Research Article Massive MIMO Channel Models: A...

Research ArticleMassive MIMO Channel Models A Survey

Kan Zheng1 Suling Ou1 and Xuefeng Yin2

1 Wireless Signal Processing and Network Lab Key Laboratory of Universal Wireless Communication Ministry of EducationBeijing University of Posts and Telecommunications (BUPT) PO Box 93 No 10 Xi Tu Cheng Road Haidian DistrictBeijing 100876 China

2Department of Electronics Science and Technology Tongji University Shanghai China

Correspondence should be addressed to Kan Zheng zkanbupteducn

Received 25 January 2014 Accepted 28 March 2014 Published 16 June 2014

Academic Editor Periklis Chatzimisios

Copyright copy 2014 Kan Zheng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The exponential traffic growth ofwireless communication networks gives rise to both the insufficient network capacity and excessivecarbon emissions Massive multiple-input multiple-output (MIMO) can improve the spectrum efficiency (SE) together with theenergy efficiency (EE) and has been regarded as a promising technique for the next generation wireless communication networksChannel model reflects the propagation characteristics of signals in radio environments and is very essential for evaluating theperformances of wireless communication systems The purpose of this paper is to investigate the state of the art in channel modelsof massive MIMO First the antenna array configurations are presented and classified which directly affect the channel modelsand system performance Then measurement results are given in order to reflect the main properties of massive MIMO channelsBased on these properties the channel models of massive MIMO are studied with different antenna array configurations whichcan be used for both theoretical analysis and practical evaluation

1 Introduction

The requirements for high rate of wireless communicationnetworks grow exponentially with the applications of smartterminals Thus the capacity of the networks has to beincreased in order to guarantee the quality of service (QoS)of mobile applications Improving the spectrum efficiency(SE) is one of the feasible ways to achieve the better networkcapacity Besides it with the excessive power consumptionof wireless communication networks both the carbon emis-sions and operator expenditure increase every year [1 2]Therefore green communication has gained more atten-tion in the academic and industrial fields and the energyefficiency (EE) has been regarded as another vital metricfor evaluating the new technique as well as the spectrumefficiency [3ndash5]

Multiple-input multiple-output (MIMO) technique hasattracted much attention in wireless communications formore than ten years because it can offer significant increases

in data throughput and link reliability without extra band-width or boosting transmission power Nowadays MIMOtogether with orthogonal frequency division multiplexing(OFDM) has been accepted as key techniques in the thirdgeneration (3G) long-term evolution (LTE) cellular networksand its advancement (Adv) The evolved Node B (eNB)equipped with multiple antennas communicates with severaltypes of user equipment (UE) at the same time frequencyresources named as multiuser MIMO (MU MIMO) canimprove the spectrum efficiency link reliability and systemenergy efficiency [6 7] In order to scale up these benefitsmassive MIMO also named as large-scale antenna systemvery large MIMO or hyper MIMO has been first putforward in 2010 [8] In massive MIMO system hundredsof antennas are used to serve tens of UEs simultaneouslyTheoretical and measurement results indicate that massiveMIMO can significantly improve the spectrum efficiency andsimultaneously reduce the radiated power [6 9] All thefeatures of massiveMIMO are shortly summarized in Table 1

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 848071 10 pageshttpdxdoiorg1011552014848071

2 International Journal of Antennas and Propagation

Table 1 Features of massive MIMO

Feature Main reason

Advantages

High spectrum efficiency [6 9] Large multiplexing gain and array gainHigh energy efficiency [6 9] Radiated energy can be concentrated on UEHigh reliability [9] Large diversity gain

Efficient linear precoderdetector [9] Favorable propagation condition for iid Rayleighchannel

Weak interuser interference andenhanced physical security [6] Orthogonal UE channels and extremely narrow beam

Simple scheduling scheme [16] Channel harden phenomenon averages out the fastfading

