Frequency Correlation Function Research Articles

A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands

High-altitude platforms (HAPs) are considered to be the most important equipment for next-generation wireless communication technologies. In this paper, we investigate the channel characteristics under the configurations of massive multiple-input multiple-output (MIMO) space and large bandwidth at millimeter-wave (mmWave) bands, along with the moving essence of the HAP and ground terminals. A non-stationary three-dimensional (3D) geometry-based stochastic model (GBSM) is proposed for a HAP communication system. We use a cylinder-based geometric modeling method to construct the channel and derive the channel impulse response (CIR). Additionally, the birth–death process of the scatterers is enclosed using the Markov process. Large-scale parameters such as free space loss and rainfall attenuation are also taken into consideration. Due to the relative motion between HAP and ground terminals, the massive MIMO space, and the wide bandwidth in the mmWave band, the channel characteristics of HAP exhibit non-stationarities in time, space, and frequency domains. By deriving the temporal auto-correlation function (ACF), we explore the non-stationarity in the time domain and the impact of various parameters on the correlations across the HAP-MIMO channels. The spatial cross-correlation function (CCF) for massive MIMO scenarios, and the frequency correlation function (FCF) in the mmWave bands are also considered. Moreover, we conduct simulation research using MATLAB. Simulation results show that the theoretical results align well with the simulation results, and this highlights the fact that the constructed 3D GBSM can characterize the non-stationary characteristics of HAP-MIMO channels across the time, space, and frequency domains.

A three‐dimensional wideband mmWave multiple‐input multiple‐output channel model for aerial reconfigurable intelligent surface‐assisted communication systems

SummaryThis paper presents a wideband millimeter wave (mmWave) channel model for aerial reconfigurable intelligent surface (ARIS) communications, in which the reconfigurable intelligent surface (RIS) is attached to an unmanned aerial vehicle (UAV) to enable intelligent signal reflections in the air. The model is established according to standard 3GPP channel models and considers important propagation factors, for example, large‐scale fading, small‐scale fading, and radiation pattern of reflection units (RUs). In addition, the model assumes three‐dimensional (3D) rotations of RIS and can capture its effects on channel characteristics. Based on the model, we propose a design method for RIS reflection phases. Statistics including channel amplitude, spatial, temporal, and frequency correlation functions (CFs), and space‐Doppler power spectral density (SD‐PSD) are obtained. The impacts of RU number, UAV height and speed, and RIS rotation on channel statistics are investigated. Results suggest that the designed reflection phases can effectively mitigate multipath fading and Doppler effect. Compared to the yaw angle of the UAV platform, channel characteristics are more sensitive to the roll and pitch angles.

Hybrid Far- and Near-Field Modeling for Reconfigurable Intelligent Surface Assisted V2V Channels: A Sub-Array Partition Based Approach

Reconfigurable intelligent surface (RIS)-assisted communications has been a hot topic due to its promising advantages for future wireless networks. Existing works on RIS-assisted channel modeling have mainly focused on far-field propagation condition with planar wavefront assumption. In essence, the far-field condition does not always hold because the RIS array dimension may be comparable to the terminal distance, especially in RIS-assisted mobile networks. To this end, we propose a hybrid far- and near-field stochastic channel model for characterizing a RIS-assisted vehicle-to-vehicle (V2V) propagation environment, which takes into account both far-field and near-field propagation conditions. To achieve the balance between the modeling accuracy and complexity for the investigation of the RIS-assisted V2V propagation characteristics, we develop a sub-array partitioning scheme to dynamically divide the entire RIS array into several smaller sub-arrays, which makes planar wavefront assumption applicable for the sub-arrays. Important channel statistical properties, including spatial cross-correlation functions (CCFs), temporal auto-correlation functions (ACFs), and frequency correlation functions (FCFs), are derived and investigated. Simulation results are provided to show the performance of the proposed sub-array partition based hybrid far- and near-field modeling solution for RIS-assisted V2V channels.

