Doppler Power Spectral Density Research Articles

A Non-Stationary Channel Model for 6G Multi-UAV Cooperative Communication

This paper proposes a novel three-dimensional (3D) non-stationary multiple-unmanned aerial vehicle (multi-UAV) cooperative channel model for sixth generation (6G) wireless communication systems. In the proposed multi-UAV cooperative channel model, the channel impulse response (CIR) of sub-channel between each UAV and ground station (GS) is calculated, including line-of-sight (LoS), non-LoS (NLoS), as well as ground reflection transmissions. The relative distance and transmission relationship among sub-channels between multi-UAVs and GS are further modeled and analyzed. To simultaneously capture the cooperative non-stationarity of multi-UAV cooperative channels in space and time domains, a novel cooperation-based space-time (S-T) non-stationary algorithm is developed based on the birth-death (BD) process for the first time. Meanwhile, the UAV-related parameters, e.g., the height and 3D movement of UAVs, are considered. Some important channel statistical properties, such as space-time-frequency correlation function (STF-CF), Doppler power spectral density (DPSD), cooperative time stationary interval, and singular value spread (SVS), are obtained. Based on the simulation results, multi-UAV cooperative channel statistical properties are analyzed. Finally, the simulation results match well with the ray-tracing results, which validates the accuracy of the proposed multi-UAV channel model.

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.

3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion

AbstractUnmanned aerial vehicles (UAVs) play a vital role in the beyond fifth‐generation (B5G) and sixth‐generation (6G) wireless communication scenarios. This paper proposes a non‐stationary three‐dimensional (3D) geometry‐based multiple‐input multiple‐output channel model for UAV to vehicle (U2V) communications considering UAV heaving motion. The proposed model incorporates the effects of UAV heaving along with the rotation, acceleration, and 3D velocity variation for matching the realistic U2V communication scenarios. The computation methods for time variant channel parameters such as Doppler frequencies, angle of arrival, and angle of departure are given and analysed. The theoretical and statistical properties, including spatial temporal correlation function, TCF, level crossing rate, average fade duration, and Doppler power spectral density are derived and analysed aiming to evaluate the proposed model. Simulation results show that the output statistical characteristics agree with the hypothetical and simulated outcomes, which shows the validity of both the channel model and theoretical derivations.The cover image is based on the Research Article 3D geometry‐based UAV to vehicle multiple‐input multiple‐output channel model incorporating Unmanned aerial vehicle heaving motion by Naeem Ahmed et al., https://doi.org/10.1049/mia2.12393

A Non-Stationary Model With Time-Space Consistency for 6G Massive MIMO mmWave UAV Channels

In this paper, a novel unmanned aerial vehicle (UAV) space-time-frequency (S-T-F) non-stationary channel model with time-space consistency for sixth generation (6G) massive multiple-input multiple-output (MIMO) millimeter wave (mmWave) wireless communication systems is proposed. In the proposed model, the line-of-sight (LoS) transmission and non-LoS (NLoS) transmission through ground reflection, single-clusters, and twin-clusters are modeled. Meanwhile, the three-dimensional (3D) continuously arbitrary trajectory and the self-rotation of UAV are imitated. To capture the time-space consistency and S-T-F non-stationarity simultaneously, a new UAV-related non-stationary modeling algorithm that integrates the visibility region (VR), frequency-dependent path gain, and survival probability is developed for the first time. In this algorithm, the UAV-related parameters are considered, including UAV’s height, 3D moving velocity, and self-rotation angles. In the proposed model, the calculation of channel impulse response (CIR) is developed, which considers the cluster density index influenced by communication scenarios, frequency, UAV’s height, and the distance between transceivers. Some important channel statistical properties, such as S-T-F correlation function (STF-CF), Doppler power spectral density (DPSD), and stationary interval, are derived. Finally, simulation results match well with ray-tracing-based results, which verifies the utility of the proposed model.

