IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019 2077

Novel 3-D Nonstationary MmWave Massive MIMOChannel Models for 5G High-Speed Train

Wireless CommunicationsYu Liu , Cheng-Xiang Wang , Fellow, IEEE, Jie Huang , Jian Sun , Member, IEEE,

and Wensheng Zhang , Member, IEEE

Abstract—In fifth generation (5G) wireless communications,high-speed train (HST) communications is one of the mostchallenging scenarios. By adopting massive multiple-inputmultiple-output (MIMO) and millimeter wave (mmWave) tech-nologies into HST communications, the underlying communicationsystem design becomes more challenging and some new channelcharacteristics have to be studied, such as the non-stationarities inspace, time, and frequency domains. This paper proposes a novelthree-dimensional space-time-frequency non-stationary mmWavemassive MIMO theoretical model, as well as a corresponding sim-ulation model for 5G HST wireless channels based on WINNER IIand Saleh–Valenzuela channel models. Cluster evolutions in space,time, and frequency domains are proposed and analyzed to ensurethe models’ non-stationarities in three domains. Moreover, basedon the proposed channel models, important time-variant channelstatistical properties are investigated, such as the time autocor-relation function, space cross-correlation function, delay powerspectrum density (PSD), angular PSD, and frequency correlationfunction. Results indicate that the statistical properties of the sim-ulation model, verified by simulation results, can match well withthose of the theoretical model.

Index Terms—5G, HST channels, massive MIMO, mmWave,space-time-frequency non-stationarity.

I. INTRODUCTION

W ITH the rapid development of information globaliza-tion, wireless communications have penetrated into

all aspects of people’s life. Wireless communication systems

Manuscript received March 19, 2018; revised June 3, 2018; accepted July 20,2018. Date of publication August 21, 2018; date of current version March 14,2019. This work was supported in part by the National Postdoctoral Program forInnovative Talents (BX201700308), in part by the China Postdoctoral ScienceFoundation Funded Project (2017M622203), in part by the Natural ScienceFoundation of China under Grant 61771293, in part by the EU H2020 ITN 5GWireless Project under Grant 641985, in part by the EU H2020 RISE TESTBEDProject under Grant 734325, in part by the Key R&D Program of ShandongProvince under Grant 2016GGX101014, in part by the Fundamental ResearchFunds of Shandong University under Grant 2017JC029, and in part by theTaishan Scholar Program of Shandong Province. The review of this paper wascoordinated by the Guest Editors of the Special Issue on Smart Rail Mobility.(Corresponding author: Cheng-Xiang Wang.)

Y. Liu, J. Sun, and W. Zhang are with the Shandong Provincial Key Labof Wireless Communication Technologies, School of Information Scienceand Engineering, Shandong University, Shandong 266237, China (e-mail:,xinwenliuyu@163.com; sunjian@sdu.edu.cn; zhangwsh@sdu.edu.cn).

C.-X. Wang and J. Huang are with the National Mobile CommunicationsResearch Laboratory, Southeast University, Nanjing 210096, China (e-mail:,chxwang@seu.edu.cn; hj_1204@sina.cn).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2018.2866414

have developed from the first to the fourth generations so far.It is expected that by 2020, the fifth generation (5G) wire-less communication systems with ultra-high user experiencedata rate, ultra-high connection density, and ultra-high traf-fic density will be emerged [1]. As a typical application sce-nario of 5G communications, high-speed trains (HSTs) receivedmuch attention in recent years. Large numbers of HST usersdemand huge communication data volume, which is far be-yond the capacity of current HST communication systems. Thewidely used Global System for Mobile Communication Rail-way (GSM-R) is mainly for low-rate train communication andcontrol, and cannot provide personal communications for trainusers. Then, the Long-Term Evolution Railway (LTE-R) sys-tem has been recommended to replace the GSM-R to providewideband HST communication services [2]. However, in bothsystems, the HST users communicate directly with the out-door base stations (BSs). This results in the spotty coverageproblem and high penetration losses of wireless signals. HSTwireless communication systems also face various challenges,such as frequent handovers, large Doppler spreads, and fasttravel through different scenarios. Moreover, the high mobilityof trains with a speed of over 500 km/h can make the communi-cation link between the mobile relay station (MRS) and outdoorBS unstable.

To solve the aforementioned problems, some potential 5Gtechnologies, such as massive multiple-input multiple-output(MIMO) and millimeter wave (mmWave), have been consid-ered to provide reliable wideband wireless communication ser-vices [3]. Massive MIMO systems can significantly improvethe spectrum efficiency and energy efficiency by equipping alarge number of antennas at the transmitter (Tx) and/or receiver(Rx) side [4]. MmWave systems cover frequency bands from30 GHz to 300 GHz and are able to provide large bandwidths inthe order of 500 MHz or larger [5]. They can provide high datarate transmissions between MRSs and outdoor BSs. Further-more, by combining massive MIMO and mmWave technologies,some challenges originating from the high speed of trains andconventional network architectures can be overcome, and theunstable data transmission services can be further improved [6].For the design, performance evaluation, and test of futureHST communication systems assembling massive MIMO andmmWave technologies, an accurate and efficient channel modelis essential [7], [8].