A Non-Stationary Cluster-Based Channel Model for Low-Altitude Unmanned-Aerial-Vehicle-to-Vehicle Communications

Under the framework of sixth-generation (6G) wireless communications, the unmanned aerial vehicle (UAV) plays an irreplaceable role in a number of communication systems. In this paper, a novel cluster-based low-altitude UAV-to-vehicle (U2V) non-stationary channel model with uniform planar antenna arrays (UPAs) is proposed. In order to comprehensively model the scattering environment, both single and twin clusters are taken into account. A novel continuous cluster evolution algorithm that integrates time evolution and array evolution is developed to capture channel non-stationarity. In the proposed algorithm, the link between the time evolution of twin clusters and that of single clusters is established to regulate the temporal evolution trend. Moreover, an improved observable radius method is applied to UPAs for the first time to describe array evolution. Based on the combination of cluster evolution and time-variant channel parameters, some vital statistical properties are derived and analyzed, including space–time correlation function (ST-CF), angular power spectrum density (PSD), Doppler PSD, Doppler spread (DS), frequency correlation function (FCF), and delay spread (RS). The non-stationarity in the time, space, and frequency domain is captured. It demonstrates that the airspeed, density of scatterers within clusters, and carrier frequency have an impact on statistical properties. Furthermore, twin clusters have more flexible spatial characteristics with lower power than single clusters. These conclusions can provide assistance and reference for the design and deployment of 6G UAV communication systems.

A three‐dimensional two‐hemisphere model for unmanned aerial vehicle multiple‐input multiple‐output channels

AbstractThe application of unmanned aerial vehicles (UAVs) has recently attracted considerable interest in various areas. A three‐dimensional multiple‐input multiple‐output concentric two‐hemisphere model is proposed to characterize the scattering environment around a vehicle in an urban UAV‐to‐vehicle communication scenario. Multipath components of the model consisted of line‐of‐sight and single‐bounced components. This study focused on the key parameters that determine the scatterer distribution. A time‐variant process was used to analyze the nonstationarity of the proposed model. Vital statistical properties, such as the space–time–frequency correlation function, Doppler power spectral density, level‐crossing rate, average fade duration, and channel capacity, were derived and analyzed. The results indicated that with an increase in the maximum scatter radius, the time correlation and level‐crossing rate decreased, the frequency correlation function had a faster downward trend, and average fade duration increased. In addition, with the increase of concentration parameter, the time correlation, space correlation, and level‐crossing rate increased, average fade duration decreased, and Doppler power spectral density became flatter. The proposed model was compared with current geometry‐based stochastic models (GBSMs) and showed good consistency. In addition, we verified the nonstationarity in the temporal and spatial domains of the proposed model. These conclusions can be used as references in the design of more reasonable communication systems.

Measurements and Characteristics Analysis of 6G Ultra-Massive MIMO Wireless Channels With Different Antenna Configurations and Scenarios

In this paper, ultra-massive multiple-input multiple-output (MIMO) channel measurements at 5.3 GHz are conducted, including different antenna array configurations and different measurement scenarios. The antenna array configurations include uniform linear array (ULA) and distributed uniform linear array (DULA). The measurement scenarios include single-user fixed-to-fixed (F2F), multi-user F2F, and single-user fixed-to-mobile (F2M) measurement scenarios. The statistical properties of ultra-massive MIMO channels are studied, including delay power spectral density (DPSD), space cross-correlation function (SCCF), angle cross-correlation function (ACCF), frequency correlation function (FCF), root mean square (RMS) delay spread (DS), RMS angle spread (AS), singular value spread (SVS), scalar product (SP), level crossing rate (LCR), average fading duration (AFD), Doppler power spectral density (PSD), etc. The specific ultra-massive MIMO channel characteristics are investigated and validated by channel measurements, including spatial non-stationarity, spherical wavefront behavior, channel hardening, and sparse properties in the angle domain. In addition, channel capacities are investigated. The channel measurement results will be a great importance for ultra-massive MIMO communication system deployments.

Physics-Based 3D End-to-End Modeling for Double-RIS Assisted Non-Stationary UAV-to-Ground Communication Channels

In this paper, we propose a three-dimensional (3D) physics-based double reconfigurable intelligent surface (RIS) cooperatively assisted multiple-input multiple-output (MIMO) stochastic channel model for unmanned aerial vehicle (UAV)-to-ground communication scenarios. The double-RIS is distributed on the surface of buildings can assist the UAV transmitter to reflect its own signals to the ground receiver (GR), and simultaneously enhance the propagation by passive beamforming on the RISs. In the proposed channel model, we derive the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">path power gains</i> for different propagation links between the UAV and GR, thus enabling the proposed channel model to effectively characterize both large- and small-scale fading characteristics of realistic UAV-to-ground communication systems. Furthermore, we derive the critical propagation properties of the proposed channel model, including the spatial cross-correlation functions (CCFs), temporal auto-correlation functions (ACFs), and frequency correlation functions (FCFs), with respect to different RIS reflection phase configurations as well as different RIS orientation angles. Numerical simulation results demonstrate the propagation characteristics of the proposed double-RIS assisted UAV-to-ground channel model behave better than those of traditional channel models with single-RIS link or LoS link, thereby validating the necessity of introducing double-RIS into UAV-to-ground communication.

