A Geometry-Based Stochastic Scattering Channel Model for V2V Communications in Dense Urban Street Environments

Jie Zhou,Zhikang Lyu,Sujie Wu,Hong Luo,Ting Liu,2,*,Genfu Shao,Shigenobu Sasaki

1 School of Electronic and Information Engineering,Nanjing University of Information Science and Technology,210044,China

2 National Mobile Communications Research Laboratory,Southeast University,Nanjing 210096,China

3 School of Electrical and Electronic Engineering,Niigata University,Niigata-city,950-2181 Japan

4 College of Communication Engineering,Hangzhou Dianzi University,Hangzhou 310000,China

Abstract: In this paper,we propose a stochastic channel model in three-dimensional (3D) space for multiple input multiple output (MIMO) vehicle-to-vehicle(V2V)communications in dense urban environments.The movement of the mobile transmitter and mobile receiver results in the V2V channel model behave temporal non-stationarity.Therefore,the time-varying parameters of the propagation paths and angles are derived to characterize such property.Using this channel model,we investigate the propagation characteristics of V2V channels in terms of the road section and moving time/directions/speeds of the transmitter and receiver.Numerical results show that the theoretical results of the propagation characteristics of the V2V channel model are very close to those of the simulation ones,which show that the proposed channel model is suitable for depicting the V2V communications in dense urban scenarios.

Keywords: V2V communication; geometric channel model;antenna array;cross-correlation function

I.INTRODUCTION

1.1 Background

Vehicle-to-vehicle(V2V)communication has recently received rapidly increasing attention in beyond fifthgeneration (5G) communications.Since multipleinput multiple-output (MIMO) has the ability to enhancing the spectrum utilization,increasing the communication system capacity,and meanwhile improving the single user transmission rate,and therefore has gradually become one of the key technologies for future mobile communications [1].For 5G or future sixth-generation(6G)systems,it is crucial to comprehensively study how to effectively utilize the spatial characteristics of fading channels,which aim to improving the performance of MIMO V2V communication systems[2,3].

1.2 Previous Studies

1.2.1 2D Channel Models It is well known that V2V communication systems has the advantages of providing new applications for ensuring traffic safety in different propagation environments [4,5].In fact,efficient V2V systems can integrate information and communication technology into transport infrastructure,cars,and other devices,which are termed intelligent transportation systems (ITSs).To improve the safety in V2V communication scenarios,many research projects have been conducted worldwide,such as the V2V-communication consortium and the European road transport telematics implementation coordinating organization.As one of the most important issues in the design of V2V communication systems,channel congestion will cause the loss of safety messages.Consequently,new channel models are required for these environments.

Recently,there have been many researches on the channel modeling for V2V communications,which aim to providing the theoretical foundation of designing and evaluating wireless communication systems[6,7].Since geometry-based channel models specify the mathematical model and related algorithms for channel modeling that are applicable to all communication scenarios,they have attracted extensive attention in current studies.In the existing literature,the authors have proposed a variety of geometry-based channel models,such as elliptical model [8],straight street model [9],rectangular model [10],and semicircular tunnel model [11].It is well known that the aforementioned channel models are two-dimensional(2D) ones,which have the advantages of simplicity and ease of description,and therefore are suitable for simulating certain environments.However,this kind of channel models fail to characterize the impacts of signal variations in the elevation plane on the propagation properties in the time,space,and frequency domains.In light of this,these channel models are not suitable for depicting the well-built areas or urban environments in which the receiving antennas are often in close proximity to and lower than surrounding buildings.In practical communication scenarios,the scattered waves may propagate by diffraction from the top of buildings to the ground,therefore channel models in three-dimensional(3D)space are more suitable for describing the V2V communications in dense urban street environments[12,13].

