Geometry-based Stochastic Model Research Articles

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 3D Non-Stationary Channel Model for 6G Wireless Systems Employing Intelligent Reflecting Surfaces With Practical Phase Shifts

In this paper, a three-dimensional (3D) geometry-based stochastic model (GBSM) for a massive multiple-input multiple-output (MIMO) communication system employing practical discrete intelligent reflecting surface (IRS) is proposed. The proposed channel model supports the scenario where both transceivers and environments move. The evolution of clusters in the space domain and the practical discrete phase shifts are considered in the channel model. The steering vector is set at the base station for the cooperation with IRS. Through studying statistical properties, the non-stationary properties are verified. We find that IRS plays a role in separating the whole channel and makes the absolute value of time autocorrelation function (ACF) larger than the situation without employing IRS. Time ACF of the case using discrete phase shifts is also compared with the continuous case.

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 General 3D Space-Time-Frequency Non-Stationary THz Channel Model for 6G Ultra-Massive MIMO Wireless Communication Systems

In this paper, a novel three-dimensional (3D) space-time-frequency (STF) non-stationary geometry-based stochastic model (GBSM) is proposed for the sixth generation (6G) terahertz (THz) wireless communication systems. The proposed THz channel model is very general having the capability to capture different channel characteristics in multiple THz application scenarios such as indoor scenarios, device-to-device (D2D) communications, ultra-massive multiple-input multiple-output (MIMO) communications, and long traveling paths of users. Also, the generality of the proposed channel model is demonstrated by the fact that it can easily be reduced to different simplified channel models to fit specific scenarios by properly adjusting model parameters. The proposed general channel model takes into consideration the non-stationarities in space, time, and frequency domains caused by ultra-massive MIMO, long traveling paths, and large bandwidths of THz communications, respectively. Statistical properties of the proposed general THz channel model are investigated. The accuracy and generality of the proposed channel model are verified by comparing the simulation results of the relative angle spread and root mean square (RMS) delay spread with corresponding channel measurements.

A General 3D Non-Stationary Wireless Channel Model for 5G and Beyond

In this paper, a novel three-dimensional (3D) non-stationary geometry-based stochastic model (GBSM) for the fifth generation (5G) and beyond 5G (B5G) systems is proposed. The proposed B5G channel model (B5GCM) is designed to capture various channel characteristics in (B)5G systems such as space-time-frequency (STF) non-stationarity, spherical wavefront (SWF), high delay resolution, time-variant velocities and directions of motion of the transmitter, receiver, and scatterers, spatial consistency, etc. By combining different channel properties into a general channel model framework, the proposed B5GCM is able to be applied to multiple frequency bands and multiple scenarios, including massive multiple-input multiple-output (MIMO), vehicle-to-vehicle (V2V), high-speed train (HST), and millimeter wave-terahertz (mmWave-THz) communication scenarios. Key statistics of the proposed B5GCM are obtained and compared with those of standard 5G channel models and corresponding measurement data, showing the generalization and usefulness of the proposed model.

Propagation Models in Vehicular Communications

In the advent of becoming reality, the era of autonomous vehicles is closer than ever, and with it, the need for faster and reliable wireless connections. The propagation channel determines the performance limits of wireless communications, and with the aid of empirical measurements, channel modeling is the best approach to predict and recreate how signal propagation conditions may perform. To this end, many different approaches and techniques have been implemented, from specific applications to general models, considering the characteristics of the environment (geometry-based or non-geometry-based) as well as seeking high performance algorithms in order to achieve good balance between accuracy and computational cost. This paper provides an updated overview of propagation channel models for vehicular communications, beginning with some specific propagation characteristics of these complex heterogeneous environments in terms of diverse communication scenarios, different combinations of link types, antenna placement/diversity, potentially high Doppler shifts, or non-stationarity, among others. The presented channel models are classified in four categories: empirical, non-geometry-based stochastic, geometry-based stochastic, and deterministic models, following the classical approach. The features and key concepts of the different vehicular communications channel models are presented, from sub 6 GHz to millimeter wave (mmWave) frequency bands. The advantages and disadvantages of the main works in the area are discussed and compared in a comprehensive way, outlining their contributions. Finally, future critical challenges and research directions for modeling reliable vehicular communications are introduced, such as the effects of vegetation, pedestrians, common scatterers, micro-mobility or spherical wavefront, which in the context of the near future are presented as research opportunities.