A Novel 3D Non-Stationary Massive MIMO Channel Model for Shortwave Communication Systems

In this paper, a novel three-dimensional (3D) non-stationary massive multiple-input multiple-output (MIMO) channel model for shortwave communication systems is proposed. Three transmission modes, i.e., groundwave, near vertical incident skywave (NVIS), and long-distance skywave are considered to eliminate the blind area and realize the full-coverage for shortwave communication. The ionospheric absorption loss and surface reflection loss during multi-hop transmissions are explored in the proposed channel model. In addition, new massive MIMO channel characteristics including the near-field spherical wavefront effect and spatial non-stationarity are considered. Temporal and frequency non-stationarities are also modeled due to the receiver (Rx) mobility and large relative bandwidth, respectively. The analytical and simulated space cross-correlation function (SCCF), time autocorrelation function (TACF), and frequency correlation function (FCF) of the proposed model are compared. The simulated path loss and singular value spread (SVS) are compared with those of the corresponding channel measurements, illustrating good fittings. In addition, the delay power spectral density (PSD) and Doppler PSD, and channel capacity are also simulated and analyzed. The proposed model can be used as a basis for the design and construction of shortwave communication systems.

Vibrational dynamics of liquid water in an external electric field.

In our present study, we have investigated the effects of an externally applied static electric field on the vibrational dynamics of liquid water (D2O) using ab initio molecular dynamics. The rate of vibrational spectral diffusion is obtained from simulated two-dimensional infrared spectra, three-pulse photon echo intensity, and frequency correlation functions and distributions. We find that the static vibrational frequency distribution undergoes a redshift of 90 cm-1 whereas the overall vibrational dynamics get slower with the relaxation time constant to be around 4.9 ps. Thus we infer that the local hydrogen bond network tends to reorganize in the presence of an external field with an increase in local structural order as evident from the overall slower vibrational dynamics and reduced molar entropy.

A Modified Geometry-Based MIMO Channel Model for Tunnel Scattering Communication Environments

In this study, a modified non-stationary geometry-based scattering model for tunnel vehicle-to-vehicle (V2V) multiple-input multiple-output Ricean fading channels is presented. The proposed channel introduces non-line-of-sight three-dimensional multi-bounced scattering propagation paths under an assumption of equivalent scattering points to depict the tunnel environments, in which the scatterers are randomly distributed on the semi-cylindrical tunnel wall (i.e., cable racks, jetfans, road signs, lighting facilities). Furthermore, the time-varying channel statistics (i.e., the space and frequency correlation functions) resulting from the relative movement between the mobile transmitter and mobile receiver are analyzed. Finally, numerical results show that the space correlations of the proposed model significantly decrease when the multi-bounced scattering rays are taken into account; moreover, when the velocity and the antenna angle γR increase, the correlations decrease therewith, which exhibits good agreement with the existing V2V scattering channel models and measured data in a real tunnel environment, demonstrating the rationality of the underlying channel model.

Statistical Characteristics of 3D MIMO Channel Model for Vehicle-to-Vehicle Communications

Spatial and temporal characteristics of the propagation channel have a significant influence on multiantenna method applicability for fifth-generation- (5G-) enabled Internet of Things (IoT). In this paper, the statistical characteristics of a novel three-dimensional (3D) geometric-based stochastic model for next-generation vehicle-to-vehicle (V2V) multiple-input multiple-output (MIMO) communications under the nonisotropic scattering environment are investigated. In both line-of-sight (LoS) and non-line-of-sight (NLoS) conditions, the proposed model investigates the spatial, frequency, and temporal domain statistical distribution of multipath received signals by using the time-variant transfer function for indoor environments. The probability density function (PDF) of separation distance between the transceiver antennas, angle-of-arrival (AoA), and angle-of-departure (AoD) in the azimuth and elevation planes is derived by using closed-form expressions. For the space, time, and frequency correlation function (STF-CF), a precise analytical expression is derived based on MIMO antenna system. We further determine the effects of several model parameters on the V2V channel performance, such as tunnel width, antenna array spacing, Ricean K -factor, and moving velocity. The statistical characteristics of the MIMO channel model are validated by simulation results, confirming the flexibility and effectiveness of our proposed model in the tunnel scenario.