Robust to individual element failure [6] Large number of antenna array elements

Disadvantages

Pilot contamination [8] Limited orthogonal pilots as of bounded coherentinterval and bandwidth

High signal processing complexity [9] Large number of antennas and multiplexing UE

Sensitive to beam alignment [6] Extremely narrow beam is sensitive to UE moving orantenna array swaying

Poor broadcast channel [6] Be blind to UE positions

In Release 11 (R11) specified by the 3rd generation partner-ship project (3GPP) the MIMO technique can only radiatethe beam in horizontal dimension as of the fixed down tilt ofantenna array In order to well exploit the vertical angular res-olution of signal propagation different kinds of the antennaarray configurations such as the rectangular spherical andcylindrical antenna array deployments have been studied in3GPP [13ndash15]With theseMIMO antenna array deploymentsthe eNB can adaptively adjust both azimuth and elevationangles of signal propagation In other words the radiatedMIMO signals can be controllable in the three-dimension(3D) space and thus called as 3D MIMO In order toenhance the system capacity 3DMIMO should employ moreantennas And massiveMIMO should adopt the rectangularspherical or cylindrical antenna array configurations for thepractical system considering the space of antennas arrayTherefore 3D MIMO with a large number of antennas canbe regarded as one of practical forms of massive MIMO

Up to now massive MIMO has been paid much attentionto by both academic and industry organizations There arelots of works done for massive MIMO such as performanceanalysis remedies for alleviating pilot contamination andchannel estimation The channel model is fundamental fortheoretical analysis as well as for performance evaluationof massive MIMO system Therefore this paper mainlyinvestigates the state of the art of the channel models for themassive MIMO system The configuration of antenna arrayas the critical factor deciding the characteristics of massiveMIMO channels is first presented briefly Based on the givenantenna array configurations the current measured activitiesof massive MIMO channels are studied for working out themain properties of massive MIMO channels which are thebasis for the precise channelmodelsWith the newpropertiestwo kinds of channel models namely correlation-basedstochastic models (CBSMs) and geometry-based stochasticmodels (GBSMs) are presented for the massive MIMO in

consideration of both the theoretical analysis and realisticsystem evaluation

The remainder of this paper is organized as followsSection 2 discusses antenna array deployments of massiveMIMO In Section 3 measurement results of massive MIMOchannel are mainly investigated In Section 4 both theCBSMs and GBSMs of massive MIMO are studied Finallywe conclude the paper in Section 5

2 Antenna Array Configuration

The antenna array structures roughly undergo three phaseswith the development of technique in manufacturing Inthe traditional passive antenna array the radiofrequencycircuit is usually connected to the physical antennas throughthe radiofrequency cable Subsequently in order to reducethe loss induced by the radiofrequency cable and save thecost of installation and maintenance the remote radio unit(RRU) separated from the baseband unit (BBU) has beenwidely adopted [21] The digital baseband signals generatedfrom the BBU are sent to the RRUs through the opticalfiber The radiofrequency circuit is as close as possible tothe physical antennas Furthermore active antenna arraysystem without radiofrequency cable may be made which ishelpful to the realization of themassive antenna array [22] Inactive antenna array both the radiofrequency circuits and theantenna elements are integrated into one circuit board whichis an important milestone for the development of antennaarray

As shown in Figure 1 there are several typical antennaarray configurations for massive MIMO systems that islinear antenna array spherical antenna array cylindricalantenna array rectangular antenna array and distributedantenna array [6] The linear array is an example of one-dimension (1D) antenna array which generally propagates

International Journal of Antennas and Propagation 3

Spherical

Cylindrical

Linear

Distributed

Rectangular

Figure 1 Antenna array configuration [6]

signals on the two-dimension (2D) plane It is usuallyassumed for theoretical analysis and realistic measurementsOn the other hand the spherical antenna array cylindricalantenna array and rectangular antenna array are some kindof 2D antenna array which can radiate the signals into anydirections in the 3D space Considering the size of antennaarray for the eNBs and UEs the spherical cylindrical andrectangular antenna array configurations are more likely tobe used in practical systems Moreover distributed antennaarray is mainly used for either indoor coverage enhancementor outdoor cooperation

