Neural Network and GBSM Based Time-Varying and Stochastic Channel Modeling for 5G Millimeter Wave Communications

Xiongwen Zhao,Fei Du,＊,Suiyan Geng,Ningyao Sun,Yu Zhang,Zihao Fu,Guangjian Wang

1 School of Electrical and Electronic Engineering,North China Electric Power University,Beijing 102206,China

2 Huawei Technologies Co.Ltd.,Chengdu Research Institute,Chengdu 611731,China

Abstract: In this work,a frame work for time-varying channel modeling and simulation is proposed by using neural network (NN) to overcome the shortcomings in geometry based stochastic model (GBSM) and simulation approach.Two NN models are developed for modeling of path loss together with shadow fading (SF) and joint small scale channel parameters.The NN models can predict path loss plus SF and small scale channel parameters accurately compared with measurement at 26 GHz performed in an outdoor microcell.The time-varying path loss and small scale channel parameters generated by the NN models are proposed to replace the empirical path loss and channel parameter random numbers in GBSM-based framework to playback the measured channel and match with its environment.Moreover,the sparse feature of clusters,delay and angular spread,channel capacity are investigated by a virtual array measurement at 28 GHz in a large waiting hall.

Keywords: time-varying channel; neural network; cluster; channel modeling; virtual array;measurement; 5G

I.INTRODUCTION

Millimeter wave (mmWave) has been caused great attention in recent years for fifth generation (5G) radio access and backhaul systems due to its large amount of available bandwidth.In 2015,the International Telecommuni- cation Union (ITU) announced the candidate frequency bands for 5G mmWave in World Radio Communication Conference,in which 24.25- 27.5,31.8 - 33.4 and 37 - 40.5 GHz etc.were assigned in world-wide for 5G systems.In China,low frequency bands 3.4 - 3.6 GHz and 4.8 - 5.0 GHz,and high frequency bands 24.75 - 27.5 GHz and 37- 42.5 GHz have been assigned to 5G technology R&D trials.So far,the 3rd Generation Partnership Project(3GPP) was completed its 5G channel model standardization [1],and in 2017,ITU was also published its preliminary draft report for 5G channel models [2].In both of [1]and [2],the carrier frequencies span from 500 MHz to 100 GHz and channel models were built by inheriting the third and fourth-generation(3G and 4G) geometry-based stochastic mod-el(GBSM) in [3]-[5],and also recommended to use GBSM-based QuaDRiGa (Quasi Deterministic Radio Channel Generator) [6][7]to implement 5G channel simulation.GBSM is very popular in 3G and 4G channel modeling and simulation,however its main drawback is that the channel models were built by stochastic ways to cause channel discontinuities between adjacent channel segments as well as inside a segment.Although QuaDRiGa platform adopted time evolution and time drafting techniques for adjacent segments and inside a segment,respectively to solve such discontinuities,but they are forced to be continuous by mathematics.GBSM in nature cannot match with a measurement environment because of its stochastic manner to generate the required channel parameters using their probability distributions in simulation,which is more useful in system level simulation but not suitable for link level case.A real world radio channel is always time-varying,which is either caused by stationary or moving scatterers.Even in a stationary environment,due to a mobile station (MS) is moving or a measurement performed at different positions,it can resolve different scatterers,so the channel is either time- or position-varying.A position-varying measurement can also be regarded as time-varying without Doppler.Therefore,from channel research perspective,we should find a way to solve time-varying channel modeling and simulation to be more accurately matched with a real world channel measurement and environment.Some work is available to investigate time-varying channels[9]-[11],in which Markov chain is a traditional method [8],however,the shortage is that it cannot live without measurement to find state transition matrix.In [9],a non-GBSM model is applied together with Markov chain to study vehicle-to-vehicle channel.A generic geometry-based stochastic model for nonisotropic scattering vehicle-to-vehicle (V2V) Ricean fading channels is proposed in [10].A non-stationary wideband massive multiple-input multiple- output (MIMO) channel by adding some deterministic solutions is investigated in [11]based on GBSM.In [12],a three-dimensional(3D) GBSM for MIMO wideband non-stationary channels between the Unmanned Aerial Vehicle (UAV) and the ground user is proposed by adding time-varying angels.In[13],a simplified ray tracing [18],namely map-based channel modeling is proposed for 5G wireless communications,ray tracing is do useful in studying time-varying channel,however it requires specificenvironment database and their corresponding electro- magnetic material parameters such as permittivities and cond- uctivities which should be based on measurements.Therefore,all the aforementioned work looks to have drawbacks when applying in time-varying channel modeling.