A Dynamic 3-D Wideband GBSM for Cooperative Massive MIMO Channels in Intelligent High-Speed Railway Communication Systems

Coordinated multipoint (CoMP) and massive multiple-input multiple-output (mMIMO) are two of promising technologies in future intelligent high-speed railway (HSR) communication systems, whose performance is fundamentally determined by the characteristics of cooperative mMIMO channels. This article proposes a dynamic three-dimensional (3-D) wideband geometry-based stochastic model (GBSM) for HSR cooperative mMIMO channels. The proposed GBSM employs a sphere model and two elliptic-cylinder models to describe common and uncommon clusters for different links, and integrates the dynamic cluster evolution in both time and array domains. Statistical properties of the cooperative mMIMO model are investigated, such as multi-link spatial cross-correlation function and sum rate capacity. A corresponding dynamic 3-D wideband simulation model for the HSR cooperative mMIMO channel is also proposed. Finally, numerical results of the statistical properties are analyzed, and the proposed model is validated by realistic HSR channel measurement data, in terms of dual-link spatial cross-correlation and channel capacity. This model is more practical and will be helpful for facilitating the design and performance evaluation of future intelligent HSR communication systems.

A Geometry-Based Beamforming Channel Model for UAV mmWave Communications.

Considering the three-dimensional (3D) trajectory, 3D antenna array, and 3D beamforming of unmanned aerial vehicle (UAV), a novel non-stationary millimeter wave (mmWave) geometry-based stochastic model for UAV to vehicle communication channels is proposed. Based on the analysis results of measured and ray tracing simulation data of UAV mmWave communication links, the proposed parametric channel model is constructed by a line-of-sight path, a ground specular path, and two strongest single-bounce paths. Meanwhile, a new parameter computation method is also developed, which is divided into the deterministic (or geometry-based) part and the random (or empirical) part. The simulated power delay profile and power angle profile demonstrate that the statistical properties of proposed channel model are time-variant with respect to the scattering scenarios, positions and beam direction. Moreover, the simulation results of autocorrelation functions fit well with the theoretical ones as well as the measured ones.

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.

Impact of UAV Rotation on MIMO Channel Characterization for Air-to-Ground Communication Systems

Unmanned aerial vehicle (UAV) communications have been considered as one of the promising technologies to support numerous applications in the fifth and sixth generations wireless networks. A deep understanding of propagation channel is necessary for the design of wireless communication systems. A three-dimensional (3D) wideband non-stationary geometry-based stochastic model (GBSM) is proposed for UAV multiple-input multiple-output (MIMO) channels in this paper. The proposed GBSM considers the both line-of-sight (LoS) and non-LoS (NLoS) components in the transmission links from a UAV transmitter (Tx) to a ground receiver (Rx), the proposed 3D GBSM is used for the first time to investigate the impact of UAV rotation, which results in time-varying channel parameters and reflects the non-stationarity of channel. Based on the proposed model, we derive and study some significant statistical properties, including the transfer function, space-time-frequency correlation function, Doppler power spectrum, and quasi-stationary interval. Numerical results show that the UAV rotation has a significant impact on channel statistical properties and non-stationarity. It is found that, even for a low range of UAV rotations, channel correlations are significantly affected, and the time correlation gradually increases with the pitch angle of UAV. Finally, the impact of using directional antennas at Tx on channel characteristics is analyzed. It is found that the channel correlation with directional antenna is significantly increased compared with the results with omnidirectional antenna. These observations and conclusions can be used as a reference for the system design and performance analysis of UAV-MIMO communication systems.

A Novel Nonstationary 6G UAV-to-Ground Wireless Channel Model With 3-D Arbitrary Trajectory Changes

In order to provide reliable and efficient connections between unmanned aerial vehicles (UAVs) and ground stations (GSs), realistic UAV-to-ground channel models are indispensable. In this article, we propose a novel 3-D nonstationary geometry-based stochastic model (GBSM) for UAV-to-ground multiple-input-multiple-output (MIMO) channels. Distinctive UAV-to-ground channel characteristics, such as time-domain nonstationarity, distinctions between different altitudes, spatial consistency, and 3-D arbitrary UAV movement trajectories, are taken into account. By adjusting parameter settings, the proposed channel model framework is sufficiently general to support multiple frequency bands and multiple scenarios, including millimeter wave (mmWave) and massive MIMO configurations. Statistical properties, including power delay profile (PDP), stationary interval, space-time correlation function (STCF), and root-mean-square (RMS) delay spread are derived and analyzed for different frequencies and scenarios. The accuracy of the proposed model is validated by comparing its statistical properties with corresponding available channel measurements. The proposed channel model will provide a fundamental support for the design, performance evaluation, and optimization of future UAV integrated sixth-generation (6G) wireless networks.

