme for handling weakly singular and near-hypersingular inner integrals and some new smoothing techniques for treating outer two-dimensional (2-D) integrals. The proposed approach has sufficient generality and efficiency for solving time-domain integral equations (TDIE) with arbitrary types of temporal basis functions and temporal discretization schemes, such as marching-on-in-time (MOT), marching-on-in-degree (MOD), and finite difference delay modeling/convolution quadrature (FDDM/CQ), etc. The numerical results for calculating some typical integrals are given to demonstrate its capability, with high accuracy and rapid convergence rate achieved.