Neural network (NN) based machine learning offers a promising way to solve time-varying radio channels to predict received signal strength and path loss models for indoor and outdoor scenarios [14]-[15].NN is also wellknown to be applied in predicting time-varying stock market,air pollution,and energy efficiency in big data center by using their historical database.So far,applications of machine learning in channel modeling are still very simple and limited.With the advent of massive antennas in 5G systems,spatial channel dimensions between a base station (BS)and MS or users are extremely expanded,the channel data measured presents time-varying and big data features.Therefore,we believe that machine learning will do come in time-varying channel modeling with advent of big channel data era.

An important issue in GBSM-based channel modeling in massive antennas is to investigate its cluster futures.In [16],Zhang et al.investigated clustering properties from 32 to massive 256 antennas based on channel measurement under 6 GHz,it's seen from the results that the clustering effect is much more obvious in case of massive antennas.However,so far there are no such channel measurement and modeling results available in 5G mmWave.

A framework is proposed by using neural networks to realize time-varying channel modeling and simulation in this work.

The novelty and contribution of this paper are that we proposed a time-varying channel modeling and simulation framework by using NN in modeling joint small scale channel parameters,and path loss models including shadow fading.Then we can use the time-varying path loss and small scale channel parameters generated by the NN models to replace those random numbers and empirical path loss in GBSM-based modeling and simulation ap-proach in order to playback the measured channel and match with the measured environment.Moreover,mmWave sparse feature of clusters and channel characterization for a large hall are also investigated.

TableI.Measurement system parameters.

Fig.1.Measurement environments and layout.(1) is for outdoor microcell.(2)and (4) are for large hall LoS scenarios,respectively.(3) and (5) are for large hall NLoS scenarios,respectively.

II.MEASUREMENT SYSTEM AND CAMPAIGNS

In this work,channel measurements using Keysight (KS) time domain channel sounder were carried out for an outdoor microcellular environment at the campus of North China Electric Power University (NCEPU) and a very large waiting hall in Qingdao high speed railway station at 26 GHz and 28 GHz with 1 GHz and 500 MHz bandwidth,respectively.In the measurements,only vertical polarization channels were measured.Figs.1 shows the outdoor microcellular and large waiting hall measurement environments [17],and measurement system parameters is listed in Table1.

In NCEPU microcellular measurement,the BS and mobile station (MS) were located in a crane and a trolley with heights of 6.1 and 1.8 meters,and equipped with a omni-directional biconical horn and a horn antenna,respectively.Virtual single- input multiple-output(SIMO) measurement was performed by rotating the horn antenna at MS with 50angular step to form 1x72 SIMO.In this paper,the line-of-sight (LoS) measurement data from the route shown in figure 1(1) is used for time-varying channel modeling with 20 measured MS positions,the maximum route length is 141 meters.There are green trees,building walls with less windows etc.existed beside the measured route,so less multipath is expected to be received in the measurement.

In the waiting hall measurements,the BS and MS were set about the same height of 2.0 meters,a biconical horn was used in BS,and a uniform linear array (ULA) with 8 array elements was applied in MS.The eight ULA antennas were connected with eight individual RF channels at the KS receiver.By moving the ULA eight times in the horizontal plane to form 1x64 virtual SIMO.Moreover,a virtual SIMO measurement was performed by rotating the ULA at MS with 600angular step to form 1x48 SIMO.There are totally 21 and 12 measured positions in the LoS and non-Lineof-sight (NLoS) scenarios as show in figure 1(4) and (5),respectively.The hall itself and the shops around are with glass windows,so rich multipath is expected to be reflected and received in the measurement.