Analytical Non-Stationary Satellite to Aircraft Channel Modeling over Open Area Based on Regular Shaped Geometry-Based Stochastic Model

Channel modeling is crucial to the development and evaluation of modern wireless communication systems including satellite communication system, since there might be critical safty-of-life applications. Also, the channel model is of great importance to the performance evaluation of mobile communication systems. In recent years, encouraged by the widely application of unmanned aerial vehicles, the research on channel modeling for aerial and aeronautical communications attract lots of interests. In the published articles, stationary and non-stationary channel models have been developed for air-to-ground communications based on regular shaped geometry-based stochastic model (RS-GBSM). The modeling of air-to-air or satellite-to-aircraft (S2A) communication is still quite simple or completely lacking. For obtaining more precise model of S2A channel, this paper presents an analytical non-stationary S2A channel mode based on RS-GBSM with considerations on line-of-sight path, specular reflection path, and ground scattering path. Analytical expressions of the channel impulse responses, the transfer functions, the auto-correlation functions, and the Doppler power spectrum density based on 3-path model are derived and simulated. Also, the distributions of the path antennation, the path delay, and the normalized Doppler shift based on uniform distribution of the scatterers are derived, simulated and fitted.

A Big Data Enabled Channel Model for 5G Wireless Communication Systems

The standardization process of the fifth generation (5G) wireless communications has recently been accelerated and the first commercial 5G services would be provided as early as in 2018. The increasing of enormous smartphones, new complex scenarios, large frequency bands, massive antenna elements, and dense small cells will generate big datasets and bring 5G communications to the era of big data. This paper investigates various applications of big data analytics, especially machine learning algorithms in wireless communications and channel modeling. We propose a big data and machine learning enabled wireless channel model framework. The proposed channel model is based on artificial neural networks (ANNs), including feed-forward neural network (FNN) and radial basis function neural network (RBF-NN). The input parameters are transmitter (Tx) and receiver (Rx) coordinates, Tx-Rx distance, and carrier frequency, while the output parameters are channel statistical properties, including the received power, root mean square (RMS) delay spread (DS), and RMS angle spreads (ASs). Datasets used to train and test the ANNs are collected from both real channel measurements and a geometry based stochastic model (GBSM). Simulation results show good performance and indicate that machine learning algorithms can be powerful analytical tools for future measurement-based wireless channel modeling.

A 3-D Geometry-Based Stochastic Model for Unmanned Aerial Vehicle MIMO Ricean Fading Channels

In this article, we propose a novel 3-D geometry-based stochastic model (GBSM), i.e., a two-cylinder model, for unmanned aerial vehicle (UAV) multiple-input–multiple-output (MIMO) Ricean fading channels. The received signal is a sum of the Line-of-Sight (LoS) component, single-bounced (SB) rays at the UAV side, SB rays at the ground station side, SB rays on the ground, and double-bounced rays. This makes our model adaptable to a wide variety of UAV communication scenarios. More importantly, the proposed UAV model is the first two-cylinder model that considers ground reflections. Moreover, our model has the ability to investigate the impact of some unique UAV-related parameters (e.g., the UAV’s moving direction, UAV’s altitude, and antenna orientation) on channel characteristics in a 3-D nonisotropic propagation environment. From the proposed model, we derive and study some significant statistical properties, including the space-time correlation function (CF), Doppler power spectral density (PSD), envelope level crossing rate (LCR), and average fade duration (AFD). Some numerical results and interesting observations are provided, which can be considered useful guidance for the design of UAV-MIMO communication systems. Finally, the utility of our model is verified by the close agreement between the theoretical results and some example measurement data.

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.

Envelope Level Crossing Rate and Average Fade Duration of a Generic 3D Non-Stationary UAV Channel Model

For the unmanned aerial vehicle (UAV) communication scenarios, the time-varying fading characteristics cased by the three-dimensional(3D) scattering environment and 3D trajectory have an important impact on establishing the reliable communication link. In this paper, a generic 3D non-stationary geometry-based stochastic model (GBSM) for UAV channels is developed. Different from the traditional 3D GBSMs, the proposed model takes the 3D arbitrary trajectories of UAV into account. On this basis, two important second-order statistical properties of fading envelope, i.e., the level crossing rate (LCR) and average fading duration (AFD), are investigated and derived in details. The obtained closed-form expressions are explicit functions of flight parameters and compatible with the results in the previous works. Numerical simulations show that the simulated results are in accordance with the theoretical and measurement data under 3D flight scenarios. The proposed model and statistical properties can be applied to the optimal design of channel coding and block interleave schemes for UAV communication systems.

