Geometry-based Stochastic Model Research Articles

Measurements and Analysis of Angular Characteristics and Spatial Correlation for High-Speed Railway Channels

Spatial characteristics of the propagation channel have a vital impact on the application of multi-antenna techniques. This paper analyzes angular characteristics and the spatial correlation for high-speed railway (HSR) channels, based on a novel moving virtual antenna array (MVAA) measurement scheme. The principle of the MVAA scheme is deeply investigated and is further verified by a theoretical geometry-based stochastic model. Using the MVAA scheme, virtual single-input multiple-output (SIMO) channel impulse response data are derived from single-antenna measurements in typical HSR scenarios, involving viaduct, cutting, and station. Based on the SIMO channel data, angle of arrival is extracted according to the unitary estimation of signal parameters by the rotational invariance techniques algorithm, and is compared with the theoretical result. Moreover, power angular spectrum and root mean square (rms) angular spread (AS) are provided, and the rms AS results are statistically modeled and comprehensively compared. In addition, spatial correlation is calculated and analyzed, and a rms AS-dependent spatial correlation model is newly proposed to describe the relationship between the angular dispersion and the spatial correlation. The presented results could be used in multi-antenna channel modeling and will facilitate the assessment of multi-antenna technologies for future HSR mobile communication systems.

A Novel 3D Non-Stationary Vehicle-to-Vehicle Channel Model and its Spatial-Temporal Correlation Properties

In this paper, a new non-stationary Vehicle-to-Vehicle (V2V) channel model is proposed. It could generate more smooth fading phase between the adjacent channel states and guarantee more accurate Doppler frequency, which is a great improvement comparing with those of the existing non-stationary geometry-based stochastic models (GBSMs) for V2V channels. Meanwhile, the spatial–temporal correlation function (STCF) as well as a temporal correlation function (TCF) and a spatial correlation function (SCF) are derived in details based on the power angle spectrums of both the mobile transmitter (MT) and mobile receiver (MR) following the Von Mises Fisher (VMF) distribution. Simulation results have demonstrated that the time-variant correlation properties of our proposed channel model have an excellent agreement with the theoretical results, which verifies the correctness of theoretical derivations and simulations. Finally, the TCF and stationary interval of the proposed model are verified by the measured results.

Map-Based Channel Model for Evaluation of 5G Wireless Communication Systems

This paper presents a channel model for the fifth generation air interface evaluations. The described model covers frequency bands from typical cellular frequencies up to millimeter waves and a variety of different environments, with emphasis on the urban outdoor. The model enables assessment of single radio links with, e.g., the massive multiple-input-multiple-output (MIMO) and very large antenna arrays, device-to-device links with both link ends moving, up to system level evaluations with a multitude of different types of transceivers. In addition to the overview, some selected model features are described in more detail. Also, a few exemplary model outputs are depicted and discussed. A comparison to corresponding geometry-based stochastic model is performed in urban outdoor environment with the second moment distributions of propagation parameters and with the multiuser (MU) MIMO sum rate capacity. The simulations indicate substantial differences in MU-MIMO performances between the models.

3D non-stationary wideband circular tunnel channel models for high-speed train wireless communication systems

This paper proposes three-dimensional (3D) non-stationary wideband circular geometry-based stochastic models (GBSMs) for high-speed train (HST) tunnel scenarios. Considering single-bounced (SB) and multiple-bounced (MB) components from the tunnel's internal surfaces, a theoretical channel model is first established. Then, the corresponding simulation model is developed using the method of equal volume (MEV) to calculate discrete angular parameters. Based on the proposed 3D GBSMs, important time-variant statistical properties are investigated, such as the temporal autocorrelation function (ACF), spatial cross-correlation function (CCF), and space-Doppler (SD) power spectrum density (PSD). Results indicate that all statistical properties of the simulation model, verified by simulation results, can match well those of the theoretical model. The statistical properties of the proposed 3D GBSMs are further validated by relevant measurement data, demonstrating the flexibility and utility of our proposed tunnel GBSMs.

