Implementation Framework and Validation of Cluster-Nuclei Based Channel Model Using Environmental Mapping for 6G Communication Systems

Li Yu,Yuxiang Zhang,Jianhua Zhang,*,Zhiqiang Yuan

1 State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing 100876,China

2 School of Electronic Engineering,Beijing University of Posts and Telecommunications,Beijing 100876,China

Abstract:With the research of the upcoming sixth generation(6G)systems,new technologies will require wider bandwidth,larger scale antenna arrays and more diverse wireless communication scenarios on the future channel modeling.Considering channel model is prerequisite for system design and performance evaluation of 6G technologies,we face a challenging task: how to accurately and effciently model 6G channel for various scenarios? This paper tries to answer it.Firstly,the features of cluster-nuclei(CN)and principle of cluster-nuclei based channel model(CNCM)are introduced.Then,a novel modeling framework is proposed to implement CNCM,which consists four steps: propagation environment reconstruction,cluster-nuclei identifcation,multipath parameters generation,and channel coeffcients generation.Three-dimensional environment with material information is utilized to map CN with scatterers in the propagation pathway.CN are identifed by geometrical and electric feld calculation based on environmental mapping,and multipath components within CN are calculated by statistical characteristics of angle,power and delay domains.Finally,we present a three-level verifcation structure to investigate the accuracy and complexity of channel modeling comprehensively.Simulation results reveal that CNCM can perform higher accuracy than geometrybased stochastic model while lower complexity compared with ray-tracing model for practical propagation environment.

Keywords:channel model;6G;cluster-nuclei;environmental mapping;scatterer;ray-tracing;geometrybased stochastic model

I.INTRODUCTION

With the commercialization of ffth generation(5G)communication systems worldwide,sixth generation(6G)research has been launched to meet the demands for higher data rate and system capacity,lower latency,ubiquitous three-dimensional(3D)coverage,heterogeneous connections and so on for future services.The potential enabling technologies for 6G include:mmWave and teraherts communication,super-large scale multiple input and multiple output(MIMO),space-air-ground integrated network(SAGIN),artifcial intelligence(AI)enabled methods,etc[1–7].

Wireless channel properties determine the ultimate performance limit of wireless communication systems.With the emergence of new technologies and applications,there are three new trends of the wireless channel:higher frequencies and wider bandwidth,larger scale antenna arrays,and more diverse wireless communication scenarios[3].These trends bring considerable challenges to the current 5G channel models.As wider bandwidth improve delay resolution,more multipath components(MPCs)can be recognized.Therefore,the channel parameters extracted from MPCs increase correspondingly,which will increase modeling complexity signifcantly.Larger antenna arrays will give rise to more sub-channels and narrower beams,hence more accurate channel parameters,e.g.,angles of MPCs are needed.Meanwhile,more sub-channels will also generate more channel parameters.Moreover,more diverse application scenarios will require an environment-dependent modeling method.Consequently,channel model with high accuracy and low complexity for various scenarios is in demand for 6G.

According to the modeling approach,the mainstream modeling methodologies can be classifed into two types: one is stochastic modeling,the other is deterministic modeling[8].Stochastic models,especially geometry-based stochastic model(GBSM)[8–11]is applied to current 5G standards,e.g.,third Generation Partnership Project(3GPP)TR 38.901[11],International Telecommunication Union(ITU)M.2412[12].GBSM is a cluster-based model,in which the scatterers are abstracted as randomly distributed in the environment,and each cluster is composed of several random rays.The clusters do not consider physical propagation characteristics,which have a strong impact on the resulting channel model[13].GBSM is applied to general scenarios,e.g.,Urban Macro(UMa),Urban Micro(UMi)defned by 3GPP,with low complexity.Another mainstream channel modeling method is deterministic model,like ray-tracing(RT)method[14,15],characterizing the propagation parameters in a computable manner.RT can be applied to a specifc scenario with high modeling accuracy,while the computational complexity will grow exponentially with refections and diffractions increasing.The features of the two methodologies are concluded in Table 1.Here is the problem: how to combine the advantages of the two modeling methodologies?

Table 1.Modeling features of RT and GBSM.