A 3D Non-Stationary Wideband Massive MIMO Channel Model Based on Ray-Level Evolution

In this paper, a novel space-time non-stationary three-dimensional (3D) wideband massive multiple-input multiple-output (MIMO) channel model is proposed. We then propose a ray-level process to model the spatial-temporal evolution of individual multipath components (MPCs), including near-field effects and (dis)appearance, and cluster-level large-scale fading. The proposed evolution process can flexibly control rays&#x2019; lifespans and smoothness of (dis)appearance in both space and time domains. In addition, we propose an improved Rayleigh-distance criterion to determine the most adequate wavefront for each cluster and ray. Existing models can easily implement the proposed criterion and make a more efficient use of computation resources. Also, a Gamma-Poisson mixture distribution is introduced to model the distribution of the number of clusters when multiple locations of the mobile station are considered. Key statistical properties of the channel, including the autocorrelation function (ACF), Doppler power spectral density (PSD), spatial cross-correlation function (S-CCF), and frequency correlation function (FCF), are derived and the impact of the ray-level evolution process on them is analyzed. We demonstrate the correctness of the derived statistical properties through numerical and simulation results.

A Novel B5G Frequency Nonstationary Wireless Channel Model

Frequency nonstationarity is an important statistical property of beyond fifth generation wireless communication channels due to extremely large bandwidths used in millimeter wave (mmWave) and teraherz communications. In this article, a general averaged power delay profile method is first introduced as a metric to determine the stationarity regions of wireless channels in the time, frequency, and spatial domains. Then, we apply this method to determine the frequency stationarity regions (FSRs) of channel measurements in a sub-6-GHz frequency band (2-4 GHz) and two mmWave frequency bands (14-16 GHz and 28-30 GHz). Frequency nonstationary (FnS) properties are found from all of the three bands. A novel FnS channel model is then proposed to model wireless channels in all frequency bands. We first split a FnS channel into a few frequency stationary (FS) subband channels and model them one by one, which are finally combined as an FnS channel model considering the cluster evolution in the frequency domain and the frequency consistency of subband channels. Simulation results show that the frequency correlation functions of the proposed FnS channel model fit well those of the measured FnS channels.

Channel modelling for vehicle‐to‐vehicle MIMO communications in geometrical rectangular tunnel scenarios

This study presents a multiple-input multiple-output (MIMO) statistical channel model for vehicle-to-vehicle (V2V) line-of-sight (LOS) and non-LOS mobile communication system in a rectangular tunnel environment. In order to improve the V2V communication system performance, the authors introduced the elevation and azimuth angles in three-dimensional modelling based on the original literature. In the proposed reference channel model, the single-bounced scattering propagation path of electromagnetic signals is considered and it is assumed that the scatterers are randomly distributed on the rectangular tunnel wall. Starting from the statistical physical channel model, the time-variant transfer functions are derived. Thereafter, the analytical expressions of the space–time–frequency cross-correlation function, the space cross-correlation function, the temporal autocorrelation function, the frequency correlation function, and MIMO channel capacity are derived. The influence of model parameters on the performance of the V2V communication system is also analysed. This work provides an innovative approach to channel modelling in a rectangular tunnel mobile communication environment.

CLS Next Gen: Accurate Frequency-Frequency Correlation Functions from Center Line Slope Analysis of 2D Correlation Spectra Using Artificial Neural Networks.

The center line slope (CLS) observable has become a popular method for characterizing spectral diffusion dynamics in two-dimensional (2D) correlation spectroscopy because of its ease of implementation, robustness, and clear theoretical relationship to the frequency-frequency correlation function (FFCF). The FFCF relates the frequency fluctuations of an ensemble of chromophores to coupled bath modes of the chemical system and is used for comparison to molecular dynamics simulations and for calculating 2D spectra. While in the appropriate limits, the CLS can be shown to be the normalized FFCF, from which the full FFCF can be obtained, in practice the assumptions that relate the CLS to the normalized FFCF are frequently violated. These violations are due to the presence of homogeneous broadening and motional narrowing. The generalized problem of relating the CLS to the FFCF is reanalyzed by introducing a new set of dimensionless parameters for both the CLS and FFCF. A large data set was generated of CLS parameters derived from numerically modeled 2D line shapes with known FFCF parameters. This data set was used to train feedforward artificial neural networks that act as functions, which take the CLS parameters as inputs and return FFCF parameters. These neural networks were deployed in an algorithm that is able to quickly and accurately determine FFCF parameters from experimental CLS parameters and the fwhm of the absorption line shape. The method and necessary inputs to accurately obtain the FFCF from the CLS are presented.