The configurations of antenna array directly affect thechannel properties furthering the performance of massiveMIMO system Taking the antenna space as an exampleit decides the mutual coupling and correlation matrix fur-thering the capacity of massive MIMO However the spacesbetween adjacent antennas in current antenna array areusually set as equal Therefore the study of the antenna arrayconfiguration on a constraint or unconstraint area is valuablefor the development of massive MIMO such as the design ofsparse antenna array

3 Channel Measurement

Lots of channel measurements have been carried out inorder to discriminate the main properties of massive MIMOchannel Typicalmeasurements are summarized inTable 2 fordifferent antenna array configurations under a given scenarioThese measurements mainly focus on the impacts of antennanumbers on the small-scale propagation characteristicsWhen the linear antenna array is employed at the eNB thenonstationary phenomenon and near-field effect are studied

as themain properties for the realistic channel model [17 23]However further measurements should be implemented tovalidate the two properties for the spherical cylindrical andrectangular antenna array configurationsWe will discuss theproperties derived from channel measurements in detail asfollows

The channel characteristics such as channel gain K-factor and angular power spectrum (APS) are measuredwith a bandwidth of 50MHz when the eNB employs alinear 128-antenna array with the antenna space of half awavelength [17] As shown in Figure 2 measurement resultsindicate that the antenna array is beyond the Rayleighdistance as of the large length of linear antenna array Thusboth the far-field and plane wavefront assumptions in thetraditional channel models are inappropriate for the massiveMIMO channelMoreover different antennas at the eNBmayobserve different sets of clusters in different time slots whichresults in the shadow fading over the linear antenna arraynamely nonstationary phenomenon

When the eNB employed a 32-antenna rectangular arraywith half a wavelength between the adjacent antennas theindoor-to-outdoor channels were measured with a band-width of 50MHz [18] The correlation between differentUE channels in measurements is higher than that in inde-pendent identical distributed (iid) Rayleigh channel sincepositions of two UEs are too close to undergo the similarchannelsMoreover the average channel correlations for bothmeasurement and iid Rayleigh channel decrease with theincreasing number of antennas namely the UE channels canbe decorrelated by the very large antenna array

Channelmeasurements for both the cylindrical and linearantenna array with 128-antenna were implemented when


Table 2 Channel measurement

Scenario Antenna configuration Antenna space Bandwidthcarrier Measured metric

Outdoor [17] 128-antenna linear array Half wavelength 50MHz26GHz Channel gain 119870-factor APS and eigenvaluedistribution correlation of antennas and users

Indoor-to-outdoor[18]

32-antenna rectangular to128-antenna cylindrical array Half wavelength 50MHz26GHz Correlation

Outdoor [19] Cylindrical and linear array with128-antenna Half wavelength 50MHz26GHz Large-scale fading and angular resolution

Outdoor [20] 112-antenna virtual array mdash 20MHz26GHz Correlation inverse condition number

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

MS2

MS3

MS1

eNB

Figure 2 Illustration of nonstationary phenomenon and near-field effect [10]

the space of adjacent antennas is half a wavelength and thebandwidth is 50MHz [19] Similar to [17] the nonstationaryphenomenon can be observed over the linear antenna arrayMeanwhile large power variation can also be experiencedover the cylindrical antenna array as of both the polarizationand directional pattern Moreover the linear antenna arrayhas superior angular resolution but only in azimuth Thecylindrical antenna array has lower angular resolution yet itcan resolve in both azimuth and elevation which may be anadvantage for some scenarios such as building coverage