Some efforts have been made in recent literatures.[16]proposes a low complexity geometry-based clustering method using the scattering points obtained from measurement-based ray tracer.The physical location of the scatterers in the environment is associated with clusters.Irregular-shaped GBSM[17]characterize different types of clusters according to the deployment of effective sactterers in practical propagation environment.Map-based hybrid channel model[11,18]is composed of a deterministic component and a stochastic component in 3GPP TR 38.901.To take into account the impacts from environmental structures,deterministic clusters generated by RT and random clusters generated by GBSM are merged to compose channel coeffcients.Although the model is more accurate than GBSM,its computational complexity is rather high.Quasi-deterministic channel model[19,20]is a stochastic map-based model that characterize the propagation in terms of clusters and MPCs.The clusters and MPCs are given by refected rays and multiple diffuse components generated from deterministic and stochastic methods,respectively.The model provides a way to combine deterministic model and stochastic model to improve modeling accuracy.However,the modeling complexity is even higher than deterministic model.In[21–23],neural networks are utilized to generate channel parameters and playback 5G channel of real propagation environment.The datasets used to train the neural network are collected from channel measurements for a specifc coverage scenario,while the generalization ability of the models for scenarios without measurement data is limited.

In[8],a cluster-nuclei based channel model(CNCM)is proposed.Here,cluster-nuclei(CN)are mapped with the environmental objects with physical meaning.Channel model with high accuracy and low complexity can be generated by limited CN for various propagation environments.However,to implement the perception of CNCM,three problems still need to be solved: i)the mapping relationship between CN and the scatterers in propagation environment,ii)the parameters and characteristics of CN with different frequencies,scenarios and antenna confgurations,iii)the stochastic characteristics of MPCs within CN.

In this paper,we propose an implementation framework based on CNCM and validate the performance.The framework consists four procedures,i.e.,propagation environment reconstruction,CN identifcation,multipath parameters generation,and channel coeffcients generation.3D reconstructed environment with the material information of major objects is utilized to map CN with scatterers in the propagation environment.Then CN are identifed by geometrical and electric feld calculation based on environmental mapping.And MPCs within CN are obtained by statistical characteristics of angle,power and delay domain.Furthermore,in order to validate the accuracy and complexity of the proposed implementation framework comprehensively,a three-level verifcation structure is presented i.e.,large scale parameter(LSP)level,smallscale parameter(SSP)level and performance level.

The main contributions and novelties of this paper are summarized as follows:

·We propose a novel implementation framework of CNCM,which takes advantages of both deterministic and stochastic models,to accurately and effciently model 6G channel.

·An environmental mapping based CN identifcation method is leveraged in the framework to generate angles,powers and delays of CN.

·A three-level verifcation structure is presented to evaluate accuracy and complexity of channel modeling.Based on the verifcation structure,the accuracy and complexity of CNCM are validated and compared with RT and GBSM.

The remainder of this article is organized as follows.In Section II,the conception and principle of CNCM are described briefy.Section III elaborates the four procedures of the proposed CNCM implementation framework.Based on the three-level verifcation structure,validation results and analysis of CNCM are shown in Section IV.Finally,conclusive remarks are addressed in Section V.

II.PRINCIPLE OF CNCM

Electromagnetic waves propagate from transmitter to receiver and may interact with the physical scatterers during the pathway.The received signal is the synthetic effects of refection,scattering and diffraction,which appear as MPC clusters.And the position,shape,size and material of the scatterer all have signifcant impacts on the propagation characteristics.Meanwhile,for a scatterer,the radio wave also have some kinds of common features when interacting with it.Thus,there must be certain relationship between the MPC clusters defned in stochastic model and the scatterers in the deterministic environment[8].