0018-9545 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

2078 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

In the open literature, a variety of HST channel models havebeen proposed and analyzed to describe various HST commu-nication scenarios [2], [7]–[19]. In [11], a deterministic raytracing HST channel model was provided to mimic HST tun-nel channels, and several channel characteristics, such as fre-quency selectivity and Doppler spread, were studied. In [12],a three-dimensional (3D) deterministic ray tracing HST tun-nel channel model was given, which studied Doppler frequencyshift and time delay when two trains met. Ray tracing chan-nel models have high accuracy by incorporating a large amountof channel information but also result in high computationalcomplexity. Both channel models in [11] and [12] adopted theconventional communication architecture that the users insidethe train communicate directly with the outdoor BS. In ruralmacrocell scenario of WINNER II and moving networks of IMT-A channel models, MRSs are deployed. Both channel modelsintroduced the time evolution concept and analyzed the chan-nel non-stationarity. However, the stationary intervals of bothmodels are considerably larger than those of real HST channelsmeasured [13]. Hence, they cannot describe real HST propa-gation environments precisely. In [14], a two-dimensional (2D)non-stationary geometry-based stochastic model (GBSM) wasproposed for HST MIMO channels. All the channel parame-ters, such as K-factor and propagation distances between the Txand Rx, are time-variant. Based on the proposed model, sometime-variant small-scale fading channel statistical properties,such as autocorrelation function (ACF), space cross-correlationfunction (CCF), and local scatterer function (LSF), were in-vestigated. Moreover, based on the IMT-A model, a 2D non-stationary HST channel model was proposed in [15]. It assumedthat the mobility of both the MRS and clusters results in thechannel non-stationarity in the time domain. According to themoving trajectories of clusters and MRS, a series of time-variantsmall-scale parameters, such as the number of clusters, delays,angle of arrival (AoA), and angle of departure (AoD), wereobtained. Then, the channel statistical properties were studied,which were verified by the measurement data. In [16], a 3D non-stationary wideband HST MIMO channel model was proposedbased on the WINNER+ channel model. The cluster evolutionin time domain was considered, and some key channel statisticalproperties were investigated. In [17] and [18], the HST chan-nel models for tunnel scenarios were studied. In [19], a novelgeometry based random-cluster model for HST channels waspresented based on measurement data. The time evolution ofthe clusters was described by random geometrical parameters.The distributions of these parameters, as well as the path loss,shadow fading, delay, and Doppler spread of each cluster can beextracted from the measurement data. All the above models [2],[9]–[19] focused on HST channels without considering massiveMIMO and mmWave technologies.

With more demanding HST communication requirements,some promising 5G technologies such as massive MIMO andmmWave technologies have been considered in HST communi-cation systems to improve the network capacity and the reliabil-ity of communication links. In [20], the performance analysis ofmassive MIMO in HST communications was investigated. Theimpacts of train speed, K-factor, and signal-to-noise ratio (SNR)

were discussed. It demonstrated that the massive MIMO tech-nology can be applied to HST communications to improve thecommunication link reliability. Moreover, in [21], a mmWavecommunication network architecture between the train and BSwas presented. A series of simulation results demonstratedthe feasibility of mmWave in HST communication systems.Future HST communication systems will devolop towards ultra-wideband with mmWave bands and massive MIMO deploy-ment. Accurate channel models that can capture the new channelcharacteristics are essential and necessary.

For the existing 5G channel models towards standardization,some of them can support high mobility scenarios, such as COST2100 [22], QuaDRiGa [23], mmMAGIC [24], and 5GCM [25].COST 2100 channel model [22] can obtain the smooth timeevolution and spatial consistency, but cannot support massiveMIMO and mmWave. QuaDRiGa model [23] was evolved fromthe WINNER+ model and can support some new characteristics,such as 3D modeling, massive MIMO, and multi-user and multi-hop networks. However, this model does not support mmWavebands. The mmMAGIC channel model [24] can support largerbandwidth (2 GHz) and wider frequency range (10–80 GHz).It considered high mobility scenarios but no detailed informa-tion was given. Based on some 6–100 GHz measurement dataand ray tracing results, 5GCM [25] was proposed which con-sidered the HST scenario but cannot support massive MIMOvery well. In [7], a general 3D non-stationary 5G channel modelwas proposed, which can capture small-scale fading channelcharacteristics of the HST, massive MIMO, and mmWave com-munication scenarios. It can describe the non-stationarities ofthe channel in space and time domains, but the frequency non-stationarity was ignored.

To the best of the authors’ knowledge, space-time-frequencynon-stationary HST channel models considering massiveMIMO and mmWave technologies are still missing in the lit-erature. This paper aims to fill the gap. Overall, the majorcontributions and novelties of this paper are summarized asfollows.

1) Based on the WINNER II and Saleh-Valenzuela (SV)channel models, a novel space-time-frequency non-stationary massive MIMO and mmWave channel modelfor HST communications is first proposed. It involvesseveral space-dependent, time-dependent, and frequency-dependent parameters to reflect the effect of massiveMIMO and mmWave technologies.

2) The corresponding space-time-frequency channel corre-lation functions are derived and the space-time-frequencyevolutions of the proposed channel model are analyzed.

3) From the proposed channel model, some statistical prop-erties such as ACF, space CCF, delay power spectrumdensity (PSD), angular PSD, and frequency correlationfunction (FCF) are studied.

The remainder of this paper is structured as follows. InSection II, a 3D non-stationary massive MIMO and mmWavechannel model for 5G HST communications is presented.Section III analyzes the channel statistical properties. Resultsand discussions are given in Section IV. Finally, conclusionsare drawn in Section V.

LIU et al.: NOVEL 3-D NONSTATIONARY MmWAVE MASSIVE MIMO CHANNEL MODELS FOR 5G HST WIRELESS COMMUNICATIONS 2079

Fig. 1. HST communications network architecture considering massiveMIMO and mmWave technologies.

II. NON-STATIONARY MMWAVE MASSIVE MIMO CHANNEL

MODELS FOR 5G HST COMMUNICATIONS

A. Description of HST Communication Network Architecture

In this section, a brief description of a HST network consid-ering massive MIMO and mmWave technologies is provided. Itadopts a two-tiered network architecture to separate the indoorand outdoor channels [14]. In outdoor channels, at least oneMRS is deployed on the top of each carriage, which can estab-lish a communication link with the indoor users and transfer allthe communication data inside train to the outdoor BS.

MRSs are deployed on the surface of train to improve thequality of received signal, and mitigate high penetration lossesof signals traveling into train carriages. The massive MIMOtechnology is adopted to improve the spectrum efficiency andenergy efficiency by installing large number of antennas at theBS and/or MRS [26], [27]. Moreover, for the outdoor commu-nications between the MRS and BS, the mmWave technologyis considered. The mmWave communications can bring hugebandwidth and achieve high data transmission rate [5]. All thesetechnologies can be applied to increase communication capac-ity and improve system performance. The HST communicationnetwork architecture considering the MRS, massive MIMO, andmmWave is illustrated in Fig. 1.