3D Wideband Non-Stationary Geometry-Based Stochastic Models for Non-Isotropic MIMO Vehicle-to-Vehicle Channels

Actual vehicle-to-vehicle (V2V) channel measurements have shown that the wide-sense stationary (WSS) modeling assumption is valid only for very short time intervals. This fact motivates us to develop non-WSS V2V channel models. In this paper, we propose a novel three-dimensional (3D) theoretical non-WSS regular-shaped geometry-based stochastic model (RS-GBSM) and the corresponding sum-of-sinusoids (SoS) simulation model for non-isotropic scattering wideband multiple-input multiple-output (MIMO) V2V fading channels. The movements of the transmitter (Tx), scatterers, and receiver (Rx) result in the time-varying angles of departure (AoDs) and angles of arrival (AoAs) that make our models non-stationary. The proposed RS-GBSMs, combining line-of-sight (LoS) components, a two-sphere model, and multiple confocal elliptic-cylinder models, have the ability to study the impacts of vehicular traffic density (VTD) and non-stationarity on channel statistics, and jointly consider the azimuth and elevation angles by using the von Mises Fisher (VMF) distribution. The proposed RS-GBSMs are sufficiently generic and adaptable to model various V2V scenarios. Based on the proposed 3D non-WSS RS-GBSMs, important local channel statistical properties are derived and thoroughly investigated. The impacts of VTD and non-stationarity on these channel statistical properties are investigated by comparing them with those of the corresponding WSS model. The proposed non-WSS RS-GBSMs are validated by measurements in terms of the channel stationary time. Finally, numerical and simulation results demonstrate that the 3D non-WSS model is more practical to characterize real V2V channels.

Nested Sparse Approximation: Structured Estimation of V2V Channels Using Geometry-Based Stochastic Channel Model

Future intelligent transportation systems promise increased safety and energy efficiency. Realization of such systems will require vehicle-to-vehicle (V2V) communication technology. High fidelity V2V communication is, in turn, dependent on accurate V2V channel estimation. V2V channels have characteristics differing from classical cellular communication channels. Herein, geometry-based stochastic modeling is employed to develop a characterization of V2V channel channels. The resultant model exhibits significant structure; specifically, the V2V channel is characterized by three distinct regions within the delay-Doppler plane. Each region has a unique combination of specular reflections and diffuse components resulting in a particular element-wise and group-wise sparsity. This joint sparsity structure is exploited to develop a novel channel estimation algorithm. A general machinery is provided to solve the jointly element/group sparse channel (signal) estimation problem using proximity operators of a broad class of regularizers. The alternating direction method of multipliers using the proximity operator is adapted to optimize the mixed objective function. Key properties of the proposed objective functions are proven which ensure that the optimal solution is found by the new algorithm. The effects of pulse shape leakage are explicitly characterized and compensated, resulting in measurably improved performance. Numerical simulation and real V2V channel measurement data are used to evaluate the performance of the proposed method. Results show that the new method can achieve significant gains over previously proposed methods.

Mobile-to-Mobile Wideband MIMO Channel Realization by Using a Two-Ring Geometry-Based Stochastic Scattering Model

In this paper, a geometry-based stochastic scattering model (GBSSM) for wideband multiple-input multiple-output mobile-to-mobile (M2M) isotropic scattering fading channels is proposed. The model is based on a two-ring scattering model which can be applied for the line-of-sight (LOS) and non-LOS scenarios by considering the single- and double-bounced components. The target of developing the GBSSM is to realize the channel in typical environments for future internet-of-thing networks such as shopping malls, logistics centers and so on to be used in the link and system level simulations in M2M new radio systems. The channel realization in this paper is more straight forward and concise to study the channel characteristics compare with the too complicated analytical solutions available so far.

Modeling Network Interference in the Angular Domain: Interference Azimuth Spectrum

The performance of wireless networks is fundamentally limited by interference [or, equivalently, the signal-to-interference ratio (SIR)]. In an attempt to characterize the interference as a direction-selective quantity and motivated by the useful analogy between classical propagation channels and wireless networks, we propose a novel network description framework, namely the interference azimuth spectrum (IAS). The IAS represents the distribution of interference in the angular domain and is parallel to the conventional power azimuth spectrum (PAS) used in propagation channels. We also extend this concept to the directional characterization of average achievable rate, assuming that interference is treated as noise. Provided with this analytical framework, we present the notion of local area outage, defined as the probability that a receiver is in the state of outage within a local area where both interference and desired signal are assumed to be wide-sense stationary (WSS). We further propose the geometry-based stochastic models (GBSMs) as a part of the IAS framework, where the interfering terminals are randomly distributed according to a specific probability density function (pdf) of their positions. The GBSMs are applicable to a wide variety of wireless network environments without and with interferer clustering. The proposed methodology would provide useful insight on the design and performance assessment of future networks, featured by opportunistic, randomized, and dense placement of nodes.