Inspired by structured learning and Bayesian learning program[24],the heuristic perception of CN is proposed to form complicated wireless channel[8].CN are defned as certain clusters which are aggregated by a large number of MPCs,with three important features: i)CN have certain shapes.ii)CN have certain mapping relationship with the scatterers in practical propagation environment.iii)Limited CN can dominate the channel impulse response(CIR)generation in various scenarios and confgurations.CN are introduced to both decrease the model complexity from numerous MPCs and improve model accuracy by giving clusters physical meaning.With the introduction of CN,the basic structure of CNCM is formed,that is,“the wave,cluster-nuclei and channel”[8].Moreover,the principle of CNCM is illustrated in Figure 1.Circles with several green dots represent CN,which have a certain mapping relationship with physical scatterers in the propagation environment.Then the characteristics of CN,e.g.,number N,powerPn,delayτn,azimuth angle of arrival(AOA)φrx,n,azimuth angle of departure(AOD)φtx,n,zenith angle of arrival(ZOA)θrx,n,zenith angle of departure(ZOD)θtx,ncan be derived from the mapping relationship.The green dots within CN denote the characteristics of MPCs,which are determined by CN and surrounding environment.The channel coeffcientsh(t,τ)is expressed by(1),

wheref(·)indicates the mapping relationship between CN and scatterer,CNnand Ωnare the characteristics of the nth CN and MPCs withinCNn,respectively.δ(τ)denotes the Dirac delta function of delayτ,andνnindicates the Doppler shift of the nth CN.

Figure 1.The principle of CNCM.

Above all,three key procedures to implement CNCM are: i)fnding the mapping relationship between CN and scatterers in the propagation environment;ii)calculating the parameters of CN;iii)generating the characteristics of MPCs based on CN.

III.IMPLEMENTATIONFRAMEWORK OF CNCM

In this section,an implementation framework of CNCM is proposed for various propagation environment with high accuracy and acceptable computational complexity.The framework combines the advantages of stochastic and deterministic modeling.The workfow of CNCM framework consists of four steps,i.e.,propagation environment reconstruction,CN identifcation,multipath parameters generation and channel coeffcients generation,as shown in Figure 2.

Figure 2.Workflow of CNCM implementation framework.

Figure 3.Specular reflection.

3.1 Propagation Environment Reconstruction

Environmental information is indispensable for modeling a practical channel.There are some state-ofthe-art methods to reconstruct practical environment with high accuracy,like radar,SLAM[25]and Google SketchUp[26].Considering the high cost of radar and SLAM,Google SketchUp is utilized to reconstruct practical propagation environment.Since environment reconstruction precision infuences channel accuracy directly,three aspects of environmental information are signifcant in the reconstruction,i.e.,the shape and position of scatterer,the boundary of propagation environment and surface material of environmental object and boundary.The corresponding electromagnetic properties,e.g.,relative permittivity and conductivity at specifed frequency can refer to the ITU deliverable[27].

3.2 CN Identification Using Environmental Mapping

The multipath clusters exhibit desirable agreement with the physical scatterers in propagation environment[28].Therefore,environmental mapping is utilized to identify CN,which incorporates the physical meaning into CN.We locate CN by the physical positions of the main scatterers which generate the aggregated MPCs in the propagation pathway from transmitter(Tx)to receiver(Rx).To this end,a simplifed RT based method is introduced to determine the spatial positions and parameters of CN.In RT[14],propagation interaction types include line of sight(LOS)propagation,specular refection,diffraction and diffuse scattering.However,diffraction has been shown much less signifcant in the mmWave bands[19,29].Considering received powers with higher order-bounce refections are relatively weak of mmWave channel[26][30],only LOS propagation,single-bounce refection(SBR)and double-bounce refection(DBR)are considered in the CN identifcation.Stochastic characteristics of MPCs within CN caused by diffuse scattering will be modeled in Section 3.3.CN identifcation is obtained by two main procedures as following: pathway calculation and power calculation.

wherePris the power received at Rx andPtis the transmission power at Tx.λis the wavelength andddenotes the distance between Tx and Rx.FtxandFrxare antenna gains at Tx and Rx,respectively.

The amplitude of electric fled of CN generated by SBR is calculated by

The related parameters of refection are shown in Figure 3.WhereErandEtare the amplitudes of electric feld at Rx and Tx.A(s)is the divergence factor,Sinis the distance from Tx to the refection point,andSris the distance from the refection point to Rx node.R is the refection coeffcient of electric feld.e⊥ande‖are perpendicular and parallel unit vectors,respectively.R⊥andR‖are Fresnel refection coeffcients for different polarizations.ε1andε2are complex relative permittivity of different media.

Figure 4.Three-level verification structure.