B. The Massive MIMO and MmWave Channel Model for HSTCommunications

Let us consider a massive MIMO system with P and Q an-tenna elements at Tx (BS) side and Rx (MRS) side, respectively.The carrier frequency is denoted by fc . By taking the elevationangles into consideration, a 3D twin-cluster model is consid-ered [7]. The corresponding channel model framework is shownin Fig. 2. For clarity, only the nth cluster pair (n = 1, 2 . . . , N)is illustrated, where N is the number of clusters. Each spherein the figure with several dots represents a cluster, which canbe moving or static with certain probability. Moreover, clustersare randomly distributed in pairs. The nth twin-cluster can bedenoted by Cn,A and Cn,Z . Here, Cn,A is a representation ofthe first bounce at the Tx side and Cn,Z is a representation

Fig. 2. A 3D non-stationary twin-cluster HST channel model.

of the last bounce at Rx side. The propagation space betweenthe two clusters can be abstracted as a virtual link [16]. Theinter-element spacings at the Tx and Rx are denoted by ΔxT

and ΔxR , respectively. It is assumed that the Tx is fixed andRx is in motion. The movement of the Rx can be denoted by avelocity vector vR with speed vR . The velocity vector of Cn,A

is denoted by vn,A with speed vn,A and the velocity vector ofCn,Z is denoted by vn,Z with speed vn,Z . It should be notedthat all the parameters are established as time-variant.

1) The Theoretical Model: Based on the WINNER II andSV channel models, the non-stationary space-time-frequencyHST channel model considering massive MIMO and mmWavetechnologies is proposed. The complex channel transfer function(CTF) consists of the line-of-sight (LoS) and non-LoS (NLoS)components. The theoretical channel model can be expressedas [7]

Hpq (t, f) = HLoSpq (t, f) + lim

Mn →∞

N (t)∑

n=1

Mn∑

mn =1

HNLoSpq ,n,mn

(t, f)

(1)

–In the LoS case

HLoSpq (t, f) =

[FT

p,V (αTLoS(t), βT

LoS(t))

FTp,H (αT

LoS(t), βTLoS(t))

]T[ejΘV V

L o S 0

0 ejΘH HL o S

]

[FR

q,V (αRLoS(t), βR

LoS(t))

FRq,H (αR

LoS(t), βRLoS(t))

] √Kpq (t)

Kpq (t) + 1e−j2π

D L o Sp q ( t )

λ

× ej2πf L o Sp q (t)·t · e−j2πf ·τ L o S

p q (t) . (2)

For the LoS component, αTLoS(t) and βT

LoS denote the azimuthangle of departure (AAoD) and the elevation angle of depar-ture (EAoD) between the center of Tx array and Cluster Cn,A ,respectively. αR

LoS(t) and βRLoS denote the azimuth angle of ar-

rival (AAoA) and the elevation angle of arrival (EAoA) betweenthe center of Cluster Cn,Z and Rx array, respectively. fLoS

pq (t)is the Doppler frequency of LoS. τLoS

pq (t) is the LoS delay be-tween the Tx and Rx, and Kpq (t) is the K-factor. Here, V and Hdenote vertical polarization and horizontal polarization, respec-tively. ΘV V

LoS and ΘH HLoS are the initial phases, which follow the

uniform distribution over the (0, 2π). Functions FTV (·), FT

H (·),FR

V (·), and FRH (·) denote the antenna patterns in the global co-

ordinate system (GCS) with the origin at the center of Tx array.

2080 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

–In the NLoS case

HNLoSpq ,n,mn

(t, f) =

[FT

p,V (αTpn,mn

(t), βTpn,mn

(t))

FTp,H (αT

pn,mn(t), βT

pn,mn(t))

]T

⎡

⎣

√κ−1

n,mnejΘV V

n , m n ejΘV Hn , m n

ejΘH Vn , m n

√κ−1

n,mnejΘH H

n , m n

⎤

⎦

[FR

q,V (αRqn,mn

(t), βRqn,mn

(t))

FRq,H (αR

qn,mn(t), βR

qn,mn(t))

]·√

Pn,mn(t)

Kpq (t) + 1·(

f

fc

)rn , m n

× ej

(ϕn , m n −2π

D T Rp q , n , m n

( t )λ

)

· ej2πfp q , n , m n (t)·t

× e−j2πf ·(τp q , n (t)+τp q , n , m n (t)) . (3)

For the NLoS component, N(t) is the time-variant cluster num-ber. Mn is the ray number within nth cluster, τpq,n (t) is thedelay between the pth Tx antenna and qth Rx antenna via nthcluster, τpq,n,mn

(t) is the relative delay between the pth Tx an-tenna and qth Rx antenna via the mn th ray with nth cluster,and κn,mn

is the cross polarization power ratio. Here, ΘV Vn,mn

,ΘV H

n,mn, ΘH V

n,mn, and ΘH H

n,mnare the initial random phases of the

mn th ray of the nth cluster in four polarization directions. Itshould be noted that the phases follow the uniform distribu-tion within (0, 2π) and rn,mn

is the frequency-dependent factor[28]. In the proposed HST channel model, all the parametersare time-variant. Moreover, the massive MIMO technology willbring spherical wavefront and cluster birth-death process alongthe antenna array axis. The mmWave will introduce the appear-ance and disappearance of clusters in the frequency domain.The channel will exhibit non-stationarities in space, time, andfrequency domains. Our proposed channel model has the ca-pability to model the space-time-frequency non-stationaritiesof HST channels. The Doppler frequency fpq,n,mn

(t) can beshown as

fpq,n,mn(t) = fT

pn,mn(t) + fR

qn,mn(t)

=(vR − vn,Z ) · φR

qn,mn(t) − vn,Aφ

Tpn,mn

(t)λ

.

(4)

It should be noted that the Doppler frequency fpq,n,mn(t)

is caused by the movement of Cluster Cn,A , Cluster Cn,Z ,and MRS. The wavelength is λ = c/fc . Moreover, the veloc-ity vectors of Cluster Cn,A , Cluster Cn,Z , and MRS can beexpressed as

vn,A = vn,A ·

⎡

⎢⎣cos ϕn,A · cos ϑn,A

cos ϕn,A · sin ϑn,A

sinϕn,A

⎤

⎥⎦

T

(5)

vn,Z = vn,Z ·

⎡

⎢⎣cos ϕn,Z · cos ϑn,Z

cos ϕn,Z · sinϑn,Z

sin ϕn,Z

⎤

⎥⎦

T

(6)

vR = vR ·

⎡

⎢⎣cos ϕR · cos ϑR

cos ϕR · sin ϑR

sin ϕR

⎤

⎥⎦

T

. (7)