A Non-Stationary 6G V2V Channel Model With Continuously Arbitrary Trajectory

In this article, a novel three-dimensional (3D) massive multiple-input multiple-output (MIMO) millimeter wave (mmWave) geometry-based stochastic model (GBSM) is proposed for sixth-generation (6G) vehicle-to-vehicle (V2V) channels. In the proposed GBSM, clusters in the environment are divided into static clusters and dynamic clusters. Furthermore, the time-variant acceleration together with the integration of time during the transmission distance update are exploited. As a result, the continuously arbitrary trajectory of the transceiver and dynamic clusters is successfully captured. To jointly model space-time-frequency (S-T-F) non-stationarity of 6G V2V channels, a new method, which properly integrates the frequency-dependent factor, birth-death (BD) process, and selective evolution of static and dynamic clusters, is developed. Key channel statistics, including the space-time-frequency correlation function (STF-CF), time stationary interval, and Doppler power spectral density (DPSD) are obtained. Simulation results demonstrate that S-T-F non-stationarity is modeled and the impacts of vehicular traffic density (VTD) and vehicular movement trajectory (VMT) on channel statistics are further analyzed thoroughly. Finally, the generality and accuracy of the proposed GBSM are validated through the comparison of simulation results and available measurement data.

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.

A 3-D Space-Time-Frequency Non-Stationary Model for Low-Altitude UAV mmWave and Massive MIMO Aerial Fading Channels

In this article, a 3-D geometry-based stochastic model (GBSM) is proposed for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) unmanned aerial vehicle (UAV) channels. The proposed model is the first mmWave massive MIMO UAV two-cylinder GBSM that enables to jointly model the channel space-time-frequency non-stationarity by a novel variable parameter-based method. In this novel method, key parameters of UAV channels are assumed to vary in space, time, and frequency domains, and the effect of the unique UAV-related parameters is further taken into account, such as the UAV’s altitude, velocity, and moving directions. Based on the proposed model, some statistical properties are derived, including the time-variant transfer function (TVTF), space-time-frequency correlation function (STF-CF), Doppler power spectral density (PSD), and the standard deviation of Doppler frequency on antenna arrays. Simulation results show that the channel non-stationarity in space, time, and frequency domains can be captured, and the aforementioned UAV channel-related parameters have a great impact on channel statistics. Finally, the utility of the proposed model is validated by the excellent agreement between simulation results and measurements.

UWB channel modeling and simulation with continuous frequency response

Ultra-wideband (UWB) technology is a prospective technology for high-rate transmission and accurate localization in the future communication systems. State-of-art channel modeling approaches usually divide the UWB channel into several sub-band channels and model them independently. By considering frequency-dependent channel parameters, a novel analytical UWB channel model with continuous frequency response is proposed. The composite effect of all frequency components within the UWB channel on the channel impulse response (CIR) of delay domain is derived based on the continuous channel transfer function (CTF) of frequency domain. On this basis, a closed-form simulation model for UWB channels and geometry-based parameter calculation method are developed, which can guarantee the continuity of channel characteristics on the frequency domain and greatly reduce the simulation complexity. Finally, the proposed method is applied to generate UWB channel with 2 GHz bandwidth at sub-6GHz and millimeter wave (mmWave) bands, respectively. The channel measurements are also carried out to validate the proposed method. The simulated CIR and power gain are shown to be in good agreement with the measurement data. Moreover, the comparison results of power gain and Doppler power spectral density (DPSD) show that the proposed UWB channel model achieves a good balance between the simulation accuracy and efficiency.

Geometry-Based Stochastic Model and Statistical Characteristic Analysis of Cell-Free Massive MIMO Channels