The electric fled of CN generated by DBR can be calculated in the same way.Then the powers of CN are obtained:

3.3 Multipath Parameters Generation

Based on the angles,delays and powers of CN,parameters of MPCs within CN are generated in this section.To model the stochastic characteristics of MPCs,angles of the MPCs within CN are generated in a random way.Since azimuth angles of MPCs follow wrapped Gaussian distribution and zenith angles of MPCs follow truncated Laplacian distribution[11],the AOAs and ZOAs of MPCs are generated by the following.

where

whereYn ～N(0,1)andWn ～uniform(0,1).CASAandCZSAare the cluster root-mean-square(RMS)azimuth angle spread of arrival(ASA)and zenith angle spread of arrival(ZSA),respectively.

The AODs and ZODs of MPCs can also be obtained using the same method as AOAs and ZOAs,respectively.The MPC delay is equal to the CN it belong to.The power angular spectrum(PAS)in azimuth of all MPCs is modeled as wrapped Gaussian distribution,and PAS in zenith dimension is Laplacian distribution[11].The power of each MPC within the nth CNis calculated by

whereCASDandCZSDare the cluster RMS azimuth angle spread of departure(ASD)and zenith angle spread of departure(ZSD).

Then normalize the MPCs powers so that the sum of all MPCs powers is equal to CN powerPnby

3.4 Channel Coefficients Generation

A MIMO channel withStransmit andUreceive antennas is considered in the framework,which can be expressed by anU×Scomplex matrix H.Channel coeffcients of CNCM are generated by the coherent sum of different CN coupling with the RX and Tx antenna radiation patterns.Based on the parameters of CN and corresponding MPCs,channel coeffcient of the link from the uth antenna element at Rx to the sth antenna element at Tx is calculated by(19).

whereFrx,Ftxare the antenna radiation patterns of Rx and Tx,pn,mandφn,mare the power and phase of the mth MPC within the nth CN,respectively.rrxis the spherical unit vector withφAOA,n,mandθZOA,n,m,and rtxis the spherical unit vector withφAOD,n,mandθZOD,n,m.drx,uand dtx,sare the location vectors of the uth receive antenna element and sth transmit antenna element,respectively.

IV.VALIDATION RESULTS

In this section,the modeling accuracy and complexity of CNCM framework are validated.Basically,a three-level verifcation structure is presented to evaluate the accuracy and complexity of channel modeling as illustrated in Figure 4.i)The LSP[11]level parameters that include RMS DS and RMS AS are presented in Section 4.1.ii)The SSP[11]level parameters,i.e.,delay,power,azimuth angle and zenith angle are elaborated by power delay profle(PDP)and power angle delay profle(PADP)in Section 4.2.iii)The performance level parameters,including channel capacity for MIMO system and modeling complexity are described in Section 4.3.

Figure 5.Detailed exhibition of simulation environment.(a)is the panorama of the indoor environment,(b)is the simulation layout.

Based on the three-level verifcation structure,simulation results of CNCM framework is compared with RT and GBSM channel models.The RT model is simulated by a full 3D ray-tracing platform developed by ZTE and BUPT.More information about the platform can refer to our previous work[26,33].The GBSM model is simulated by ITU-R IMT-2020 simulation platform[12,34],which is offcially certifcated for the evaluations of global 5G candidate radio interface technologies.The LSPs of GBSM follow statistical distributions extracted from the measurement data.

The simulation scenario is a typical furnished indoor conference room and the panorama the environment is presented in Figure 5a,with the geometrical size 10.97×6.62×2.40m3.The Tx is fxed at north-east corner and 16 Rx positions were distributed uniformly in various locations in the room,as shown in 5b.The height of Tx and Rx are both 1.55 m.Furthermore,the simulation parameters of RT and GBSM platforms are calibrated by the channel measurement data of the room at 28 GHz to guarantee the precision of the simulations.And the simulation layout,including the positions,sizes and numbers of scatterers,Tx and Rx in the room,is identical to the channel measurement campaign.Therefore,the simulation results of the RT platform are quite close to the measurement data for the practical propagation environment.More confgurations and details of the measurement campaign can refer to[26].

Figure 6.Simulated and fitted CDFs of RT,CNCM and GBSM models.(a)is the RMS delay spread.(b)is the RMS angular spread.