A scalable virtual antenna array with 112-antenna wasemployed at the eNB in order to investigate the channelcharacteristics for massive MIMO in [20] Both the line ofsight (LoS) and non-line of sight (NLoS) scenarios werestudied with a bandwidth of 20MHz The correlation andinverse condition number were measured to evaluate theorthogonality of two-channel vectors and multiple channelvectors respectively The difference of inverse conditionnumbers for measured channel and iid Rayleigh channelbecomes larger with more multiple UE andor deployingmore antennas Deploying more antennas will make thechannels of multiple UE more orthogonal However thereis less improvement when the number of antennas exceedsa given number which mainly relies on the propagationenvironment and UE positions

The measurements for the characteristics of elevationangles are extensive for 3D MIMO system recently [11 24]The main measurement results of rectangle antenna array

have been concluded in 3GPP [11] The channel model ofrectangle antenna array comprising these characteristics isalso established which will be studied in the next section

4 Channel Model

Two kinds of channel models namely correlation-basedstochastic models (CBSMs) and geometry-based stochasticmodels (GBSMs) are widely used to evaluate the perfor-mances of the wireless communication systems The com-plexity of the former is lower and ismainly used for analyzingthe theoretical performance of MIMO systems Howeverthe accuracy is limited for the realistic MIMO system andit is difficult to model wireless channels considering thenonstationary phenomenon and spherical wave effects Incontrast the latter can accurately reflect the realistic channelproperties and is more suitable for massive MIMO channeleven with the higher computation complexity The currentchannel models have been summarized in Table 3 Thissection discusses the CBSMs for theoretical analysis andGBSMs for the realistic performance evaluation according tothe categories in Table 3

41 CBSM The CBSMs are mainly used as the theoreticalmodel to evaluate the performance ofmassiveMIMO systemThe current analysis generally assumes that the UEs employsingle antenna in consideration of the complexity and spaces


Table 3 Channel models of massive MIMO

Modeling method Category Property

CBSM

iid Rayleigh channel model Elements of fast fading are iid complex Gaussian variables

Correlation channel model Contain correlation between transmit antennas orand receiveantennas

Mutual coupling channel model Consider antenna impedance load impedance and mutualimpedance

GBSM2D channel model Propagate beam on 2D plane such as linear array

3D channel model Propagate beam on 3D plane such as spherical rectangular andcylindrical array

for the terminal equipment with low carrier frequencyTherefore the following CBSMs are discussed when the UEemploys single antenna which are easy to be extended tothe cases that the UE with multiple antennas works at themillimeter wave Moreover massive MIMO is more likely tobe used in time division duplex (TDD) system at presentsince the downlink channel state information (CSI) can beacquired from the uplink due to TDD reciprocity featureTherefore only the uplink channel is taken as an example forstudy in this section

Let us consider an uplink MIMO system that 119870 single-antenna UE transmits signals to the eNB equipped with119873 antennas simultaneously When the NLoS channel isassumed the channel model can be generalized by

G = HD12 (1)

whereD = diag1205731 1205732 120573

119870 is the large-scale propagation

matrix and120573119896= 120601119889minus120572

119896120585119896 120601 is a constant related to the antenna

gain and carrier frequency 119889119896is the distance between the

eNB and the 119896th UE 120572 is the path loss exponent and 120585119896is

the log-normal shadow fading with 10 log10120585119896sim N(0 120590

2

sh)H isin C119873times119870 is the fast fading matrix

According to the fast fading matrix the CBSMs canbe further simplified into three kinds of channels namelyiid Rayleigh fading model correlation channel model andmutual coupling channelmodelWe discuss these three kindsof models as follows in detail

411 iid Rayleigh Channel Model The iid Rayleigh fadingchannel model is widely adopted for the theoretical analysisof the massive MIMO system which assumes there is nocorrelation and mutual coupling between transmit antennasor receiver antennas The elements of the fast fading matrixH = [h