It is worth mentioning that propagation characteristics of V2V channels are related to the typical physical properties of the practical street environments.This motivates researchers to conduct the research on the impacts of the width of the street,moving time/directions/velocities of the transmitter and receiver,roadside buildings on the V2V propagation characteristics in the time,space,and frequency domains.To achieve this research goal,3D channel modeling for V2V communication environments has been widely done in the existing literature.For example,K.B.Baltzis [14]developed a channel model in 3D space for V2V communications,where the propagated angles were separated into the azimuth and elevation planes to investigate the channel characteristics from different perspectives.On the basis of the WINNER II and Saleh-Valenzuela channel models,the authors in Ref.[15]proposed a channel model in 3D space for investigating the correlation properties of the propagation paths.In Ref.[16],the authors proposed a MIMO V2V channel model in 3D space for in dense urban street environments,which considered the propagation characteristics of V2V channels for different physical properties of streets,such as the width of the street and the road section.Unfortunately,the aforementioned geometric channel models neglected the fact that the vehicles were in principle moving in 3D space,therefore,these models cannot be used to accurately characterize the propagation properties of different propagation links in street communication scenarios[17].Furthermore,many researchers conducted the research on channel modeling by carrying out the measurements for different parameters configurations.Specifically,the authors in[18]proposed a geometric channel model for V2V communication environments,which adopted the visual single propagation path instead of the multiple bounce ones for characterizing the propagation properties of V2V channels from different perspectives.By conducting the channel measurements,the authors in Ref.[19]proposed a polar directional V2V channel model based on the measured data.However,these models almost focus on singleor double-bounce conditions,but have not discussed the Rakesh multi-bounce condition in detail.If the transmitted waves experienced an unlimited-bounce propagation path,namely the bounce number tended to infinity,those previous scattering channel models would be no longer applicable.

1.3 Main Contributions

In this paper,let us present a geometry-based stochastic scattering channel model for V2V communications in dense urban street environments,as shown in figure 1.The contributions of this article are summarized as follows:

• We propose a 3D geometry-based stochastic scattering channel model for V2V communications in dense urban street environments.The impacts of the typical physical properties of the streets on the V2V channel characteristics in the time,space,and frequency domains are derived and investigated.The simulation results show that the proposed channel model has the ability to describing the practical V2V communication scenarios.

• In the proposed channel model,the time-varying parameter of the propagation paths and angles are derived to characterize the channel nonstationarity in the time domain.Furthermore,we consider the impacts of the road sections and moving time/directions/speeds of the transmitter and receiver on the correlation properties of different propagation links.

• The proposed algorithm for V2V channel modeling has considered the trade-off of the generality and complexity.To be specific,when we properly adjust the model parameters,such as the width of the street and the road section,the proposed channel model has the ability to characterizing the main propagation characteristics for V2V communications in dense urban scenarios,which shows the generality of the proposed V2V channel model.

The rest of this paper is organized as follows.In Section II,the physical properties of the proposed V2V channel model are derived and discussed.In Section III,the complex impulse responses for different widths of the street and different road sections are derived.In Section IV,the V2V channel propagation characteristics in the time,space,and of the proposed V2V channel are derived and studied.Numerical theoretical and simulation results are shown in Section V.Finally,Section VI concludes this paper.

Notation: The lowercase,boldface lowercase,and boldface uppercase letters such asx,x,and X represent the scalar,vector,and matrix,respectively.E[·]is the expectation operation,∥·∥is the Frobenius norm,(·)∗is the complex conjugate operation,[·]Tis the transpose operation,andj=is the imaginary unit.

