Time-frequency Correlation Function Research Articles

A Wideband Non-Stationary Air-to-Air Channel Model for UAV Communications

Unmanned aerial vehicle (UAV) communications have recently drawn great attention. To analyze and optimize the UAV communication systems, accurate and efficient UAV channel models are essential. Most existing UAV channel models are based on the assumption that both transmitter (Tx) and receiver (Rx) have fixed velocity and moving direction. However, in the realistic communication scenarios, the Tx and Rx of UAV may experience changes in both speeds and trajectories. In this paper, a three-dimensional (3D) non-stationary geometry-based stochastic model (GBSM) is proposed for air-to-air (A2A) channels in UAV communication scenarios. A 3D Markov mobility model is used to characterize the movements of the UAV in both horizontal and vertical directions. The mobility model enables to adjust the degree of mobility randomness and covers different UAV mobility trajectories, which makes it more realistic and suitable for simulating various scenarios. In addition, some important statistical properties such as time-frequency correlation function and Doppler power spectrum are derived and analyzed. The numerical results show that the impact of vertical movement of the UAV on the time correlation function under constant-speed is larger than that of horizontal movement, however, the above phenomenon is mitigated and the non-stationarity properties of the channel are significantly affected when randomness of the mobility model is introduced. Furthermore, it is found that the movement properties of the UAV only lead to non-stationarity in the time domain. The results are useful for A2A non-stationary channel simulation and UAV communication system evaluation.

Mobility Model-Based Non-Stationary Mobile-to-Mobile Channel Modeling

Non-stationary mobile-to-mobile (M2M) channel modeling has gained strong momentum as it is vital for developing M2M communications technology. Traditional geometry-based channel models (GSCMs) for M2M communications usually assume fixed velocity and moving direction, which differs from the realistic M2M scenarios and also makes it difficult to incorporate non-stationarity of channel into the regular-shaped GSCMs. In this paper, a mobility model-based method is proposed to incorporate non-stationarity into M2M channel modeling by introducing dynamic velocities and trajectories. A revised Gauss–Markov mobility model is first presented together with the cluster-based two-ring M2M reference model. The mobility model uses tuning parameters to adjust the degree of mobility randomness and covers different M2M mobility trajectories. Then, a closed-form time-variant time-frequency correlation function and the Doppler power spectrum are derived from the model. Based on the numerical analysis, it is found that for a regular-shaped GSCM with a fixed M2M scattering environment, the motion does not introduce non-stationarity, however, the dynamic motion (i.e., the changes of velocity and moving direction) leads to non-stationarity, which is reflected by the time-variant time correlation function and Doppler spectrum. Different propagation modes, cluster number, and intra-cluster nonisotropic scattering also have major impacts on channel non-stationarity. Moreover, the randomness of the mobility model is found to significantly increase the degree of channel non-stationarity. These conclusions are useful for M2M non-stationary channel simulation and communication system evaluation.

Geometrical-Based Modeling for Millimeter-Wave MIMO Mobile-to-Mobile Channels

A geometric multiple-input multiple-output (MIMO) channel model is proposed for millimeter-wave (mmWave) mobile-to-mobile (M2M) applications based on the two-ring reference model, where cluster-based nonisotropic scattering at both ends of the radio link is considered. The proposed model employs a few clusters of scatterers located on two rings centered on the transmitter and receiver, and intracluster azimuth spread of scatterers is further characterized according to mmWave channel characteristics. From the model, the time-frequency correlation function, power delay profile (PDP), and the Doppler power spectrum are derived. By adjusting the cluster number, cluster center position, and the degree of intracluster nonisotropic scattering, the model is adaptable to a variety of mmWave M2M scenarios. Model validation is further conducted by comparing the simulated PDPs with mmWave outdoor measurements. Based on a detailed investigation of channel correlation functions, it is found that a small number of clusters leads to high channel correlation, and the degree of intracluster nonisotropic scattering has major impact on correlation only if cluster number is small. In addition, the Doppler power spectrum is similar to the U-shaped spectrum, and several factors (e.g., small cluster number, high intracluster azimuth spread, and large antenna spacing) introduce significant fluctuations in the Doppler power spectrum. Finally, the model is implemented with directional antennas for safety related M2M scenarios, which leads to high channel correlation compared with using omnidirectional antennas. These observations and conclusions can be considered as a guidance for the mmWave M2M MIMO system design.