Modeling of 300 GHz Chip-to-Chip Wireless Channels in Metal Enclosures

This paper proposes a two dimensional (2-D) statistical channel model for Terahertz (THz) chip-to-chip wireless communication in desktop size metal enclosures. This model differs from traditional statistical channel models as it models both traveling and resonant waves that exist inside metal enclosures. Based on the cavity environment and the statistical properties of the channel inside the metal cavity, the geometrical model which describes propagation in resonant cavity as a superposition of LoS, single bounced (SB), double bounced (DB), and multi-bounced (MB) rays is proposed. Based on the geometrical model, a parametric reference model is proposed. Furthermore, the path loss model that captures signal strength variation in a resonant cavity is proposed. Frequency correlation functions (FCF) and power delay profiles (PDP) for different possible chip-to-chip communication scenarios are derived and compared with the measured ones. The results show a good agreement between the simulated and measured statistics.

Propagation of a Rectangular Chaotic-Phase Radio Pulse in a Cold Plasma Medium

Characteristics analysis of the dispersive distortions of a rectangular microsecond chaotic-phase radio pulse modeled using the third-order Chebyshev map of the first kind propagating in a cold plasma medium is performed. Propagation of the pulse away from the radiator is accompanied by the pulse transformation toward a noiselike shape with formation of a “tail”, the length of which can multiply and exceed initial pulse duration. It is established that, in a wide range of parameters describing the randomness degree of the instantaneous phase of the emitted pulse, the medium does not significantly influence subsequent changes in its autocorrelation and frequency correlation functions during propagation.

Exponential frequency correlation function and its application in Doppler shift estimation

A Doppler shift estimation problem of a noisy received signal consisting of multiple moving targets that have similar radial velocities is addressed here. Traditional Doppler shift estimation algorithms based on Fourier transform (FT) frequently exhibit low resolution. Here, an exponential frequency correlation function (EFCF) is proposed by introducing a sensitivity exponent p that controls its output signal-to-noise ratio (SNR) and velocity resolution into the expression of a classical frequency correlation function (FCF). On the basis of the proposed EFCF, a novel Doppler shift estimation algorithm can adaptively select the exponent of the EFCF to achieve the optimum Doppler shift estimation effect in an echo signal based on the elimination algorithm. Moreover, the proposed method is performed on the basis of the fast FT and product operation. Thus, it can be easily implemented. Numerical simulations demonstrate that the performance of the proposed method is significantly improved compared with the existing algorithms.

Distortions of a Rectangular Radio Pulse with Chaotic Carrier in a Dispersive Resonantly Absorbing Gas Medium

We briefly describe the possible character and peculiarities of dispersion-induced distortions of a rectangular pulse with chaotic carrier modeled using the third-order Chebyshev map of the first kind propagating in a resonantly absorbing gas medium. It is established that, as the pulse goes away from the radiator, its envelope exhibits transformation toward a noiselike shape. In a rather wide region of parameters of the dispersive medium, distortions of the envelope are not accompanied by breakage or principal changes of its autocorrelation and frequency correlation functions.

A 3-D Geometry-Based Stochastic Model for UAV-MIMO Wideband Nonstationary Channels

In this paper, we propose a 3-D geometry-based stochastic model for multi-input multioutput wideband nonstationary channels between the unmanned aerial vehicle (UAV) and the ground user. The proposed model uses a single concentric-cylinders model, where the signal is a superposition of a line-of-sight component and single-bounced rays. In order to describe the nonstationarity of the channel, time-varying angels have been properly derived and added in the proposed model. At the same time, based on the reference model, we derive the expressions of the channel statistical properties of the space–time–frequency correlation function and space-Doppler power spectral density. In addition, corresponding deterministic and stochastic simulation models are developed based on the reference model. Moreover, we investigate the influence of some important UAV-related parameters on channel statistical properties as well as the channel nonstationarity. Some interesting observations and conclusions are obtained, which are helpful for the design of UAV communication systems. Finally, the great agreement between simulation models and the reference model demonstrates not only the utility of simulation models but also the correctness of the theoretical derivations and simulations.