1 h2 h

119870] are iid Gaussian random variables

namely ℎ119899119896

sim CN(0 1) (119899 = 1 2 119873 119896 = 1 2 119870)The favorable propagation is themost important property

of the iid Rayleigh fading channel in the massive MIMOsystem [8] namely

1

119873G119867G asymp D 119873 ≫ 119870 (2)

According to the large number of laws we can find one char-acteristic of the favorable propagation is the orthogonality ofdifferent UE channels

1

119873h119867119894h119895asymp

0 119894 = 119895

1 119894 = 119895(3)

Another is the channel harden phenomenon namely theEuclidean norm of each UE channel approximates to thelarge-scale fading factor [9]

1

119873

1003817100381710038171003817g1198961003817100381710038171003817

2

asymp 120573119896 119896 = 1 2 119870 (4)

The favorable propagation can not only better the per-formance but also simplify the algorithm design of mas-sive MIMO system The orthogonality can alleviate theinteruserintercell interference which is helpful to improvethe system capacity Channel harden phenomenon can miti-gate the impact of fast fading on the scheduling gain whichsimplifies the complexity of scheduling scheme [16]

412 Correlation Channel Model In order to reflect theantenna correlation caused by the insufficient antenna spaceand the scattering environments the correlation channelmodel is established to evaluate the performance of themassive MIMO system [25] The fast fading channel vectorof each one of UE can be formed by the correlation matrixmultiplied by standard complex Gaussian vector namely

h119896= R119896k119896 119896 = 1 2 119870 (5)

where the steering matrix R119896isin C119873times119863119896 contains 119863

119896steering

vectors with different angles of arrival (AoAs) for the 119896th UEand k119896sim CN(0 I

119863119896)

When the linear antenna array is assumed at the eNB thesteering matrix R

119896can be written as

R119896=

1

119863119896

[a (1205791198961) a (120579

1198962) a (120579

119896119863119896)] (6)

where 120579119896119894

is the 119894th AoA of 119896th UE and the steering vectora(120579119896119894) isin C119873times1 is given as

a (120579119896119894) = [1 119890

(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879

(7)

where 119889 is the distance between the adjacent antennas and 120582is the carrier wavelength


For the rectangle antenna array the steering vector can beattained by the steering matrix namely

a (120579119896119894 120601119896119894)

= vec [1 119890(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879

otimes [1 119890(1198952120587119889120582) sin120601119896119894 119890(1198952120587(119873minus1)119889120582) sin120601119896119894]

(8)

where 120579119896119894

and 120601119896119894

represent azimuth of arrival (AoA) andelevation of arrival (EoA) respectively vecsdot denotes vector-ization of matrix Note that AoA denotes the abbreviation ofangle of arrival or azimuth of arrival for linear antenna arrayor rectangle antenna array respectively

This correlation channel model introduces the AoAswhich can be utilized to distinguish the UE and improvethe accuracy of channel estimation [26] When the UE islocated at different orientations the UE channels can almostbe separated by angle information thereby alleviating thepilot contamination It is also helpful to analyze the interuseror intercell interference and develop UEs scheduling or cellcooperation to alleviate the interference

413 Mutual Coupling Channel Model Since the number ofantennas increases sharply in the massive MIMO system themutual impedance has to be considered as of the limited spacefor antenna arrayMoreover the load impedance and antennaimpedance should also be characterized in order to reflect therealistic channel model

The channel vector of the 119896thUE can bewritten as followsin consideration of both the impedances and correlation [27]

h119896= ZR119896k119896 119896 = 1 2 119870 (9)

whereZ isin C119873times119873 represents themutual couplingmatrixR119896isin

C119873times119863119896 denotes the steering matrix containing 119863119896steering

vectors of the receiver antenna array and k119896sim CN(0 I

119863119896)