II.VIRTUAL GEOMETRICAL STREET SCATTERING MODEL AND MIMO

2.1 Scattering Space Channel Model

Let us consider a geometry-based stochastic scattering channel model for V2V communications in dense urban street environments in 3D space,as illustrated in Figure 1.Specifically,Figure 1(a)describes the model parameters of the proposed V2V channel model in the initial motion state of the transmitter and receiver.In this case,the transmitter and receiver start to move,which means the moving timetis equal to zero.Figure 1(b) describes the model parameters of the proposed V2V channel model in the real-time motion state of the transmitter and receiver.In this case,time-parameter parameters of the propagation paths and angles are required to be derived and considered to characterize the non-stationarity of the V2V channel model.In the proposed channel model,two cars,which are respectively named as BS and MS,move on a road in the same directions or on different roads with different widths.It is obviously noted that the waves transmitted from the transmitter experience different propagation paths before arriving at the receiver,they are LOS and NLOS propagation links.Since the authors in the current research works assume that the LOS propagation links are not related to the NLOS propagation links[20],we follow this assumption in the following discussions.It is obviously noted that the von Mises Fisher probability density function (PDF) can be used to match a variety of scatter distributions in V2V communication environments[15]; therefore,we adopt such distribution function to minic the scattering environments for V2V communications in dense urban street scenarios.Here,χp,εp,χq,εq,χl,εlare the elevation and azimuth angles of MS or BS antenna arrayθp,φp,θl,φlare the elevation(EAOD)and azimuth(AAOD)angles of the cluster at MS,whileθqandφqare the elevation angle of arrival (EAOA) and azimuth angle of arrival(AAOA),respectively.ζp,ϕp,ζl,ϕl,ζq,ϕqrepresent the elevation and azimuth angles with the velocity vectors of receiver or transmitter,and vp,vq,vl,vcdenote the velocity vectors of the receiver,transmitter,and clusters.

2.2 Antenna Element and Array for MIMO System

The uniform rectangular array of MS and BS configuration unit antennas is widely used in mobile communication owing to its simple structure and omnidirectional characteristics.In radio communication applications,an MIMO antenna receiving system can improve the channel capacity of the system.In principle,when the number of the transmit/receive antennas is large,the characteristics of the antenna array cannot be neglected.Hence,a uniform rectangular array with a near-field assumption is used,which is expressed as follows:

whereMTis the total number of transmitting antennas;ap(t)is the complex amplitude of thep-th antenna at the transmitting antenna;α(φp,θp) is the received signal vector of uniform matrix; 0≤φp ≤2π,and 0≤θp ≤π.As shown in figure 2,φqandθqare the horizontal azimuth angle of arrival and the elevation of theq-th at the receiving antenna,respectively.AnI ×MRuniform rectangular antenna array is set on theXYplane of the coordinate system.

2.3 MIMO System Channel Capacity

For MIMO communication systems,when the transmitter is unable to obtain the channel information in wireless communications,the optimal solution is to distribute the power equally to each antenna array element,and the average channel capacity can be expressed as:

where IQdenotes the identity matrix,SNR accounts for the signal to noise ratio,and H is the transmission matrix of the channel,i.e.,

where Rt/ris the element correlation matrix of the receiver or transmitter,and Hwrepresents the complex Gaussian random matrix with the same distribution.

Here,hpqdenotes the transmission coefficient corresponding to the propagation from the antennapto antennaq.TheMTandMRare the numbers of the antennas at the transmitter and receiver,respectively.

2.4 AOA and AOD of the Propagation Environment Signal

By properly adjusting the model parameters,such as the width of the street and the road section,the proposed channel model has the ability to characterizing the main propagation characteristics for V2V communications in dense urban scenarios.Specifically,when theωxis equal to 0,the proposed channel model can describe the communication scenario with straight streets.Also,the proposed channel model has the ability to depicting the standard T-intersection street scenarios asxT1+xT2=Wb+wmn.To simplify the calculation,it is assumed that all scatters are located in a circular region with a radius ofRin the scattering region except for the road region.Assuming that the coordinates of scatters can be expressed in the Cartesian coordinate system DS(t)=[xs(t),ys(t),zs(t)]T,the 3D locations of BS and MS should be timevariant and their initial locations can be denoted as DT(t)=[xp(t),yp(t),zp(t)]Tand DR(t)=[xq(t),yq(t),zq(t)]T,respectively.When the cars are moving in the cross,the 3D locations of the MT can be denoted as DT′(t)=[xl(t),yl(t),zl(t)]T,and the coordinates ofSTm,SRn,SCkcan be expressed in the Cartesian coordinate system as DS′(t)=[xi(t),yi(t),zi(t)]T(i=m,n,k).