A 3D Non-Stationary GBSM for Vehicular Visible Light Communication MISO Channels

The potential of using visible light communication (VLC) technologies for vehicular communication networks has recently attracted much attention. The underlying VLC channels, as a foundation for the proper design and optimization of vehicular VLC communication systems, have not yet been sufficiently investigated. Vehicular VLC link impairments can have a significant impact on the system performance and capacity. Such impairments include the optical wireless channel distortion and background noise. This paper proposes a novel three-dimensional (3D) regular-shaped geometry-based stochastic model (RS-GBSM) for vehicular VLC multiple-input single-output (MISO) channels. The proposed 3D RS-GBSM combines a two-sphere model and an elliptic-cylinder model. Both the line-of-sight (LoS) and single-bounced (SB) components are considered. The proposed model jointly considers the azimuth and elevation angles by using von-Mises-Fisher (VMF) distribution. Based on the proposed model, the relationship between the communication range and the received optical power is analyzed and validated by simulations. The impact of the elevation angle in the 3D model on the received optical power is investigated by comparing with the received optical power of the corresponding two-dimensional (2D) model. Furthermore, the background noise is also modeled to evaluate the system's signal-to-noise ratio (SNR).

Three-Dimensional Modeling of mmWave Doubly Massive MIMO Aerial Fading Channels

Aerial networks represent a complementary technology for the provision of fifth-generation (5G) wireless communication services via high- and low-altitude platforms (HAPs/LAPs) or airborne vehicles. This paper proposes a three-dimensional (3-D) regular-shaped geometry-based stochastic model (RS-GBSM) for millimeter wave (mmWave) massive multiple-input–multiple-output (MIMO) aerial fading channels. A birth–death process is used to model the non-stationary properties of clusters on both the spatial and temporal domains. In addition, the channel statistical properties are studied and mathematical expressions for the space-time-frequency correlation function (STFCF) and the Doppler power spectral density (PSD) are derived. Based on the RS-GBSM, a statistical simulation model is also developed to confirm the numerical results.

An Angle Rotate-QAM aided Differential Spatial Modulation for 5G Ubiquitous Mobile Networks

As a novel multiple-input multiple-output (MIMO) wireless transmission technique, differential spatial modulation (DSM) can reduce the computational complexity, and henceforth provides a feasible communications option in terms of the intelligence computing for fifth generation (5G) ubiquitous mobile networks. In this paper, a novel high-rate design scheme relying on angle rotate quadrature amplitude modulation (ARQAM) is proposed for DSM schemes. Through layering QAM symbols, the final transmit matrix can be expressed as the superposition of the different layered matrices. Numercial results indicate that the proposed scheme outperforms the identical-throughput multi-ring APSK-aided and PSK-aided DSM schemes. Additionally, we investigate the impact of two-dimensional (2D) and three-dimensional (3D) regular-shaped geometry-based stochastic model (RS-GBSM) for non-isotropic scattering narrowband MIMO vehicle-to-vehicle (V2V) Ricean fading channel for the proposed ARQAM-aided DSM. Its performance is limited by the V2V channel required for differential detection. Moreover, the influences adopted with 3D MIMO channel model are more significant than 2D MIMO channel model.

Air-to-ground 3D channel modeling for UAV based on Gauss-Markov mobile model

Air-to-ground (A2G) communication has been attracted great attention due to the gradual popularization of unmanned aerial vehicle (UAV). In this paper, a 3D geometry-based stochastic model (GBSM) for A2G channels is proposed. Meanwhile, the Gauss-Markov mobile model is adopted to generate dynamic trajectories. According to different scattering environments, we establish a reference model and a statistical simulation model for A2G channels, and derive their respective time correlation functions. In particular, the purpose of establishing the statistical simulation model is to reduce complexity, and we verify the consistency of the two models. Then, we analyze the dynamic motion scenarios generated by Gauss-Markov process, and their effects on A2G channel correlation. Finally, the good conformities of time correlation curves with the existing measurement data and sphere model verify the reliability of our proposed models.