4.1 LSP Level Results

The RMS DS and AS are the most common parameters to characterize the delay and angular dispersion of the channel[35],which are calculated as the secondorder central moment of the power delay profle and power angle spectrum,respectively.Specifcally,by using the delays and powers extracted from rays,CN and clusters,the RMS DS can be calculated as follows.

whereτmeanis the mean excess delay:

whereτlandp(l)denote the delay and power of lth ray,CN and cluster from RT,CNCM and GBSM,respectively.The RMS AS can also be obtained as(20),by replacing delay with angle.

To analyze the statistical characteristics of the LSPs generated by the three modeling methods,200 channel realizations are implemented.Figure 6 illustrates the cumulative distribution function(CDF)plots and comparisons of the RMS DS and AS for the simulation environment,respectively.The log-normal ftting of RMS DS and AS values are demonstrated in Table 2,withµandσdenoting the mean and standard deviation,respectively.It’s shown that the CDF plots of RMS DS and AS extracted by the CNCM are almost identical with that of RT.Meanwhile,the CDF plots of RMS DS and AS extracted by the GBSM also ft the RT well.Since the GBSM simulation platform has already been calibrated by the LSPs extracted from the measurement data,CDFs can also perform well from the perspective of statistical characteristics.

Table 3.Average simulation times of the three modeling methods.

Figure 7.LSPs of RT,CNCM and GBSM with respect to the specific positions.(a)is the RMS delay spread.(b)is the RMS angular spread.

Figure 8.PDPs extracted from RT,CNCM and GBSM with respect to the 13th simulated position.(a)PDP of RT.(b)PDP of CNCM.(c)PDP of GBSM.

Figure 9.PADPs extracted from RT,CNCM and GBSM with respect to the 13th simulated position.(a)PADP of RT.(b)PADP of CNCM.(c)PADP of GBSM.

Table 2.Statistical values for large scale parameters.

Then the LSPs in different channel realizations with respect to the specifc simulation positions are illustrated in Figure 7.Since RT and CNCM are environment adaptive methods,the LSPs of different channel realizations are stable at each position.Moreover,the RMS DS and AS of CNCM can still ft RT quite well at each position.While the LSP results simulated by GBSM present noticeable variation in terms of different channel realizations,owing to the randomly generated clusters.Herein,the normalized mean square error(NMSE)criterion is applied to measure the difference among the RT,CNCM and GBSM at different positions in each channel realization.The NMSE of LSPs between different models is calculated by(22).The NMSE of RMS DS is 5.2%between CNCM and RT.While it varies obviously between GBSM and RT in the 200 channel realizations,and the lowest value is 11.5%.Analogously,NMSE of RMS AS is 0.3%between CNCM and RT,while it also clearly varies between GBSM and RT with the minimal value 4.3%,in different channel realizations.Therefore,it can be concluded that CNCM exhibits better environment adaptive ability than GBSM for a specifc propagation environment.

whereNdenotes the number of simulation positions,LSPrepresents RMS DS or AS,andmodeldenotes CNCM or GBSM.LSPmodel(n)andLSPRT(n)are the LSP ofmodeland RT at the nth simulation position,respectively.

4.2 SSP Level Results

The SSP level parameters including power,delay,azimuth angle,and zenith angle of MPCs are elaborated by PDPs and PADPs.Figure 8 illustrates the PDPs of MPCs simulated by RT,CNCM and GBSM models at the 13th simulation position,where x,y axes indicate delay and normalized power,respectively.It’s shown that the PDP of CNCM almost agree with that of RT,especially for MPCs with large power and low delay.Because of the high order and diffuse refections,RT has more MPCs with relatively low power and high delay,whereas the overall contribution of the additional MPCs is quite small.By contrast,PDP of GBSM reveals obvious randomness and discreteness,which is different from RT.Because both the delay and power of MPCs are randomly generated by GBSM,which are irrelevant to practical propagation environment.

Figure 10.Visualization of the dominant CN.