Envelope Level Crossing Rate and Average Fade Duration of Nonisotropic Vehicle-to-Vehicle Ricean Fading Channels

This paper proposes a generic geometry-based stochastic model for nonisotropic scattering vehicle-to-vehicle (V2V) Ricean fading channels. With the proposed model, the level crossing rate (LCR) and average fade duration (AFD) are derived. The resultant expressions are sufficiently general and subsume many well-known existing LCRs and AFDs as special cases. The derived LCR and AFD are further investigated in terms of some important parameters, e.g., the shape of the scattering region (two-ring or ellipse), mean angle, angle spread, and directions of movement of the Tx and Rx (same or opposite direction). More importantly, in this paper, the impact of the vehicular traffic density on the LCR and AFD for nonisotropic scattering V2V Ricean fading channels is investigated for the first time. Excellent agreement is observed between the theoretical LCRs/AFDs and corresponding measured data, thus demonstrating the validity and utility of the proposed model.

A Semiempirical MIMO Channel Model in Obstructed Viaduct Scenarios on High-Speed Railway

A semiempirical multiple-input multiple-output (MIMO) channel model is proposed for high-speed railway (HSR) viaduct scenarios. The proposed MIMO model is based on the combination of realistic single-input single-output (SISO) channel measurement results and a theoretical geometry-based stochastic model (GBSM). Temporal fading characteristics involvingK-factor and Doppler power spectral density (PSD) are derived from the wideband measurement under an obstructed viaduct on Zhengzhou-Xi’an HSR in China. The GBSM composed of a one-ring model and an elliptical model is employed to describe the entire propagation environment. Environment-related parameters in the GBSM are determined by the measured temporal fading properties. And a close agreement is achieved between the model results and measured data. Finally, a deterministic simulation model is established to perform the analysis of the space-time correlation function, the space-Doppler PSD, and the channel capacity for the measured scenario. This model is more realistic and particularly beneficial for the performance evaluation of MIMO systems in HSR environments.

A Nonstationary Wideband MIMO Channel Model for High-Mobility Intelligent Transportation Systems

The recent development of high-speed trains (HSTs), as a high-mobility intelligent transportation system, and the growing demands of broad-band services for HST users, introduce new challenges to wireless communication systems for HSTs. The deployment of mobile relay stations on top of the train carriages is one of the promising solutions for HST wireless systems. For a proper design and evaluation of HST wireless communication systems, we need accurate channel models that can mimic the underlying channel characteristics for different HST scenarios. In this paper, a novel nonstationary geometry-based stochastic model (GBSM) is proposed for wideband multiple-input multiple-output HST channels in rural macrocell scenarios. The corresponding simulation model is then developed with angle parameters calculated by the modified method of equal areas. Both channel models can also be used to model nonstationary vehicle-to-infrastructure channels in vehicular communication networks. The system functions and statistical properties of the proposed channel models are investigated based on a theoretical framework that describes nonstationary channels. Numerical and simulation results demonstrate that the proposed channel models have the capability to characterize the nonstationarity of HST channels. The statistical properties of the simulation model, verified by the simulation results, can match those of the proposed theoretical GBSM. An excellent agreement is achieved between the stationary intervals of the proposed simulation model and those of relevant measurement data, demonstrating the utility of the proposed channel models.