Assume that the spacings between the BS and MS antenna elements areδTandδR,respectively.The instantaneous locations of the MS,BS,and cluster at the time instantt′can be written by

Notice that when the cars are moving in the cross,the scattering clustersSTm,SRn,SCkare concentrated at the cornersa,b,andc,respectively.Then,the timevarying closed-form functions of the angles,they are EAOD and AAOD,of the propagation paths MS-STm-BS,MS-SRn-BS,and MS-SCk-MR can be expressed as follows:

When the cars are moving on the same road,the functions of the time-varying parameters of the angles,they are EAOD and AAOD,can be calculated by

where∥·∥means the normalization operation.

The VMF distribution can be used to simulate the statistical characteristics of AOA and EOA with the MIMO antenna fading channel,where elevation and azimuth angles are independent,respectively.The probability density function for the angles can be expressed as

where−π/2≤θ ≤π/2 and−π ≤φ ≤π;anddenote the mean azimuth of arrival (MAOA) and mean elevation of arrival (MEOA) with clusters,respectively.Thekis the centralized parameter indicated with the directional expansion.

III.V2V FADING CHANNEL MODEL

In this section,the analytical expression of the vehicle mounted fading channel in different road sections can be derived by using two methods.When the cars are driving in the same road,the superposition of the impulse responses of three parts are shown as shown below:

where(τ′,t) and(τ′,t) represent the impulse responses of the LOS and NLOS propagation components,respectively.

In the following,the time-variant transfer function(TVTF) is used to replace the impulse response.The TVTF is the time-variant of the impulse responsehpq(τ′,t),which is the Fourier transform relative to the transmission delay.hpq(τ′,t)can be adopted from the Fourier transformHpq(f′,t).The expression of TVTF can be expressed as

where(f′,t) and(f′,t) represent the TVTFs of the LOS and NLOS propagation components,respectively.

The scattered component of a single bounce carries more energy than that of double reflection.Hence,in this study,only the effects of a single bounce at the transmitter and receiver are considered.

with

where Sp(t)and Sq(t)are the vectors of LOS,Sps(t)and Sqs(t)are respectively the EAOD,EAOA,AAOD,and AAOA angle unit vectors of thes-th scattering branch in thee-th of NLOS.For example,thep-th of transmitting antenna and cluster can be written by

whereCRdenotes Rician factor,< · >represents the inner product,λ=2πf0/c0presents the wave length,f0means the carrier frequency,c0denotes the light speed,Rp/qis the 3D location of thep-th of MS orq-th of BS antenna elements.fLOS,fpsandfqsdenote the Doppler shifts in an non-stationary MIMO system.Apand Aqdenote thep-th of MS orq-th of BS antenna vector,stands for the distance vector between transmitter and receiver,accounts for the distance vector from the cluster to theq-th of receiver antenna array or from the cluster to thep-th of transmitter antenna array.The random phaseLOS andψps/qsof the fading envelope range in the intervals of 0∼πand−π ∼−π,respectively.

It is well known that scatterers always exist in every corner of the street when cars are moving in the cross.The time-varying impulse response of propagation links in wireless channels is composed of the superposition of the impulse responses can be written by

By Fourier transform,the TVTF can be obtained as follows:

with

whereξSTrepresents the average power ofSTm.ThefTmandfRmare the Doppler shifts caused by the transmitter and receiver,respectively;fTmaxandfRmaxare the maximum frequencies of the transmitter and receiver,respectively.τ′lmqis the transmission delay,i.e.,DTmis the distance between the arrayland the scattererSTm,andDRmis the distance between the scattererSTmand the arrayq.

IV.PHYSICAL CHANNEL PARAMETER ANALYSIS

To analyze the orthogonal frequency division multiplexing technology of V2V communication,it is crucial to consider the propagation characteristics of V2V channels in the time,space,and frequency domains.