Cell-free massive multi-input multi-output (MIMO) systems exhibit many characteristics that differ from those of traditional centralized massive MIMO systems, and there are still research gaps in the modeling of cell-free massive MIMO channels. In this paper, a geometry-based stochastic model (GBSM) that combines the double-ring model and hemisphere model to comprehensively consider the distribution of scatterers in the environment was proposed for cell-free massive MIMO channels. Combined with the line-of-sight (LoS) path, single scattering path, and double scattering path components, the channel matrix between the access points (APs) and the user was derived. The proposed model fully considers geometric parameters such as the arrival/departure direction, elevation angle, time delay, and distance, which can accurately characterize the channel. Then, we proved that the traditional channel model, standard block-fading model, and spatial basis expansion model (SBEM) adopted in a cell-free massive MIMO system could not describe the nonstationarity in the space, time, and frequency domains, whereas the proposed GBSM could. Statistical characteristics of the channel were analyzed, including the space cross-correlation function (CCF), time autocorrelation function (ACF), Doppler power spectral density (PSD), level crossing rate (LCR), and average fade duration (AFD). Then, we investigated the proposed model by simulating the space CCF, time ACF, Doppler PSD, LCR, and AFD under the conditions of two different scatterer densities. Through simulations and analyses, some new features of cell-free massive MIMO channels were identified, providing a theoretical basis for in-depth research on cell-free massive MIMO systems. Finally, the measurement-based scenario and the WINNER II channel model are compared to demonstrate that the GBSM is more practical to characterize real cell-free massive MIMO channels.

A Mixed-Bouncing Based Non-Stationary Model for 6G Massive MIMO mmWave UAV Channels

This paper proposes a novel three-dimensional (3D) mixed-bouncing based unmanned aerial vehicle (UAV) channel model with space-time-frequency (S-T-F) non-stationarity for sixth generation (6G) massive multiple-input-multiple-output (MIMO) millimeter wave (mmWave) wireless communication systems. In the proposed mixed-bouncing based model, the line-of-sight (LoS) transmission, single-bouncing transmission, and multi-bouncing transmission are simultaneously modeled. A new parameter, i.e., cluster density index, is defined and developed. The influence of communication scenarios, frequency, UAV’s height, and distance between transceivers on cluster density index is also analyzed. To capture the S-T-F non-stationarity, a mixed-bouncing based S-T-F non-stationary algorithm is developed based on the birth-death (BD) process and frequency-dependent factor for the first time. In the developed algorithm, the non-stationarity is captured from the perspectives of both single-clusters and twin-clusters. Meanwhile, the impact of UAV-related parameters, such as the UAV’s height and 3D moving velocity, on the non-stationary modeling is considered. Based on the simulation results, the impact of cluster density index on the important channel statistical properties, such as S-T-F correlation function (STF-CF) and Doppler power spectral density (PSD), is explored. Finally, the simulation results match well with the measurement and ray-tracing (RT)-based results, validating the accuracy of the proposed model.

A 3-D Non-Stationary Model for Beyond 5G and 6G Vehicle-to-Vehicle mmWave Massive MIMO Channels

This paper proposes a novel three-dimensional (3D) non-stationary irregular-shaped geometry-based stochastic model (IS-GBSM) for beyond fifth-generation (B5G) and sixth-generation (6G) vehicle-to-vehicle (V2V) millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) channels. By distinguishing dynamic clusters and static clusters, the proposed IS-GBSM for the first time explores the impact of vehicular traffic density (VTD) on channel statistics in B5G/6G V2V mmWave massive MIMO scenarios. Furthermore, a novel method is developed to model the channel space-time-frequency non-stationarity. In the developed method, dynamic/static correlated clusters are first generated by an improved <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -Means clustering algorithm. Then, by employing a birth-death process based on correlated clusters, the consistency in birth and death between dynamic/static correlated clusters during time-array evolution is modeled. Key channel statistical properties, e.g., space-time-frequency correlation function (STF-CF) and Doppler power spectral density (DPSD), are derived. Simulation results demonstrate that the space-time-frequency non-stationarity is captured and the influence of VTDs on channel statistics is explored. Finally, the close agreement is achieved between simulation results and measurements, verifying the utility of proposed IS-GBSM.