The 3D AoD vectors between the pth Tx array element andmn th ray of Cluster Cn,A can be expressed as

φTpn,mn

(t) =

⎡

⎢⎢⎣

cos βTpn,mn

(t) · cos αTpn,mn

(t)

cos βTpn,mn

(t) · sin αTpn,mn

(t)

sin βTpn,mn

(t)

⎤

⎥⎥⎦

T

. (8)

The AoA vectors between the mn th ray of Cluster Cn,Z and theqth Rx array element can be expressed as

φRqn,mn

(t) =

⎡

⎢⎢⎣

cos βRqn,mn

(t) · cos αRqn,mn

(t)

cos βRqn,mn

(t) · sin αRqn,mn

(t)

sin βRqn,mn

(t)

⎤

⎥⎥⎦

T

. (9)

Moreover, the delay between the pth Tx and qth Rx via mn thray of nth cluster consists of the delay of first bounce, the delayof last bounce, and the virtual link delay τpq ,n,mn

(t). The totaldelay can be expressed as

τpq,n,mn(t) =

∥∥DT Rpq,n,mn

(t)∥∥

c+ τpq ,n,mn

(t)

=

[∥∥DTpn,mn

(t)∥∥ +

∥∥DRqn,mn

(t)∥∥]

c+ τpq ,n,mn

(t).

(10)

The distance between the pth Tx and mn th ray in Cluster Cn,A

can be expressed as

DTpn,mn

(t) = DTpn,mn

(t0) + vn,A · t (11)

DTpn,mn

(t0) = DTpn,mn

(t0) · φTpn,mn

(t0). (12)

The distance between the mn th ray in Cluster Cn,Z and qth Rxcan be expressed as

DRqn,mn

(t) = DRqn,mn

(t0) + vn,Z · t (13)

DRqn,mn

(t0) = DRqn,mn

(t0) · φRqn,mn

(t0). (14)

The mean power of mn rays within nth cluster can be obtainedby

Pn,mn(t) = e

(−τ n , m n ( t ) )(χ −1)E [τ n , m n ( t ) ] · 10−

Z n , m n10 (15)

where χ denotes the delay scaling parameters, E[τn,mn(t)] is

the mean relative delay via the mn th ray of the nth cluster,and Zn,mn

is the shadowing of each ray per cluster following aGaussian distribution.

The generation process of the space-time-frequency non-stationary 5G HST channel model is shown in Fig. 3. It takesthe array, time, and frequency evolutions into consideration. Allthe aforementioned parameters are listed as Table I.

LIU et al.: NOVEL 3-D NONSTATIONARY MmWAVE MASSIVE MIMO CHANNEL MODELS FOR 5G HST WIRELESS COMMUNICATIONS 2081

TABLE IDEFINITION OF PARAMETERS

Fig. 3. The generation process of the HST channel model.

2) The Simulation Model: Based on the proposed theoreticalHST channel model, the simulation model can be developedby using the discrete angles. Here, the method of equal area(MEA) is used to obtain the discrete AAoDs, EAoDs, AAoAs,and EAoAs. The simulation model can be expressed as

Hpq (t, f) = HLoSpq (t, f)+

N (t)∑

n=1

Mn∑

mn =1

HNLoSpq ,n,mn

(t, f). (16)

C. Cluster Evolution in Space, Time, and Frequency Domainsfor HST Channel Model

The non-stationarities of our proposed HST channel modelresult from two mechanisms, i.e., the time-variant parametersand the birth-death process of clusters in space/time/frequencyaxes. The clusters in a specific HST scenario can exist overa certain time period [2]. During this period, the number of

clusters can be seen as unchanged. When it is over the period,some of previous clusters disappear and some new clusters ap-pear [7]. In this section, the space, time, and frequency clusterevolutions for the proposed HST channel model are developed,as shown in Fig. 4. The flowchart in Fig. 4 can be described indetails as follows.

Firstly, a series of initial cluster sets are generated at timet [16]. Some parameters, such as number of rays in a clus-ter, delays of rays, power, angular parameters, and virtual linkdelay, need to be assigned. These parameters are generated ran-domly and different parameters follow different distributions.The number of rays follow a Poisson distribution. The virtuallink delays of clusters and the delays of rays are assumed tofollow exponential distributions. Moreover, the angular parame-ters, such as AAoAs, AAoDs, EAoAs, and EAoDs, are assumedto be wrapped Gaussian distributions [7].

Secondly, to describe the cluster evolution more accurately,two types of sampling intervals can be used in the evolutionprocess [16]. The first type is the channel sampling intervals,such as Δi in space (antenna array) domain, Δt in time domain,and Δf in frequency domain. The channel parameters shouldbe updated continuously during these periods. The other typeof sampling intervals are the periods in which the clusters areneeded to be updated. These intervals can be described by Δie ,Δte , and Δfe . During Δie , Δte , and Δfe , the birth and death ofclusters occur. Here, we take the cluster evolution in time domainas an example. For the proposed channel model, it will generatesome clusters initially. These clusters can be updated during theaforementioned sampling intervals. Some of these clusters dis-appear and others survive. Moreover, some new clusters appear.Each cluster has its own survival probability Psurv (Δte), whichis calculated by the relative velocities of clusters. By extend-ing time domain to space-time-frequency domain, the survival

2082 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

Fig. 4. The flowchart of space-time-frequency cluster evolution of theproposed HST channel model.

probability of a cluster in the proposed space-time-frequencychannel model should consist of three parts. The final survivalprobability is jointly influenced by space, time, and frequencydomains, which can be calculated as

Psurv (Δie ,Δte ,Δfe)

= Psurv (Δie) · Psurv (Δte) · Psurv (Δfe)

= e−λR · A (p , q , p ′ , q ′ , Δ i e )

D i · e−λR · T ( v R , Δ t e )D t · e−λR · F (Δ f e )

D f . (17)

Note that Di , Dt , Df , and F (Δfe) can be determined by chan-nel measurements. Meanwhile, a lot of new clusters need to

be generated. Let us assume that the birth rate is λG and thedeath rate is λR . The number of newly generated clusters canbe expressed as

E[Nng (i + Δie , t + Δte , f + Δfe)]

=λG

λR(1 − Psurv (Δie ,Δte ,Δfe)). (18)

Thirdly, the newly generated clusters and the survival clus-ters need to be updated. For the newly generated clusters,some parameters such as delay, power, and angular parametersare assigned randomly just as the initialization process. For thesurvival clusters, the corresponding delay, power, and angularparameters are updated from the previous time instant. Follow-ing the steps above, the space-time-frequency non-stationarityof the channel model can be guaranteed.