III.FRAMEWORK OF TIME-VARYING CHANNEL MODELING AND SIMULATION BY NEURAL NETWORKS (NN)

3.1 GBSM cluster-based MIMO channel modeling and simulation

In GBSM cluster-based MIMO channel modeling and simulation,the following equation is applied to calculate channel coefficient [1][2]

whereFrx,u,θandFrx,u,φare the receive antenna elementufield patterns in the direction of the spherical basis vectors,θˆ andφˆ respectively,Ftx,s,θandFtx,s,φare the transmit antenna elementsfield patterns in the direction of the spherical basis vectors,θˆ andφˆ ,respectively.rˆrx n m,,is the spherical unit vector with azimuth arrival angleφn,m,AOAand elevation arrival angleθn,m,ZOA.rˆtx n m,,is the spherical unit vector with elevation arrival angleφn,m,ZOAand elevation departure angleθn,m,ZOD.are random initial phases for each sub-pathmin clusternfor four different polarization combinations (θθ,θφ,φθ,φφ).is the location vector of receive antenna elementuandis the location vector of transmit antenna elements,κn,mis the cross polarization power ratio in linear scale,vn,mis Doppler frequency component andλ0is the wavelength of the carrier frequency.The main procedure for GBSM channel coefficient generation is available in [1][2].In the procedure,a cluster is equivalent to a path,in each cluster assume that there exists some specificnumber of sub-paths,e.g.in frequency band under 6 GHz [4]-[5],20 sub-paths is assumed,which can result in cluster fading.

GBSM-based modelling has its inherent drawbacks,in general a cluster cannot be equivalent to a path.It's well-known that a cluster is formed by multipath with specificdelay and spatial angular resolutions.Therefore,GBSM-based modelling is do over estimate the number of clusters.Moreover,in a cluster or a path,some sub-paths should be included which is not true assumption in measurement.Moreover,in GBSM simulation procedure,we should first develop the empirical path loss model and probability density functions(PDFs) for the large scale parameters based on measurement,such as shadow fading (SF),root-mean-square delay and angular spread,Ricean factor (K-factor) etc.,then use the PDFs first to generate their random numbers,and further to generate the small scale channel parameters,e.g.excess delay,angle-of- departure (AoD) and angle-of-arrival (AoA) which are required in eqn.(1) for channel simulation.Because the random numbers of channel parameters and empirical path loss model are applied,its simulated channel coefficient in nature cannot match with the measurement environment even if QuaDRiGa platform was solved the channel discontinuities between adjacent segments and inside a segment using time evolution and drafting techniques.

3.2 Framework of time-varying channel modeling and simulation by NN

In this Section,we discard traditional cluster-based GBSM modelling and simulation approach,and propose a new approach for time-varying channel modelling and simulation by using neural networks.Our proposed framework herein is called a multipath-based framework,in which there are no cluster and sub-path concepts.For a multiple antenna measured snapshot,SAGE (Space-Alternating Generalized Expectation- maximization) result has already included the number of paths together with their corresponding amplitude,phase,AoD,AoA,cross-polarization ratio(XPR) etc.In this work,we propose to use NN models to generate path loss plus shadow fading and the joint small scale channel parameters by using SAGE post- processed data for all measured snapshots.Then use the developed NN models to predict the time-varying path loss including SF and small scale channel parameters to replace the corresponding empirical path loss model and random channel parameters in cluster-based GBSM simulation approach.The new procedure of channel coefficient generation based on NN is shown in figure 2.

Fig.2.New procedure of channel coefficient generation based on NN models.