4.1 Space-Time-Frequency Cross Correlation Function

It is well known that the propagation links of V2V channels have different correlation properties in different time,space,and frequency domains.In the existing literature,the authors are inclined to adopt the space-time-frequency cross-correlation functions(STF CCFs) to study the correlation properties of propagation links of V2V channels in the time,space,and frequency domains.Therefore,we follow this research solution in the following.We have

It is worth mentioning that the LOS and NLOS propagation links are independent to each other,therefore we do not consider the correlation properties between the LOS and NLOS propagation links in the following.Instead,we consider the correlation properties of the LOS propagation links in the time,space,and frequency domains; we consider the NLOS propagation links in the time,space,and frequency domains.In light of this,the correlation properties of the propagation links in the proposed channel model can be written by

with

4.2 Space Cross Correlation Function

In order to characterize the correlation properties of the propagation Links in the V2V channel model,we are required to derive the space cross correlation function(CCF),which can be shown as follows:

4.3 Time-Frequency Cross Correlation Function

Whend′=0,the time-frequency CCF (TF CCF) can be obtained,namelyρpqp′q′(v′,t′)=ρpqp′q′(0,0,v′,t′).In the proposed channel model,the TF CCF can be defined by

According to the mathematical relationships of the propagation paths and angles at the transmitter and receiver,it is not hard to derive the TF CCF of the V2V channel model as follows:

4.4 Time Autocorrelation Function

In order to characterize the correlation properties of propagation links in the V2V channel model in the time domain,it is crucial to derive the time autocorrelation function(ACF)as follows: The time characteristic of the proposed channel model can be achieved by the time autocorrelation function(ACF),ρpqp′q′(t′)=ρpqp′q′(0,0,0,t′).It is defined as:

The ACF of the propagation links in the V2V channel model can be written by

4.5 Space Cross-Correlation Function of Receiving Antenna Array Elements

It is well known that the spatial resource is rich is wireless communication scenarios; therefore,it is crucial to excavate the propagation characteristic in the space domain for V2V communication scenarios.In the existing literature,we notice that were inclined to investigate the correlation properties of propagation links for different antenna spacings.This is mainly due to the fact the design of the MIMO communication systems are related to the configuration of the antennas.In light of this,we consider the correlation properties of the propagation links for different antenna spacings,which can be expressed as follows:

wherePAis the average efficiency of the receiving antenna,uq(θ,ψ)represents the voltage vector of the receiving antenna,ρ(ϕ)is the antenna transposition vector,which is a column vector obtained by multiplying the antenna vector at the receiving signal.The spatial correlation is can be obtained as shown in Eq.(54):

whereσidenotes the normalized weighting coefficient of thei-th sampling pulse,andρirepresents the correlation.Taking theqand theq+1 antenna elements into account,the space CCF can be expressed as

and

Thus,the expression of the space CCF between theqandq+1 elements of the antenna array is:

whereca,bis the voltage conversion relation between the receiving antenna and the load resistance,ca,b=za,b/zQ+za,b.

V.NUMERICAL ANALYSIS

Based on the derivations of the correlation functions in the previous section,in the following,we will discuss the correlation properties of the LOS and NLOS propagation links in the V2V channel model in the time,space,and frequency domains.Unless otherwise specified,the setting of the V2V channel model parameters for simulations are summarized as follows:R=50 m,wm=2 m,wn=2 m,D1=D2=8 m,andP=Q=32.The inclination angles at the transmitting and receiving ends areχp=χq=εp=εq=45◦;the motion angles between the transmitter and the receiver areζp=ϕp=30◦,ζq=ϕq=120◦;θp(0)=45◦,φp(0)=60◦,θq(0)=30◦,andφq(0)=135◦.The motion velocities arevp=vq=15 m/s.The maximum Doppler frequencies at the transmitting and receiving ends arefTmax=fRmax=91 Hz andfc=5.9 GHz.