Geometry-Based Statistical Modeling of Non-WSSUS Mobile-to-Mobile Rayleigh Fading Channels

In this paper, we present a novel geometry-based statistical model for small-scale non-wide-sense stationary uncorrelated scattering (non-WSSUS) mobile-to-mobile (M2M) Rayleigh fading channels. The proposed model builds on the principles of plane wave propagation to capture the temporal evolution of the propagation delay and Doppler shift of the received multipath signal. This is different from existing non-WSSUS geometry-based statistical channel models, which are based on a spherical wave propagation approach, that in spite of being more realistic is more mathematically intricate. By considering an arbitrary geometrical configuration of the propagation area, we derive general expressions for the most important statistical quantities of nonstationary channels, such as the first-order probability density functions of the envelope and phase, the four-dimensional (4-D) time-frequency correlation function (TF-CF), local scattering function (LSF), and time-frequency-dependent delay and Doppler profiles. We also present an approximate closed-form expression of the channel's 4-D TF-CF for the particular case of the geometrical one-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of non-WSSUS M2M Rayleigh fading channels.

The time-frequency method of signal analysis in internal combustion engine diagnostics

The paper presents the results of the study of applicability of time-frequency correlation functions to solving the problems of internal combustion engine fault diagnostics. The proposed methods are theoretically justified and experimentally tested. In particular, the method’s applicability is illustrated by the example of specially generated signals that simulate the vibration of an engine both during the normal operation and in the case of a malfunction in the system supplying fuel to the cylinders. This method was confirmed during an experiment with an automobile internal combustion engine. The study offers the main findings of the simulation and the experiment and highlights certain characteristic features of time-frequency autocorrelation functions that allow one to identify malfunctions in an engine’s cylinder. The possibility in principle of using time-frequency correlation functions in function testing of the internal combustion engine is demonstrated. The paper’s conclusion proposes further research directions including the application of the method to diagnosing automobile gearboxes.

Modeling of Non-WSSUS Double-Rayleigh Fading Channels for Vehicular Communications

This paper deals with the modeling of nonstationary time-frequency (TF) dispersive multipath fading channels for vehicle-to-vehicle (V2V) communication systems. As a main contribution, the paper presents a novel geometry-based statistical channel model that facilitates the analysis of the nonstationarities of V2V fading channels arising at a small-scale level due to the time-varying nature of the propagation delays. This new geometrical channel model has been formulated following the principles of plane wave propagation (PWP) and assuming that the transmitted signal reaches the receiver antenna through double interactions with multiple interfering objects (IOs) randomly located in the propagation area. As a consequence of such interactions, the first-order statistics of the channel model’s envelope are shown to follow a worse-than-Rayleigh distribution; specifically, they follow a double-Rayleigh distribution. General expressions are derived for the envelope and phase distributions, four-dimensional (4D) TF correlation function (TF-CF), and TF-dependent delay and Doppler profiles of the proposed channel model. Such expressions are valid regardless of the underlying geometry of the propagation area. Furthermore, a closed-form solution of the 4D TF-CF is presented for the particular case of the geometrical two-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of small-scale nonstationary V2V double-Rayleigh fading channels.

Polarized Channel Model for Body Area Networks Using Reflection Coefficients

A geometry-based propagation model is proposed for wideband polarized body area network (BAN) channels. Reflection coefficient functions ( $\Gamma$ -functions) are derived as a function of geometry-based channel modeling parameters for more precise modeling of polarized BAN channels than existing polarized channel models, which exclude the reflection coefficients or use constant-valued reflection coefficients. Conservation-of-polarization (CoP) propagation planes along with geometrical $\Gamma$ -functions, which we call the CoP - ${\mit\Gamma} $ plane methodology , are used to derive the channel polarization functions. Statistical characteristics of polarized BAN channels such as the cross-polarization discrimination (XPD) and time–frequency correlation function (TF-CF) are provided based on this new CoP- $\Gamma$ plane methodology. The model is validated with measurement data taken at 13 GHz and shown to be in excellent agreement.