In our proposed multipath-based modeling and simulation approach,GBSM channel coefficient in eqn.(1) should be changed as eqn.(2) by removing cluster number ofn,and putting inside the sum symbol,which is normalized power with respect to all the multipath in a snapshot.In eqn.(2),mis now defined as number of multipath or path andMis the maximum number of multipath included in a snapshot.

In the following parts 1) and 2),the NCEPU microcellular measurement data is used to predict the LoS path loss including SF and joint small scale channel parameters by using NN.Note that when building the NN models,all the measurement samples are used in network training,the only purpose is to playback the input samples by using developed NN models.

1)TheNN Model for Path Loss including SF

figure 3 shows path loss by the measurement,linear regression and NN.In linear regression,close-in (CI) path loss model [15]is applied,in which the free space path loss at m is 60.74 dB at 26 GHz,the path loss exponent is 1.935 and the standard deviation(STD) is 2.13 dB.In the NN modeling,radial basis function (RBF) NN is applied with three network layers,namely input,hidden,and output layers,respectively.In the hidden layer,20 neurons are included.The NN path loss model *.net (an black box) is then obtained by Matlab neural network toolbox with respect to distance and saved in offline usage for modeling path loss plus SF.It's seen from figure 3 that the NN path loss model agrees very well with measurement,the root-mean-square-error(RMSE) is about 0.28 dB.

2) The NN Model forJoint Small Scale Channel Parameters

figure 4(1) shows the 3D results for joint small scale channel parameter predicted by the developed NN model for the power,excess delay and direction-of-arrival (DoA) with respect to measurement distance and number of path,in which (a) is measured power,(b) is predicted power.(c) is measured excess delay,(d) is predicted excess delay.(e) is measured DoA,and (f) is predicted DoA.

Figure 4(2) is a planar view,the colorbars are for the power,excess delay and DoA,respectively.Figure 4(2) (a),(c),(e) are for the measurement results,and figure 4(2) (b),(d),(f) are the corres- ponding results predicted by the NN model.It's seen that there exists a bit difference between the measurement and NN results for the power and excess delay.For a specificmeasurement distance,the small scale channel parameters for each path can be well predicted by NN.

In developing the joint small scale channel parameters NN model,again we use RBF NN which includes three layers as applied in path loss,but the hidden layer is now divided in two sub-layers in which the first sub-layer has 20 neurons,and the second sub-layer includes 600 neurons.It's seen from figure 4 that the NN model can predict channel small scale parameters well with small RMSEs compared with measurement.The maximum RMSEs of the power,excess delay and DoA for the received paths between the measurement and predicted by NN are 0.44 dB,0.15 ns and 0.19o,respectively.

Fig.3.The NN path loss model including SF.

Fig.5.Sparse feature of clusters at the large hall using SAGE.(a)-(d) are for the array elements of 8,16,32,and 64,respectively.

In this work,the NN model (*.net) is built for joint small scale parameters by using RBF,which can generate all the small scale parameters corresponding to their number of paths for all the measured snapshots.When building the RBF model,the SIMO measured snapshots are first processed by SAGE as its input.The final NN model is a function of number of snapshot or distance,which can generate all the small scale parameters required in eqn.(2) and figure 2 for generation of time-varying channel coefficient.

To build a NN model for joint small scale channel para- meters may take a bit time,which depends on how large of measurement data.However,when the NN model is built,it can be used in offline channel simulation,which is very fast to generate small scale channel parameters because it's only a function of number of snapshot or distance.

IV.MILLIMETER WAVE CHANNEL CHARACTERIZATION FOR THE LARGE WAITING HALL

Based on 1x64 virtual SIMO and ULA rotation measurements in the large waiting hall of Qingdao high speed railway station as shown in Figs.1 (4) and (5),mmWave channel characterization are analyzed by using SAGE algorithm.There are totally 21 and 12 measurement positions in the LoS and NLoS scenarios,respectively.