Novel 3D Geometry-Based Stochastic Models for Non-Isotropic MIMO Vehicle-to-Vehicle Channels

This paper proposes a novel three-dimensional (3D) theoretical regular-shaped geometry-based stochastic model (RS-GBSM) and the corresponding sum-of-sinusoids (SoS) simulation model for non-isotropic multiple-input multiple-output (MIMO) vehicle-to-vehicle (V2V) Ricean fading channels. The proposed RS-GBSM, combining line-of-sight (LoS) components, a two-sphere model, and an elliptic-cylinder model, has the ability to study the impact of the vehicular traffic density (VTD) on channel statistics, and jointly considers the azimuth and elevation angles by using the von Mises Fisher distribution. Moreover, a novel parameter computation method is proposed for jointly calculating the azimuth and elevation angles in the SoS channel simulator. Based on the proposed 3D theoretical RS-GBSM and its SoS simulation model, statistical properties are derived and thoroughly investigated. The impact of the elevation angle in the 3D model on key statistical properties is investigated by comparing with those of the corresponding two-dimensional (2D) model. It is demonstrated that the 3D model is more accurate to characterize real V2V channels, in particular for pico cell scenarios. Finally, close agreement is achieved between the theoretical model, SoS simulation model, and simulation results, demonstrating the utility of the proposed models.

Average-Instantaneous, Unimodal and Multimodal Scattering Responses in Spatial Gaussian Channels

The long-standing problem of identifying the scattering mechanism that triggers the observance of a heavy-tailed power azimuth spectrum is undertaken using a geometry-based stochastic approach. More specifically, the unimodal power azimuth spectrum (PAS) and joint power angular scattering response (PASR) are derived under the 2-D Gaussian scattering model. At first, it is formally shown that, under free-space propagation, a Gaussian scatter distribution in 2-D space gives rise to an angular power spectrum that may be well modeled by the Gaussian function. Numerical results are presented for higher path-loss exponents, where it is shown that heavy-tailed functions such as the Lorentzian and Laplacian functions provide good fits to the derived spectrum. To complement earlier research works in this area, a recently introduced geometry-based stochastic model is extended in order to express the instantaneous multimodal PASR, which significantly contributes to the estimated correlation statistics as shown in the paper. The 2-D spatial channel model developed herein, allows the distance from the observation point to vary, which enhances the validity of the derived PAS and PASR. Statistical results are provided for various distances from the observation point in order to facilitate any potential practical use of the derived 2-D model. Finally, an analytical expression for the correlation experienced between two antenna patterns is derived under the proposed model.

Wideband Channel Modeling and Intercarrier Interference Cancellation for Vehicle-to-Vehicle Communication Systems

In this paper, we propose a new regular-shaped geometry-based stochastic model (RS-GBSM) for non-isotropic scattering wideband multiple-input multiple-output vehicle-to-vehicle (V2V) Ricean fading channels. By correcting the unrealistic assumption widely used in current RS-GBSMs, the proposed model can more practically study the impact of the vehicular traffic density on channel statistics for different time delays. From the proposed model, we derive the Doppler power spectral density (PSD) and find that highly dynamic Doppler spectrum appears for V2V channels. Excellent agreement is achieved between the derived Doppler PSD and measured data, demonstrating the utility of the proposed model. To combat the intercarrier interference (ICI) caused by highly dynamic Doppler spectrum in real orthogonal frequency division multiplexing based V2V systems, this paper proposes a new type of ICI cancellation scheme, named as precoding based cancellation (PBC) scheme. The proposed scheme can be easily implemented into real V2V systems with the same ICI mitigation performance as the current best ICI cancellation scheme that has high complexity. To further improve the performance of the proposed PBC scheme, a new phase rotation aided (PRA) method, namely constant PRA (CPRA) method, is proposed. Compared with the existing PRA method, the CPRA method has better performance and much less implementation complexity. Therefore, the proposed PBC scheme with the CPRA method is the best ICI cancellation scheme for real V2V systems.

Human Body Influence on Terminal in Wireless Communication

This paper presents a statistical characterization of communication channel under influence of human body on mobile terminal using the concept of super antenna and geometry-based stochastic models. The disturbances are inserted into the channel trough modified radiation patterns. We have concluded in this work that the human body changes the communication channel from a Nakagami to a Weibull distribution for the studied scenarios. Furthermore, its presence in antenna near field results in worse level cross rate proportional to the distance between the terminal and disturbers.