Shallow Water Acoustic Channel Modeling Based on Analytical Second Order Statistics for Moving Transmitter/Receiver

Underwater acoustic channels are among the most challenging communication media. Time-varying multipath fading, long delay spread, significant Doppler spread, and frequency-dependent path loss are the main aspects of such channels. In this paper we present a statistical shallow water channel model for moving transmitter/receiver based on analytical second order statistics. To do so, we first propose a channel impulse response (CIR) model that captures most of the physical properties of shallow waters. Then we find the probability density function (PDF) of the angle of arrival (AoA) for paths with different number of surface and bottom reflections. To find closed form expressions for the second order statistics of the CIR, we approximate the PDFs of AoA with half-circular Rice PDF: a novel PDF introduced in this work. By mathematical tractability of this new PDF, analytical statistics including autocorrelation function, scattering function, and time-frequency correlation function are derived. The results are compared with experimental findings for verification.

Overview of frequency bandwidth determination techniques of useful signal in case of leaks detection by correlation method

In this paper an overview of useful signal detection methods on the background of intense noise and limits determination methods of useful signal is presented. The following features are considered: peculiarities of usage of correlation analysis, cross-amplitude spectrum, coherence function, cross-phase spectrum, time-frequency correlation function in case of frequency limits determination as well as leaks detection in pipelines. The possibility of using time-frequency correlation function for solving above named issues is described. Time- frequency correlation function provides information about the signals correlation for each of the investigated frequency bands. Data about location of peaks on the surface plot of a time- frequency correlation function allows making an assumption about the spectral composition of useful signal and its frequency boundaries.

Increasing the Efficiency of Using Hardware Resources for Time-Frequency Correlation Function Computation

In the article the techniques of increasing efficient of using multi-core processors for the task of calculating the fast Fourier transform were considered. The fast Fourier transform is led on the basis of calculating a time time-frequency correlation function. The time-frequency correlation function allows increasing the information content of the analysis as compared with the classic correlation function. The significant computational capabilities are required to calculate the time-frequency correlation function, that by reason of the necessity of multiple computing fast Fourier transform. For computing the fast Fourier transform the Cooley-Tukey algorithm with fixed base two is used, which lends itself to efficient parallelization and is simple to implement. Immediately before the fast Fourier transform computation the procedure of bit-reversing the input data sequence is used. For algorithm of calculating the time-frequency correlation function parallel computing technique was used that experimentally allowed obtaining the data defining the optimal number of iterations for each core of the CPU, depending on the sample size. The results of experiments allowed developing special software that automatically select the effective amount of subtasks for parallel processing. Also the software provides the choice of sequential or parallel computations mode, depending on the sample size and the number of frequency intervals in the calculation of time-frequency correlation function.

Prospects of Frequency-Time Correlation Analysis for Detecting Pipeline Leaks by Acoustic Emission Method

In the current work the relevance of nondestructive test method development applied for pipeline leak detection is considered. It was shown that acoustic emission testing is currently one of the most widely spread leak detection methods. The main disadvantage of this method is that it cannot be applied in monitoring long pipeline sections, which in its turn complicates and slows down the inspection of the line pipe sections of main pipelines. The prospects of developing alternative techniques and methods based on the use of the spectral analysis of signals were considered and their possible application in leak detection on the basis of the correlation method was outlined. As an alternative, the time-frequency correlation function calculation is proposed. This function represents the correlation between the spectral components of the analyzed signals. In this work, the technique of time-frequency correlation function calculation is described. The experimental data that demonstrate obvious advantage of the time-frequency correlation function compared to the simple correlation function are presented. The application of the time-frequency correlation function is more effective in suppressing the noise components in the frequency range of the useful signal, which makes maximum of the function more pronounced. The main drawback of application of the time- frequency correlation function analysis in solving leak detection problems is a great number of calculations that may result in a further increase in pipeline time inspection. However, this drawback can be partially reduced by the development and implementation of efficient algorithms (including parallel) of computing the fast Fourier transform using computer central processing unit and graphic processing unit.