Figure 5(1) are for the LoS results by using SAGE at a specific measurement position,respectively,in which (a) - (d) are for 8,16,32 and 64 antennas,respectively.It's seen that multipath spatial resolution is greatly improved when increasing the number of antennas.However,the number of clusters is kept almost the same.By investigating all the LoS measurement positions,it's found that the number of clusters is about 5.Figure 5(2) shows the sparse feature of clusters in a specificmeasured position in the NLoS scenario by SAGE,it's also seen that multipath spatial resolution is improved a lot when increasing the number of antennas,but the number of clusters is also kept almost the same.By investigating all the NLoS measurement positions,it's found that the number of clusters is about 7.Compared with the results under 6 GHz in [14],number of clusters are reduced a lot,which shows sparse feature of clusters in millimeter wave band.

Figs.6(1) and 6(2) show the cluster features for the LoS and NloS scenarios,respectively by rotating the ULA at the same measurement positions as in figure 5.It's seen from figure 6 and 5 that the numbers of clusters are almost doubled in the ULA rotation measurement and the clusters are distributed in the whole azimuth plane.

Figure 7 shows the cumulative distribution function (CDF) for the large scale parameters of rms delay and angular spread derived from all measurement positions with different array elements of 8,16,32,64 and ULA rotation.It's seen from figure 7(1) and (3) that larger delay spread is found in the NLoS scenario as expected in figure 5(3),large angular spread is found in both LoS and NLoS scenarios as shown in figure 7(2) and (4) because of rich multipath existed in large angular range as seen from figure 6.Moreover,higher rms delay and angular spread are found by rotating the 8-element ULA which is equivalent to an omni-directional array as expected in figure 6.Fig.8 shows channel capacities with different array elements of 8,16,32,64 and ULA rotation.It's seen that the capacities are increased linearly when SNR is more than 0 dB.As the array elements are doubled,the capacity is increased about 1 bit/s/Hz.Channel capacities with different array elements in the NLoS case are also investigated,the results are almost the same as the LoS scenario for a specific SNR.However,the SNR dynamic range in the NLoS is about 10 dB lower than the LoS scenario,the maximum channel capacity can be therefore reached in the LoS scenario.Comparisons of the statistical values of the rms delay and angular spread as well as the channel capacities for the hall environment based on Figure 7 and 8 are shown in Table2.

V.CONCLUSION

A framework is proposed by using neural networks to realize time-varying channel modeling and simulation in this work.Based on the outdoor microcellular measurement at 26 GHz,two neural networks models are built for modeling time- varying path loss together with shadow fading and joint small scale channel parameters,which can replace the empirical path loss model and those random numbers of channel parameters in the GBSM-based channel modeling and simulation approach.The NN models can playback the measured path loss including shadow fading and small scale parameters accurately to be used in time-varying channel simulation,which is expected to overcome the shortcomings in cluster-based GBSM statistical modeling approach and to match with real measured environ- ment.Channel simulation platform based on neural network is now under developing at NCEPU radio channel team,the simulation and validation results are expected to be available in the near future.Moreover,in this work,sparse feature of clusters is found by the virtual array measurement at 28 GHz in the large hall.When increasing array elements,the spatial resolution of finding multipath is greatly improved,however,the number of clusters seems to be kept almost unchanged.In the hall measurements,larger rms delay spread is found in the NLoS scenario,large rms angular spread is found in both LoS and NLoS scenarios.High-er rms delay and angular spread are found with rotating the 8-element ULA.The channel capacities are increased linearly when SNR is more than 0 dB,and as the array elements are doubled,the capacity is increased about 1 bit/s/Hz.

Fig.6.Distribution of clusters for ULA rotation measurement at the large hall.

Fig.7.Large scale channel parameters at the hall environment for ULA with different array elements,and ULA rotation.

Fig.8.Comparison of channel capacity with different array elements for the LoS scenario in the hall environment.

TableII.Comparisons of the statistical values of the rms delay and angular spread as well as the channel capacities for the hall environment.