III. STATISTICAL PROPERTIES ANALYSIS

In this section, we will derive typical statistical properties ofthe proposed non-stationary simulation HST channel model.

A. The Delay PSD

The time-variant delay PSD Υ(t, τpq ) of channel between thepth Tx antenna and the qth Rx antenna can be expressed as

Υ(t, τpq ) =N (t)∑

n=1

Mn∑

mn =1

|hpq,n,mn(t)|2

× δ (τpq − τpq,n (t) − τpq,n,mn(t)) . (19)

The time-variant delay PSD is influenced by the time-dependentmean powers of rays with clusters and delays of rays parame-ters. The cluster power can be obtained from the channel impulseresponse (CIR) hpq,n,mn

(t), which is the inverse Fourier trans-form of CTF. All these parameters are related to the continuouslyupdated geometrical relationship.

B. Space-Time-Frequency Correlation Function

The correlation function of two arbitrary CTF of Hpq (t, f)and H∗

p ′q ′(t, f) can be defined as the summation of all theclusters with no inter-correlation. To investigate the correla-tion properties, the space-time-frequency correlation functionRH (Δt,Δf,ΔxT ,ΔxR ) can be calculated as

RH (Δt,Δf,ΔxT ,ΔxR )

= E[Hpq (t, f) · H∗p ′q ′(t − Δt, f − Δf)]

= RLoSH (Δt,Δf,ΔxT ,ΔxR ) + RNLoS

H (Δt,Δf,ΔxT ,ΔxR )(20)

where E[·] denotes the expectation operator, and (·)∗ denotes thecomplex conjugate operation. The propagation channel consistsof two parts: the LoS and NLoS components. The LoS compo-nent is calculated by the locations of the Tx and Rx. The NLoScomponents are generated randomly. Assuming that the LoSand NLoS components are independent with each other. (20)can be expressed as the summation of LoS component

LIU et al.: NOVEL 3-D NONSTATIONARY MmWAVE MASSIVE MIMO CHANNEL MODELS FOR 5G HST WIRELESS COMMUNICATIONS 2083

correlation and NLoS components correlation. Thedetailed space-time-frequency correlation functionRLoS

H (Δt,Δf,ΔxT ,ΔxR ) and RNLoSH (Δt,Δf,ΔxT ,ΔxR )

can be rewritten as–In the LoS case,

RLoSH (Δt,Δf,ΔxT ,ΔxR ) =

Kpq (t)Kpq (t) + 1

HLoSpq (t, f)

· HLoS∗p ′q ′ (t − Δt, f − Δf)

(21)

–In the NLoS case,

RNLoSH (Δt,Δf,ΔxT ,ΔxR )

=1

Kpq (t) + 1

N (t)∑

n=1

Mn∑

mn =1

HNLoSpq ,n,mn

(t, f)

· HNLoS∗p ′q ′,n,mn

(t − Δt, f − Δf). (22)

According to the above equations, the time-variant space CCFcan be obtained by imposing Δt = 0 and Δf = 0 in (20) andcan be expressed as

ρH (ΔxT ,ΔxR ) = RH (ΔxT ,ΔxR , 0, 0)

= ρLoSH (ΔxT ,ΔxR ) + ρNLoS

H (ΔxT ,ΔxR ).(23)

By setting ΔxT , ΔxR , and Δf in (20) as 0, the space-time-frequency correlation function can be reduced as the time-variant ACF, which can be expressed as

rH (Δt) = RH (Δt, 0, 0, 0) = rLoSH (Δt) + rNLoS

H (Δt). (24)

C. The FCF

By setting ΔxT , ΔxR , and Δt in (20) as 0, the time-variantfrequency correlation function (FCF) can be obtained, whichcan be expressed as

κH (t,Δf) = E[Hpq (t, f) · H∗

pq (t, f − Δf)]

=RH (Δf, 0, 0, 0)=κLoSH (t,Δf) + κNLoS

H (t,Δf).(25)

D. The Doppler PSD

By taking the Fourier transform of ACF with respect to Δt,the time-variant Doppler PSD can be obtained, which can beillustrated as

SH (t, fD ) =∫ ∞

−∞rH (Δt)e−j2πfD ΔtdΔt

=∫ ∞

−∞

(rLoSH (Δt) + rNLoS

H (Δt)) · e−j2πfD ΔtdΔt.

(26)

E. The Angular PSD

The time-variant angular PSD Λ(t,Ω) of channel can beacquired by the CIR hpq,n,mn

(t). It describes the distribu-tion of power spectrum in the angular domain, which can be

expressed as

Λ(t,Ω) =N (t)∑

n=1

Mn∑

mn =1

|hpq,n,mn(t)|2δ(Ω − Ωpq ,n − Ωpq ,n,mn

)

(27)

where Ω denotes the AoAs or AoDs, Ωpq ,n is the mean angleof the nth cluster, and Ωpq ,n,mn

is the angle offset of the mn thray in the nth cluster.

F. The Stationary Intervals in Space-Time-Frequency Domain

The stationary interval is the period during which the channelcan be seen as unchanged compared with the neighbor channel.To obtain the stationary interval in space-time-frequency do-main, the time-variant correlation matrix distance (CMD) canbe applied [29]. The CMD can be calculated in space-time-frequency domain as follows

dcorr (Δts ,Δfs,Δis)

= 1 − tr{RH (t; f ; i)RH (t + Δts ; f + Δfs ; i + Δis)}‖RH (t; f ; i)‖F‖RH (t + Δts ; f + Δfs ; i + Δis)‖F

(28)

where RH (t; f ; i) is the correlation function of channel trans-fer function. Δts is the time stationary interval, Δfs is thefrequency stationary, and Δis is the space stationary interval.The above stationary intervals can be used to evaluate the non-stationary behaviors of HST channels in space/time/frequencydomains.