A Non-Stationary 3D Model for 6G Massive MIMO mmWave UAV Channels

This paper proposes a non-stationary three-dimensional (3D) irregular-shaped geometry-based stochastic model (IS-GBSM) for fifth generation (5G) and beyond massive multiple-input multiple-output (MIMO) millimeter wave (mmWave) unmanned aerial vehicle (UAV) channels. This is the first sixth generation (6G) massive MIMO mmWave UAV IS-GBSM that can model the UAV channel space-time non-stationarity, and can describe the impact of some unique UAV-related parameters, e.g., the UAV&#x2019;s moving direction, height, and speed, on channel statistical properties. To better represent the space-time non-stationarity in UAV scenarios, a novel UAV-related space-time cluster evolution algorithm is developed. The developed algorithm considers the characteristics of UAV communications on the modeling of space-time non-stationarity. Based on the proposed model, some channel statistical properties are derived and thoroughly investigated, including the space-time-frequency correlation function, Doppler power spectral density, envelope level crossing rate, and average fade duration. Some numerical results and interesting observations are given, and the impact of UAV-related parameters on channel statistical properties is explored, which can provide assistance for the design of 6G massive MIMO mmWave UAV communication systems. Finally, the applicability of the proposed model is verified by the close agreement between simulation results and measurement.

A 3D Geometry-Based THz Channel Model for 6G Ultra Massive MIMO Systems

In this paper, a 3D geometry-based double-spherical terahertz (THz) channel model is proposed for ultra massive multiple-input multiple-output (MIMO) communications. To reflect real THz ultra massive MIMO communications, the characteristic of nano-material array antenna and the high loss of THz bands are considered in channel modeling. Based on the proposed geometry-based stochastic model (GBSM), power delay profile (PDP), space-time-frequency correlation function, and the Doppler power spectral density are derived and analyzed. Furthermore, the proposed model is validated by comparing the simulated results with the measurement reference. Influences of channel parameters, namely, antenna element spacing, carrier frequency, number and location of clusters, on the correlation functions are investigated. The results indicate that antenna element spacing and number of clusters have significant impacts on channel correlation, and the decreasing of correlation function becomes slower when antenna element spacing decreases. Moreover, location of clusters also affects the drop rate of correlation function. The influences of the number of clusters and concentration of intra-cluster multipath components (MPCs) on the Doppler power spectral density are analyzed. It is found that a larger number of clusters and a more concentrated distribution of intra-cluster MPCs increase the degree of Doppler spectrum variation. The proposed channel model and the corresponding statistical properties are insightful for designing and realizing THz ultra massive MIMO systems for 6G and beyond.

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 3D Cluster-Based Channel Model for 5G and Beyond Vehicle-to-Vehicle Massive MIMO Channels

In this paper, we propose a three-dimensional (3D) cluster-based model for the fifth generation (5G)/beyond 5G (B5G) vehicle-to-vehicle (V2V) massive multiple-input multiple-output (MIMO) wideband channels. It is the first cluster-based irregular shaped geometry-based stochastic model (IS-GBSM) to distinguish the dynamic clusters and static clusters in vehicular massive MIMO communication scenarios. This model not only considers the high time-variance, the time non-stationarity, and the vehicular traffic density (VTD) of V2V channels, but also models the massive MIMO channel characteristics, such as spherical wavefronts by 3D vector calculation and space non-stationarity. Meanwhile, this model for the first time integrates the VTD into birth-death process to model the channel characteristics of V2V and massive MIMO jointly and deeply, where a novel VTD-combined time-array cluster evolution algorithm for 5G/B5G V2V massive MIMO channel model is developed. Based on the proposed model, we derive some expressions of channel statistical properties, including time-space-frequency correlation function (STF-CF) and Doppler power spectral density (DPSD). The influence of several parameters, e.g., VTDs, vehicle moving directions, and antenna spacings, on the channel characteristics are sufficiently explored, which can provide assistance for the design of vehicular massive MIMO communication systems. Finally, the utility of the proposed model is verified by the close agreement between simulation results and measurement data.

A Novel GBSM for Non-Stationary V2V Channels Allowing 3D Velocity Variations.