Geometrically Based Statistical Model for Polarized Body-Area-Network Channels

A new geometry-based channel model is proposed for wide-band polarized body-area-network channels consisting of four propagation modes, i.e., cylindrical surface scattering (CSS) for above-ground off-body scattering (BS), BS for body diffracted and on-BS, ground scattering (GS), and line-of-sight. A conservation-of-polarization plane methodology is used for the CSS and GS propagation modes. For the BS propagation mode, a geometrical theory of diffraction is used and related to CSS. The channel cross-polarization discrimination (XPD) and time-frequency correlation function (TF-CF) are derived from the model. Comparisons of the XPD and the TF-CF that are obtained from the model (with appropriate physical parameters) and those obtained from wide-band measurements at 13-GHz are in good agreement. We observed the GS propagation mode to be the dominant mode in our experiments. The azimuth angle of arrival (AAoA) of a ground reflected wave is shown in theory to have a significant effect on the XPD.

Non-Stationary Propagation Model for Scattering Volumes With an Application to the Rural LMS Channel

The design of efficient positioning algorithms in navigation satellite systems, like GNSS, operating in land mobile environments demands for detailed models of the radio channel. On the one hand, the models need to accurately describe scattering and shadowing/obstruction caused by vegetation. On the other hand, they have to incorporate the steady change in the propagation constellation due to the receiver displacement. In this paper we propose a model of the non-stationary radio channel in a scenario where a mobile receiver drives past a scattering volume, such as a ball or a cuboid, while the transmitter is elevated, like in satellite positioning applications. Such a volume may represent the canopy of a single tree, the canopies of trees in a grove, or a small forest. Scattering by the volume is characterized by means of multiple point-source scatterers that are assumed to form a marked spatial point process. The system functions of the radio channel are given. An integral form of the time-frequency correlation function of the component in the system functions contributed by the scattering volume is obtained as a direct consequence of Campbell's Theorem. Furthermore, a closed-form approximation of this integral form is derived for time lags corresponding to displacements along the receiver trajectory for which the plane wave assumption holds. The approximation takes into account the steady change in the propagation constellation. The proposed model is validated by means of Monte Carlo simulations and by comparing its prediction capabilities with experimental data in a scenario where a mobile receiver drives past a roadside tree. A good agreement is observed, despite the simplicity of the model.

An Improved Iterative Nonlinear Least Square Approximation Method for the Design of SISO Wideband Mobile Radio Channel Simulators

In this paper, we present an improved version of the iterative nonlinear least square approximation (INLSA) method for designing measurement-based single-input single-output (SISO) wideband channel simulators. The proposed method aims to fit the time-frequency correlation function (TFCF) of the simulation model to that of a measured channel. The parameters of the simulation model are determined iteratively by minimizing the Frobenius norm, which serves as a measure for the fitting error. In contrast to the original INLSA method, the proposed approach provides a unique optimized set of model parameters, which guarantees a quasi-perfect fitting with respect to the TFCF. We analyze the performance of the proposed method in terms of the goodness of fit to the measured data. The investigations will be carried out with respect to the TFCF and the scattering function. We demonstrate that the proposed approach is a powerful tool for the design of measurement-based wideband channel simulators, which are important for the performance evaluation of mobile communication systems under real-world propagation conditions.

A Three-Dimensional Geometry-Based Statistical Model of2×2Dual-Polarized MIMO Mobile-to-Mobile Wideband Channels