IV. RESULTS AND DISCUSSIONS

In this part, the statistical properties of the proposed HSTchannel models are studied and analyzed. The related simulationparameters are listed as follows. The generation rate λG = 80/m,and the recombination rate λR = 4/m. The moving speed ofMRS is vR = 100 m/s, and the BS is fixed. The moving speedsof Cn,A and Cn,Z are selected as vn,A = 30 m/s and vn,Z =30 m/s, respectively. The carrier frequency is set as fc = 58 GHz,and the antenna elements at Tx and Rx are both set as 32. Thenumber of rays in each cluster is set as 20. The percentage ofmoving clusters is PF = 0.3 [30]. The initial AAoD ϕn,A andEAoD ϑn,A of the nth twin cluster at the Tx side are ϕn,A = π

3 ,ϑn,A = π

4 . Moreover, the initial AAoA ϕn,Z and EAoA ϑn,Z ofthe nth twin cluster at the Rx side are ϕn,Z = π

3 , ϑn,A = π4 . All

the angular parameters are randomly generated by the Gaussiandistribution. The initial distance between the pth Tx antennaelement and mn th ray of nth cluster Cn,A is DT

pn,mn(t0)= 50 m,

and the initial distance between the mn th ray of nth cluster Cn,Z

and qth Rx antenna element is DRqn,mn

(t0) = 100 m. The lengthof railway between the Tx and Rx is set as D = 200 m [14].All the simulations are conducted in the NLoS case. The restparameters are randomly generated refer to the WINNER IIchannel model [31]. The MEA is employed to obtain the discreteAoA and AoD angular parameters, respectively. The k value ofthe von Mises distribution is selected as 6.

2084 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

Fig. 5. The delay PSDs of the non-stationary HST simulation channel modelat (a) t = 2 s and (b) t = 4 s (DT

pn ,m n(t0) = 50 m, DR

qn ,m n(t0) = 100 m,

λG = 80/m, λR = 4/m, vn ,A = 30 m/s, vn ,Z = 30 m/s, vR = 100 m/s).

A. Time-Variant Delay PSD

By imposing the time-dependent mean powers and delays ofclusters, the cluster delay PSD can be acquired. Moreover, usingthe mean delays of rays within one cluster and the correspondingpowers of rays, the ray delay PSD can also be exhibited as inFig. 5. From this figure, we can observe the profile of poweralong with the delay at different time instants. The delay PSDsare different at time instants t = 2 s and t = 4 s .

B. Time-Variant ACF

Based on the massive MIMO and mmWave HST channelmodel, the non-stationarity of the proposed channel model canbe described effectively. By adopting ΔxT = 0, ΔxR = 0, andΔf = 0, the ACF of theoretical model can be obtained. Then,using the MEA method, the ACF of simulation model can beacquired. The comparisons of time ACFs of theoretical model

Fig. 6. The time-variant ACFs of the theoretical model and simulation model(fc = 58 GHz, DT

pn ,m n(t0) = 50 m, DR

qn ,m n(t0) = 100 m, λG = 80/m, λR

= 4/m, vn ,A = 30 m/s, vn ,Z = 30 m/s, vR = 100 m/s).

Fig. 7. The comparison of time-variant ACFs of simulation model and simu-lation results (fc = 58 GHz, DT

pn ,m n(t0) = 50 m, DR

qn ,m n(t0) = 100 m, λG

= 80/m, λR = 4/m, vn ,A = 30 m/s, vn ,Z = 30 m/s, vR = 100 m/s).

and simulation model are illustrated in Fig. 6. From this figure,we can see that the simulation model provides a good approxi-mation of the theoretical model. Moreover, the absolute valuesof ACFs at different time instants, i.e., t = 2 s and t = 4 scan be obtained. At different time instants, there are differentACFs of proposed HST channel model, which demonstrates thatthe proposed model can capture the non-stationarity of channel.To validate the accuracy of the proposed HST channel model,the ACFs of simulation model and the corresponding simula-tion results for both Cluster1 and Cluster2 are compared inFig. 7. It should be noted that both of ACFs are normalizatedby Cluster1. It can be observed from Fig. 7 that the simulationmodel can match well with the simulation results. The simula-tion model align well with simulation results for Cluster1 andCluster2 cases.

LIU et al.: NOVEL 3-D NONSTATIONARY MmWAVE MASSIVE MIMO CHANNEL MODELS FOR 5G HST WIRELESS COMMUNICATIONS 2085

Fig. 8. The FCFs of the proposed simulation channel model at different fre-quencies fc (DT

pn ,m n(t0) = 50 m, DR

qn ,m n(t0) = 100 m, λG = 80/m, λR =

4/m, vR = 100 m/s).

Fig. 9. The angular PSD of the proposed simulation channel model(DT

pn ,m n(t0) = 50 m, DR

qn ,m n(t0) = 100 m, vn ,A = 30 m/s, vn ,Z =

30 m/s, vR = 100 m/s).

C. The FCF

The absolute values of the FCFs of the 3D massive MIMOand mmWave HST channel model are illustrated in Fig. 8. Fromthis figure, we can notice that the FCFs are different at fc =38 GHz, 58 GHz, and 78 GHz, which show the frequency non-stationarities of the proposed channel model.

D. Angular PSD

The simulated normalized angular PSD at the moving Rx ofthe 3D massive MIMO and mmWave channel model is illus-trated in Fig. 9. It can be observed that the clusters show ap-pearance and disappearance properties on the massive MIMOarray axis, which exhibit the clusters birth and death from space

domain. Moreover, the angular shifts can be obtained, whichresult from the spherical wavefront effect of massive MIMO.

V. CONCLUSIONS

In this paper, a novel 3D space-time-frequency non-stationarymmWave massive MIMO theoretical channel model for 5G HSTcommunication channels has been proposed. The correspond-ing simulation channel model has been developed using theMEA. Based on the proposed theoretical and simulation mod-els, their statistical properties have been investigated, includingtime-variant ACF, space CCF, delay PSD, angular PSD, andFCF. Numerical and simulation results have shown that the sta-tistical properties of the simulation model can match well withthose of the theoretical model. Moreover, due to the movementsof clusters and MRS, the statistical properties experience differ-ent behaviors at different time instants, which has demonstratedthat our proposed models can mimic the non-stationarity ofHST channels. By introducing the model parameters in space,time, and frequency domains, the joint space-time-frequencynon-stationarity of the proposed HST channel model has beeninvestigated.