A new non-stationary (NS) geometry-based stochastic model (GBSM) is presented for developing and testing the communication systems of vehicle-to-vehicle (V2V) applications, which considers the three-dimensional (3D) scattering environments and allows 3D velocity as well. In this paper, the proposed GBSM for NS V2V channels allowed 3D velocity variations and was more suitable for actual V2V communications because it provided smoother transitions between the consecutive channel segments. The time-variant channel coefficient and the channel parameters, i.e., Doppler frequencies, path delay and power, angle of arrival (AoA), and angle of departure (AoD), were analyzed and derived. Likewise, the theoretical statistical properties as the probability density function (PDF), the auto-correlation function (ACF), and Doppler power spectral density (DPSD) were also analyzed and derived under the von Mises–Fisher (VMF) distribution. Finally, the theoretical and measured results were well coordinated alongside the implemented results, which confirmed the feasibility of the introduced model along with the theoretical expressions.

A Study of 2D Non-Stationary Massive MIMO Channels by Transformation of Delay and Angular Power Spectral Densities

In this article, we propose a transformation method to model space-time-variant (STV) two-dimensional non-stationary wideband massive multiple-input multiple-output (MIMO) channels. This method enables us to obtain the STV joint probability density function of the time of arrival and angle of arrival (AOA) at any time instant and antenna element of the array from a predefined configuration of the scatterers. In addition, we introduce a simplified channel modeling approach based on STV parameters of the AOA distribution and demonstrate that key statistical properties of massive MIMO channels, such as the STV temporal autocorrelation function and Doppler power spectral density, can be derived in closed form. As examples of application, we study multiple array-variant properties of three widely-used geometry-based stochastic models (GBSMs): the Unified Disk, Ellipse, and Gaussian scattering models. Furthermore, we present numerical and simulation results of the statistical properties of these three GBSMs and compare them with those obtained using the conventional spherical wavefront approach. We point out possible limitations of the studied channel models to properly represent massive MIMO channels.

3‐D Massive MIMO Channel Model for High‐Speed Railway Wireless Communication

AbstractIn the fifth generation (5G) wireless communication, high‐speed railway (HSR) communication is one of the most challenging scenarios. By adopting massive multi‐input multioutput (mMIMO) technology in HSR communication, the design of the underlying communication system becomes more challenging. Some new channel characteristics must be studied, such as nonstationarity in space, time, and frequency domains. In this paper, two models are established for the two states of HSR. When the HSR stops, a three‐dimensional (3‐D) stationary channel model based on the single‐ring distribution of the scatterers is established. When the HSR moves, a 3‐D nonstationary geometric random channel model (GRCM) based on the cylinder distribution of the scatterers by introducing the birth and death process of the propagation path and time‐varying characteristics of the channel parameters is established. Moreover, a time evolution algorithm for time‐varying channel parameters is proposed, and a modularization study of key parameter update algorithms is conducted. Finally, based on the proposed 3‐D nonstationary geometric random channel model, important time‐varying channel statistical characteristics, such as time autocorrelation function (ACF), spatial cross‐correlation function (CCF), Doppler power spectral density (DPSD), and stationary interval are studied. Simulation results indicate that the properties of the proposed channel models, verified by simulation results, can match well with those of the theoretical model.

A Novel 3D UAV Channel Model for A2G Communication Environments Using AoD and AoA Estimation Algorithms

In this article, we propose a three-dimensional (3D) multi-input multi-output (MIMO) channel model for air-to-ground (A2G) communications in unmanned aerial vehicles (UAV) environments, where the UAV transmitter and ground receiver are in motion in the air and on the ground, respectively. A novel angular estimation algorithm is proposed to estimate the real-time azimuth angle of departure (AAoD), elevation angle of departure (EAoD), azimuth angle of arrival (AAoA), and elevation angle of arrival (EAoA) based on the non-stationary nature of the channel model. In the model, we investigate the time-varying spatial cross-correlation functions (CCFs) and temporal auto-correlation functions (ACFs) with respect to the different moving directions and velocities of the UAV transmitter and ground receiver. Furthermore, we derive and study the Doppler power spectral densities (PSDs) and power delay profiles (PDPs) of the proposed channel model. Numerical results show that characteristics of the proposed channel model are very close to those of practical measurements, which provide a new and practical approach to evaluate the performance of next generation UAV-MIMO communication systems.