To further investigate angular characteristics,PADPs of rays,CN and clusters are simulated by RT,CNCM and GBSM respectively,at the 13th simulation position,as illustrated in Figure 9.The x,y,z axes and color bar denote the AOA,ZOA,delay and normalized power,respectively.It’s demonstrated that the PADPs of CNCM and RT have almost common MPCs with strong power and relatively low delay.Obviously,RT model have much more MPCs with high delay and large angular dispersion,which are generated by high order refection and diffraction.However,the power of these MPCs are almost lower than-25 dB,which have little impact on channel coeffcients.Therefore,in terms of CIR generation,the PADPs of RT and CNCM agree well.While the MPCs distribution of GBSM are random with larger delay spread as depicted in the PADP.

As defned in[8],CN are associated with scatterers in the propagation environment and dominant in CIR generation.To gain more insights into the physical meaning of CN,a visual CN distribution in the propagation environment of the 13th simulation position is demonstrated in Figure 10.Every red circle denotes one of the main CN among the propagation channel from Tx to Rx.CN1 is generated by LOS propagation.CN2 and CN3 are generated by the ceiling and foor,respectively.CN4,CN5 and CN6 are generated by walls of north,east and west,respectively.CN7 and CN8 are generated by the desks nearby Tx and Rx,respectively.The power of the eight CN account for 93.5% of total power of CIR.Therefore,the channel of a practical propagation environment can be composed by limited number of CN.

Figure 11.CDFs of channel capacity of RT,CNCM and GBSM(SNR=15 dB).

4.3 Performance Level Results

Although channel model can be characterized by LSP and SSP of clusters and MPCs,channel capacity is a signifcant metric to evaluate comprehensively the modeling performance for MIMO channel[36].Uniform planar arrays(UPA)with 16 antenna elements[37]are applied to the simulation of RT,CNCM and GBSM models at both Tx and Rx.The MIMO capacity of simulated channel at each Rx position is calculated by[38]

whereρis the signal to noise ratio(SNR)andβis normalization factor such that

whereSandUare the numbers of Tx and Rx antenna elements,respectively.

Figure 11 illustrates the CDFs of channel capacity generated by RT,CNCM and GBSM.It can be seen that the capacity CDF of CNCM is much closer to the RT model,and the relative channel capacity gap between CNCM and RT is 2.7% at 50% CDF point.While the capacity CDF of GBSM have a larger span than that of CNCM due to randomly generated clusters.It can be concluded that,channel capacity of CNCM is also in better agreement with RT than that ofGBSM,with 14.3%accuracy increase compared with GBSM at 50%CDF point.

Furthermore,the complexity of the three models is investigated.Simulation platforms of RT,CNCM and GBSM are ran on a desktop computer equipped with an i7 8750H CPU and 16 GB DDR4-2666 MHz RAM.The average simulation time is demonstrated in Table 3.Although the simulation scenario in this paper is not complex,RT simulation costs 1260.3 seconds once,approximately 663 times of GBSM.While the average simulation time of CNCM is 3.1 seconds,only 1.6 times of GBSM.It can concluded that CNCM can balance the modeling accuracy and complexity better than the current mainstream channel models.

V.CONCLUSION

An implementation framework of CNCM is proposed for 6G systems,which takes advantages of both stochastic and deterministic models to accurately and effciently model 6G channel.Environmental mapping is utilized to identify the CN which dominate CIR generation with physical meaning.Moreover,a threelevel verifcation structure of channel modeling is presented to validate modeling accuracy and complexity.Simulation results show that the LSP and SSP level parameters of CNCM agree with the measurementcalibrated RT well,while those of GBSM are random with obvious variation for different channel realizations.Therefore,CNCM exhibits better environment adaptive ability than GBSM for a specifc propagation environment.Moreover,from channel capacity perspective,modeling accuracy of CNCM increases 14.3% compared with GBSM at 50% CDF point.Lastly,the modeling complexity of the three models is described.Average modeling time of CNCM is 1.6 times of GBSM,while only less than 1%of RT.This work offers a heuristic channel modeling framework with high accuracy and low complexity for various application scenarios in 6G communication systems.More scenarios at more bands with channel measurement data will be further validated in the future work.

ACKNOWLEDGEMENT

This research was supported by National Science Fund for Distinguished Young Scholars(No.61925102)and Beijing University of Posts and Telecommunications-China Mobile Research Institute Joint Innovation Center.