REFERENCES

[1] C.-X. Wang et al., “Cellular architecture and key technologies for 5Gwireless communication networks,” IEEE Commun. Mag., vol. 52, no. 2,pp. 122–130, Feb. 2014.

[2] C.-X. Wang, A. Ghazal, B. Ai, P. Fan, and Y. Liu, “Channel measurementsand models for high-speed train communication systems: A survey,” IEEECommun. Surv. Tut., vol. 18, no. 2, pp. 974–987, Apr.–Jun. 2016.

[3] K. Guan et al., “On millimeter wave and THz mobile radio channel forsmart rail mobility,” IEEE Trans. Veh. Technol., vol. 66, no. 7, pp. 3349–3516, Jul. 2017.

[4] S. Wu, C.-X. Wang, H. Haas, H. Aggoune, M. M. Alwakeel, and B.Ai, “A non-stationary wideband channel model for massive MIMO com-munication systems,” IEEE Trans. Wireless Commun., vol. 14, no. 3,pp. 1434–1446, Mar. 2015.

[5] J. Huang, C.-X. Wang, R. Feng, J. Sun, W. Zhang, and Y. Yang, “Multi-frequency mmWave massive MIMO channel measurements and charac-terization for 5G wireless communication systems,” IEEE J. Sel. AreasCommun., vol. 35, no. 7, pp. 1591–1605, Jul. 2017.

[6] B. Ai et al., “Challenges toward wireless communications for high-speedrailway,” IEEE Trans. Intell. Transp. Syst., vol. 15, no. 5, pp. 2143–2158,Oct. 2014.

[7] S. Wu, C.-X. Wang, H. Aggoune, M. M. Alwakeel, and X. You, “A general3D non-stationary 5G wireless channel model,” IEEE Trans. Commun.,vol. 66, no. 7, pp. 3065–3078, Jul. 2018.

[8] C.-X. Wang, J. Bian, J. Sun, W. Zhang, and M. Zhang, “A survey of 5Gchannel measurements and models,” IEEE Commun. Surv. Tut., vol. 20,no. 4, pp. 3142–3168, Fourth Quarter 2018.

[9] K. Guan, Z. Zhong, B. Ai, and T. Kurner, “Propagation measurementsand analysis for train stations of high-speed railway at 930 mHz,” IEEETrans. Veh. Technol., vol. 63, no. 8, pp. 3349–3516, Oct. 2014.

[10] S. Knorzer, M. A. Baldauf, T. Fugen, and W. Wiesbeck, “Channel analysisfor an OFDM-MISO train communications system using different anten-nas,” in Proc. IEEE 66th Veh. Technol. Conf., Baltimore, MD, USA, Oct.2007, pp. 809–813.

[11] D. J. Cichon, T. Becker, and W. Wiesbeck, “Determination of time-variantradio links in high-speed train tunnels by ray optical modeling,” in Proc.IEEE Antennas Propag. Soc. Int. Symp., Newport Beach, CA, USA, Jun.1995, pp. 508–511.

[12] D. J. Cichon, T. Zwick, and W. Wiesbeck, “Ray optical modeling ofwireless communications in high-speed railway tunnels,” in Proc. IEEEVeh. Technol. Conf., Atlanta, GA, USA, May 1996, pp. 546–550.

[13] B. Chen, Z. Zhong, and B. Ai, “Stationarity intervals of time-variantchannel in high speed railway scenario,” China Commun., vol. 9, no. 8,pp. 64–70, Aug. 2012.

2086 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

[14] A. Ghazal, C.-X. Wang, B. Ai, D. Yuan, and H. Haas, “A non-stationarywideband MIMO channel model for high-mobility intelligent transporta-tion systems,” IEEE Trans. Intell. Transp. Syst., vol. 16, no. 2, pp. 885–897,Apr. 2015.

[15] A. Ghazal et al., “A non-stationary IMT-A MIMO channel model forhigh-mobility wireless communication systems,” IEEE Trans. WirelessCommun., vol. 16, no. 4, pp. 2057–2068, Apr. 2017.

[16] J. Bian et al., “A WINNER+ based 3D non-stationary wideband MIMOchannel model,” IEEE Trans. Wireless Commun., vol. 17, no. 3, pp. 1755–1767, Mar. 2018.

[17] Y. Liu, C.-X. Wang, C. F. Lopez, and X. Ge, “3D non-stationary widebandcircular tunnel channel models for high-speed train wireless communica-tion systems,” Sci. China Inf. Sci., vol. 60, no. 8, pp. 1–13, Aug. 2017.

[18] Y. Liu, A. Ghazal, C.-X. Wang, X. Ge, Y. Yang, and Y. Zhang, “Channelmeasurements and models for high-speed train wireless communicationsystems in tunnel scenarios: A survey,” Sci. China Inf. Sci., vol. 60, no. 8,pp. 1–17, Oct. 2017.

[19] X. Yin, X. Cai, X. Cheng, J. Chen, and M. Tian, “Empirical geometrybased random-cluster model for high-speed-train channels in UMTS net-works,” IEEE Trans. Intell. Transp. Syst., vol. 16, no. 5, pp. 2850–2861,Oct. 2015.

[20] Y. Cui and X. Fang, “Performance analysis of massive spatial modulationMIMO in high-speed railway,” IEEE Trans. Veh. Technol., vol. 65, no. 11,pp. 8925–8932, Nov. 2016.

[21] H. Song, X. Fang, and Y. Fang, “Millimeter-wave network architecturesfor future high-speed railway communications: Challenges and solutions,”IEEE Wireless Commun., vol. 23, no. 6, pp. 114–122, Dec. 2016.

[22] L. Liu et al., “The COST 2100 mIMO channel model,” IEEE WirelessCommun., vol. 19, no. 6, pp. 92–99, Dec. 2012.

[23] S. Jaeckel, L. Raschkowski, K. Brner, and L. Thiele, “QuaDRiGa: A 3-Dmulti-cell channel model with time evolution for enabling virtual fieldtrials,” IEEE Trans. Antennas Propag., vol. 62, no. 6, pp. 3242–3256, Jun.2014.

[24] “3rd generation partnership project, technical specification group radioaccess network, study on 3D channel model for LTE (Release 12),”3GPP, Sophia Antipolis Cedex, France, 3GPP TR 36.873, V12.0.0,Jun. 2015.

[25] “5G channel model for bands up to 100 GHz,” Aalto University, Aalto,Finland, v2.0, Mar. 2014.