A three-dimensional (3D) model for wide-band dual-polarized (DP) multiple-input-multiple-output (MIMO) mobile-to-mobile (M2M) channels is proposed. Using geometrical scattering based on concentric spheres at the transmitter (Tx) and at the receiver (Rx), a 3D parametric reference model for2×2M2M DP multipath fading channels is developed. The channel model assumes the use of colocated half-wavelength dipole antennas for vertical and horizontal polarizations at both transmit and receive stations. Model parameters include the velocities of the Tx and Rx nodes, the distance between the nodes, the 3D antenna pattern gains, the azimuth and elevation angles of arrival and departure, the geometrical distribution of the scatterers, the Rician K-factors defining the fading envelope distributions, the maximum Doppler frequency, the scattering loss factors, the cross-polar power discrimination ratio (XPD), and the copolarization power ratio (CPR). Using the proposed model, expressions for joint time-frequency correlation functions (TFCFs) are derived which are used to investigate system behavior over different wide sense stationary uncorrelated scattering (WSSUS) channel realizations. The numerical results illustrate the sensitivities of the TFCF to simultaneous time and frequency offsets for the2×2DP-MIMO architectures.

Statistical Modeling of MIMO Mobile-to-Mobile Underwater Channels

This paper proposes a geometry-based statistical model for wideband multiple-input-multiple-output (MIMO) mobile-to-mobile (M-to-M) shallow-water acoustic (SWA) multipath fading channels. Based on the reference model, the corresponding MIMO time-frequency correlation function, Doppler power spectral density, and delay cross-power spectral density are derived. These statistics are important tools for the design and performance analysis of MIMO M-to-M SWA communication and sonar systems. Finally, the derived statistics are compared with the experimentally obtained channel statistics, and close agreement is observed.

Range spread measurement of underwater scatterers and channels using active sonar probing signals and a cross-correlation process

A method for measuring range spread of underwater scatterers and channels based on the cross-correlation processing of the tones of a multicomponent waveform has been developed. The correlation terms which comprise the measure are samples of the time-frequency correlation functions (TFCF) of scatterers and channels. The measure has been used to characterize the time-frequency spread and represents the signal coherence. This paper will provide a review of two frequency correlation function representations and their characterization using the aggregate coherence measure, termed correlation mass. The sensitivity of this measure as a function of waveform parameters, scatterer structure, and measurement platform motion will be defined and its robustness on a multiping basis assessed. It will be shown that this measure can be decomposed into correlated components resulting from interaction with a scatterer and a channel. Essentially the composite correlation is obtained by sampling the product of the scatterer and channel TFCF’s. Data from in-water experiments and digital sonar simulations will be presented which validates the linear systems model of the composite scattering process. [Work supported by ONR.]

Active sonar coherence measurements of underwater scatterers and channels using a cross correlation process

The concept of coherence is fundamental and quite important in all fields dealing with fluctuating quantities. A new method for measuring coherence based on the cross correlations of the tones of a multi-component waveform has been developed. The correlation terms which comprise the measure are samples of the time-frequency correlation functions (TFCF) of scatterers and channels. The measure has been used to characterize the time-frequency spread associated with scatterers and channels and represents the signal coherence. This paper will provide a review of scattering function representations and aggregate coherence measures as derived from a correlation matrix. The new coherence measure termed correlation mass will be defined. It will be shown that this measure can be decomposed into correlated components resulting from interaction with a scatterer and a channel. In other words the composite correlation is obtained by sampling the product of the scatterer and channel TFCF’s. Data from in-water experiments and digital sonar simulations will be presented which validates the linear systems model of the composite scattering process.

Calculation of System and Correlation Functions for WSSUS Channels from Wideband Measurements

System and correlation functions of WSSUS channels are commonly accepted means for channel description in mobile communications. After a brief recapitulation of the theory for WSSUS channels, methods are derived for using system and correlation functions for the examination of measured channel characteristics. The derived methods additionally lead to a simple interpretation of the relations between the functions. Finally results are given for the Time-Variant Impulse Response, the Scattering Function and the Time-Frequency Correlation Function calculated from measured data in an indoor environment

The ambiguity function applied to underwater acoustic signal processing: A review

This paper traces the development of Ambiguity Function Analysis as applied to underwater acoustic signal processing. Based on Woodward's time-frequency correlation function (Woodward, 1953) the dependence of range and Doppler resolution is illustrated for a number of signal waveforms in a white noise background. The effect of unwanted signals (clutter) and noise on the ambiguity function is discussed in detail. An approach to the solution of the more difficult problem of ambiguity function synthesis is suggested.