The physical properties of V2V communication in dense urban street environments are related to the parameter settings of the Rician factorCR.Specifically,whenCRis equal to 0,it means the waves from the transmitter all experience the LoS rays before arriving at the receiver.However,when theCRis not equal to 0,the waves from the transmitter experience the LOS and NLOS rays before reaching the receiver.In addition,when the value ofCRis small,the propagation waves are mainly reflected by the scatterers in wireless channels described by the NLOS propagation rays,rather than the LOS propagation rays.In this case,the scatter distribution is dense.When the value ofCRis high,the received scattered power is more likely to experience the LOS propagation rays rather than the NLOS propagation rays.In this case,the scatter distribution is sparse.Figures 3 and 4 show the space CCFs of the proposed channel model for different antenna spacings of the transmit and receive arrays.An important phenomenon is that when we rise the value of the adjacent antenna spacing at the transmitter or the receiver,the correlation properties in the space domain of the propagation link will decrease obviously.Furthermore,we notice that the results in figures 3 and 4 fit the measurements in[21]very well,which shows that the spatial CCFs of the V2V channel models gradually decrease as increasing the adjacent spacing of the antenna array.

Figure 5 shows the comparison results of the correlation properties in the time domain for different Rician factorsCR.It is obvious that the moving directions of the transmitter and receiver have some influences on the V2V channel propagation characteristics.Specifically,when MS and BS move in the opposite directions,they areφp=πandφq=0,the values of the temporal ACFs are obviously different from those of the correlations when MS and BS move in the same direction,i.e.,φp=φq=0.Another important phenomenon is that when we rise the value of the propagation delayτof the waves between the transmitter and receiver,the correlation properties in the time domain of the propagation link will decrease obviously.The agreement between the analytical and simulation results further validates the accuracy of the conclusions of the correlation properties in the time domain of the propagation links in the V2V channel model.

Figure 6 shows the TF CCFs of the NLOS propagation links in the V2V channel model.As can be seen,when the moving time or frequency increases,the correlation value gradually decreases from 1 to 0,and then fluctuates slightly in a stable state.Figure 7 shows the correlation properties of the LOS propagation links in the V2V channel model.An important phenomenon can be seen is that the curves of the ST CCFs for the case ofCR=0 are different from those forCR=2,indicating that the ST CCFs are related to the physical properties of the scatter environment between the transmitter and the receiver.

Figure 8 shows the comparisons of time ACFs between the simulation and analytical results with respect to the model parameters.Within the propagation delayτincreases from 0 to 0.01 s,the temporal correlations drop heavily.However,the descendants of the temporal correlations tend to be stable as delayτis larger than 0.01 s.It also can be seen that when we increase the distance between the centers of the transmit and receive antenna arrays,the path length of the waves propagated from the transmitter to the receiver will increase,which results in the decreasing of the temporal ACFs.The figure shows that the distribution trend of the temporal ACFs are consistent with the results in[22].

VI.CONCLUSION

In this study,we have proposed a statistical channel model based on the mathematical relationships of the propagation paths and angles at the transmitter and receiver.Two types of vehicle running scenarios were proposed under the condition of LOS and NLOS,and the space fading closed-form expressions based on the arrival and transmission angles of the receiver and the transmitter as well as the reference model under the two scenarios were derived.The influences of antenna spacing,time delay,and frequency on spatial fading correlation were analyzed by the simulation.It has been shown that the theoretical results of the correlation properties of the propagation links in the time,space,and frequency domains fit very well with the simulation results;therefore,our study provides a theoretical reference for the research on channel modeling to realize accurate and efficient urban road wireless communication systems.According to the results of the derived autocorrelation function and the simulation model,the simulation model fitted well with the reference model,and the physical channel model had desirable accuracy in terms of describing the intersection of dense city streets.Our study provides a theoretical reference for the research on channel modeling to realize accurate and efficient urban road wireless communication systems.

ACKNOWLEDGEMENT

This work was supported by the National Natural Science Foundation of China(NSFC)(No.61971167 and 62101274),Natural Science Foundation of Jiangsu Province(BK20210640),and Open Research Fund of National Mobile Communications Research Laboratory,Southeast University(No.2021D03).