Cooperative MIMO Channel Modeling and Multi-Link Spatial Correlation Properties

In this paper, a novel unified channel model framework is proposed for cooperative multiple-input multiple-output (MIMO) wireless channels. The proposed model framework is generic and adaptable to multiple cooperative MIMO scenarios by simply adjusting key model parameters. Based on the proposed model framework and using a typical cooperative MIMO communication environment as an example, we derive a novel geometry-based stochastic model (GBSM) applicable to multiple wireless propagation scenarios. The proposed GBSM is the first cooperative MIMO channel model that has the ability to investigate the impact of the local scattering density (LSD) on channel characteristics. From the derived GBSM, the corresponding multi-link spatial correlation functions are derived and numerically analyzed in detail.

Geometry-Based Stochastic Modeling for MIMO Channel in High-Speed Mobile Scenario

The geometry-based stochastic channel models are proposed in this paper for the terrain cutting, suburb, and urban scenarios in high-speed railway. First, the special scenarios in high-speed railway are described. And the channel models based on the geometry scenarios are introduced. Some channel parameters are based on measurement data. Then, the space-time correlation functions in analytical form are obtained in suburb and urban scenarios. Finally, the space correlation characteristics in three scenarios are compared.

An adaptive geometry-based stochastic model for non-isotropic MIMO mobile-to-mobile channels

In this paper, a generic and adaptive geometrybased stochastic model (GBSM) is proposed for non-isotropic multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) Ricean fading channels. The proposed model employs a combined two-ring model and ellipse model, where the received signal is constructed as a sum of the line-of-sight, single-, and doublebounced rays with different energies. This makes the model sufficiently generic and adaptable to a variety of M2M scenarios (macro-, micro-, and pico-cells). More importantly, our model is the first GBSM that has the ability to study the impact of the vehicular traffic density on channel characteristics. From the proposed model, the space-time-frequency correlation function and the corresponding space-Doppler-frequency power spectral density (PSD) of any two sub-channels are derived for a non-isotropic scattering environment. Based on the detailed investigation of correlations and PSDs, some interesting observations and useful conclusions are obtained. These observations and conclusions can be considered as a guidance for setting important parameters of our model appropriately and building up more purposeful measurement campaigns in the future. Finally, close agreement is achieved between the theoretical results and measured data, demonstrating the utility of the proposed model.

A geometry-based stochastic MIMO model for vehicle-to-vehicle communications

Vehicle-to-vehicle (VTV) wireless communications have many envisioned applications in traffic safety and congestion avoidance, but the development of suitable communications systems and standards requires accurate models for the VTV propagation channel. In this paper, we present a new wideband multiple-input-multiple-output (MIMO) model for VTV channels based on extensive MIMO channel measurements performed at 5.2 GHz in highway and rural environments in Lund, Sweden. The measured channel characteristics, in particular the nonstationarity of the channel statistics, motivate the use of a geometry-based stochastic channel model (GSCM) instead of the classical tapped-delay line model. We introduce generalizations of the generic GSCM approach and techniques for parameterizing it from measurements and find it suitable to distinguish between diffuse and discrete scattering contributions. The time-variant contribution from discrete scatterers is tracked over time and delay using a high resolution algorithm, and our observations motivate their power being modeled as a combination of a (deterministic) distance decay and a slowly varying stochastic process. The paper gives a full parameterization of the channel model and supplies an implementation recipe for simulations. The model is verified by comparison of MIMO antenna correlations derived from the channel model to those obtained directly from the measurements.

Reduced Complexity Channel Models for IMT-Advanced Evaluation

Accuracy and complexity are two crucial aspects of the applicability of a channel model for wideband multiple input multiple output (MIMO) systems. For small number of antenna element pairs, correlation-based models have lower computational complexity while the geometry-based stochastic models (GBSMs) can provide more accurate modeling of real radio propagation. This paper investigates several potential simplifications of the GBSM to reduce the complexity with minimal impact on accuracy. In addition, we develop a set of broadband metrics which enable a thorough investigation of the differences between the GBSMs and the simplified models. The impact of various random variables which are employed by the original GBSM on the system level simulation are also studied. Both simulation results and a measurement campaign show that complexity can be reduced significantly with a negligible loss of accuracy in the proposed metrics. As an example, in the presented scenarios, the computational time can be reduced by up to 57% while keeping the relative deviation of 5% outage capacity within 5%.