[26] S. Wu, C.-X. Wang, H. Aggoune, M. M. Alwakeel, and Y. He, “A non-stationary 3D wideband twin-cluster model for 5G massive MIMO chan-nels,” IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 1207–1218, Jun.2014.

[27] C.-X. Wang, S. Wu, L. Bai, X. You, J. Wang, and C.-L. I, “Recent ad-vances and future challenges for massive MIMO channel measurementsand models,” (Invited Paper) Sci. China Inf. Sci., vol. 59, no. 2, pp. 1–16,Feb. 2016.

[28] R. C. Qiu, “A study of the ultra-wideband wireless propagation channeland optimum UWB receiver design,” IEEE J. Sel. Areas Commun., vol. 20,no. 9, pp. 1628–1637, Dec. 2002.

[29] R. He et al., “Characterization of quasi-stationarity regions for vehicle-to-vehicle radio channels,” IEEE Trans. Antennas Propag., vol. 63, no. 5,pp. 2237–2251, May 2015.

[30] T. Zwick, C. Fischer, D. Didascalou, and W. Wiesbeck, “A stochasticspatial channel model based on wave-propagation modeling,” IEEE J. Sel.Areas Commun., vol. 18, no. 1, pp. 6–15, Jan. 2000.

[31] K. Pekka, “WINNER II channel models part II radio channel measurementand analysis results,” IST-4-027756, WINNER II D1.1.2, v1.0, Sep. 2007.

Yu Liu received the B.Sc. and M.Eng. degrees incommunication and information systems from QufuNormal University, China, in 2010 and 2013, re-spectively, and the Ph.D. degree in communicationand information systems from Shandong University,China, in 2017. Since August 2017, she has beena Postdoctoral Research Associate with the Schoolof Information Science and Engineering, ShandongUniversity. Her main research interests include non-stationary wireless MIMO channel modeling, high-speed train wireless propagation characterization and

modeling, and channel modeling for special scenarios.

Cheng-Xiang Wang (S’01–M’05–SM’08–F’17) re-ceived the B.Sc. and M.Eng. degrees in commu-nication and information systems from ShandongUniversity, Jinan, China, in 1997 and 2000, respec-tively, and the Ph.D. degree in wireless communica-tions from Aalborg University, Aalborg, Denmark, in2004.

He was a Research Assistant with the Ham-burg University of Technology, Hamburg, Germany,from 2000 to 2001, a Visiting Researcher withSiemens AG Mobile Phones, Munich, Germany,

in 2004, and a Research Fellow with the University of Agder, Grimstad,Norway, from 2001 to 2005. Since 2005, he has been with Heriot–Watt Univer-sity, Edinburgh, U.K., where he was promoted to a Professor in 2011. In 2018,he joined Southeast University, Nanjing, China, as a Professor and ThousandTalent Plan Expert. He has authored and coauthored 2 books, 1 book chapter,and more than 340 papers in refereed journals and conference proceedings. Hiscurrent research interests include wireless channel modeling and (B)5G wire-less communication networks, including green communications, cognitive radionetworks, high mobility communication networks, massive MIMO, millimetrewave communications, and visible light communications.

Dr. Wang is a Fellow of the IET and HEA, and is recognized as a Web of Sci-ence 2017 Highly Cited Researcher. He served or is currently serving as an Editorfor nine international journals, including the IEEE TRANSACTIONS ON VEHICU-LAR TECHNOLOGY since 2011, the IEEE TRANSACTIONS ON COMMUNICATIONS

since 2015, and the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS

from 2007 to 2009. He was the leading Guest Editor for the IEEE JOURNAL ON

SELECTED AREAS IN COMMUNICATIONS (Special Issue on Vehicular Commu-nications and Networks). He is also a Guest Editor for the IEEE JOURNAL ON

SELECTED AREAS IN COMMUNICATIONS (Special Issue on Spectrum and En-ergy Efficient Design of Wireless Communication Networks and Special Issueon Airborne Communication Networks), and the IEEE TRANSACTIONS ON BIG

DATA, (Special Issue on Wireless Big Data). He served or is serving as a TPCMember, TPC Chair, and General Chair of more than 80 international confer-ences. He received nine Best Paper Awards from the IEEE Globecom 2010, theIEEE ICCT 2011, ITST 2012, the IEEE VTC 2013, IWCMC 2015, IWCMC2016, the IEEE/CIC ICCC 2016, and the WPMC 2016.

Jie Huang received the B.Sc. degree in informa-tion engineering from the Xidian University, Xi’an,China, in 2013, and the Ph.D. degree in communi-cation and information systems from Shandong Uni-versity, Jinan, China, in 2018. Since August 2018,he has been a Postdoctoral Research Associate withthe Mobile Communications Research Laboratory,Southeast University, Nanjing, China. His current re-search interests include millimeter wave and massiveMIMO channel measurements, parameter estimation,channel modeling, wireless big data, and 5G wirelesscommunications.Jian Sun (M’08) received the Ph.D. degree fromZhejiang University, Hangzhou, China, in March2005. Since July 2005, he has been a Lecturer withthe School of Information Science and Engineer-ing, Shandong University, Jinan, China. In 2011,he was a visiting scholar with Heriot–Watt Univer-sity, Edinburgh, U.K., supported by U.K.–China Sci-ence Bridges: R&D on (B)4G Wireless Mobile Com-munications (UC4G) project. His research interestsinclude signal processing for wireless communica-tions, channel sounding and modeling, propagation

measurement and parameter extraction, MIMO, and multicarrier transmissionsystems design and implementation.

Wensheng Zhang (S’08–M’11) received the M.Sc.degree in communication and information systemsfrom Shandong University, Jinan, China, in 2005,and the Ph.D. degree in communication engineeringfrom Keio University, Tokyo, Japan, in 2011. From2005 to 2007, he was a Lecturer with the Schoolof Communication, Shandong Normal University,Jinan, China. In 2011, he was a Visiting Researcherwith Oulu University, Oulu, Finland. Since 2012,he has been a Lecturer with the School of Informa-tion Science and Engineering, Shandong University,

Jinan, China, where he was promoted to an Associate Professor in 2016. His re-search interests include random matrix theory and big data analysis, visible lightcommunication networks, intelligent wireless communication systems, and 5Gwireless communications.