According to [27 28] the mutual coupling matrix can beexpressed as

Z = (119885119860+ 119885119871) (Γ + 119885

119871I)minus1 (10)

with

Γ =

[[[[[[

[

119885119860

119885119872

0 sdot sdot sdot 0

119885119872

119885119860

119885119872

sdot sdot sdot 0

0 119885119872

119885119860

sdot sdot sdot 0

d d

0 0 sdot sdot sdot 119885

119872119885119860

]]]]]]

]

(11)

where 119885119860 119885119871 and 119885

119872represent the antenna impedance

load impedance and mutual impedance respectively Herethemutual impedances are only considered between adjacentantennas which can be seen from the nonzero 119885

119872 The

further discussion about the mutual coupling based on theelectromagnetic analysis can be found in [29 30] Thereforethe transmit correlationmatrix can be written as follows [27]

Σ119873= 119864 [HH119867] = 119870ZRR119867Z119867 (12)

where R = [R1R2 R

119870] As the UE is geometrically

distributed the received correlation matrix can be assumedas I119870 Then we can getH sim CN(0Σ

119873otimes I119870)

Mutual coupling channel model is more practical formassive MIMO It is helpful to analyze the effects of antennaspace on the performance of massive MIMO which issignificant for designing the antenna array configurationespecially the sparse antenna array

42 GBSM GBSMs are mainly used for evaluating theperformance of practical wireless communication systemswhich accurately comprise the channel properties Consider-ing the elevation or not the GBSMs of massiveMIMO can beclassified into two kinds namely 2D and 3D channel modelsWhen the linear antenna array is employed at the eNB the tiltangle is fixed and the 2D channel model is precisely enoughfor evaluating the performance However if the sphericalcylindrical or rectangular antenna array configurations areadopted at the eNB the 3D channel model in considerationof both elevation and azimuth should be established forevaluation

421 2119863 Channel Model Employing the linear antennaarray the nonstationary phenomenon and spherical wave-front have been discriminated as the main properties forthe massive MIMO channel through channel measurements[17 19]The properties are helpful to decorrelate the channelsfor different type ofUE thereby providing a favorable channel[17] However they raise the difficulty to establish the channelmodel for the massive MIMO systemTherefore the realisticchannel model comprising the properties is still on the way atpresent [10]

Similar to [17 19] the nonstationary phenomenon isalso observed through the measurements for the linear 128-antenna array in a semiurban area [31] In order to test theperformance of proposed algorithms for the more practicalmassive MIMO system much work has been done on thechannel modeling of massive MIMO reflecting this non-stationary phenomenon Therefore a cluster-based channelmodel comprising the nonstationary phenomenon has beenestablished which can be seen as the extension of the COST2100 channel model

In consideration of both the nonstationary phenomenonand spherical waveform effect an elliptical GBSM was givenfor massive MIMO with linear antenna array [23 32 33]First clusters on lots of confocal ellipses with different majoraxis represent different resolvable delays which make theGBSM possesses the spherical wavefront property Then thebirth-death process of clusters is introduced to describe thenonstationary property Numerical results of the establishedchannel demonstrate that the phases responses of the linearantenna array are no longer linear and the AoAs of theantenna array shift gradually which coincides with themeasurement results in the realistic environments

422 3D Channel Model The 3D channel models have beeninvestigated in the academic for several years already such as[34 35] Meanwhile several projects have been established


especially for the 3D channel model such as WINNER +project [36] However most of these models mainly dependon the literature survey rather than on realisticmeasurements[24] Thus they are considered insufficient or obviouslyquestionable for the realistic channel properties such as thecross-correlationmatrix of large-scale parametersThereforethe existing 3D channel models need to be improved throughrealistic measurements and further used to evaluate therealistic scenarios

In WINNER + projects the main procedures of 3DMIMO channel model have been described in detail [11 1237] as shown in Figure 3Themain parameters of 3D channelmodel contain shadow fading (SF) delay spread (DS) K-factor AoA azimuth of departure (AoD) EoA and elevationof departure (EoD) especially the EoA and EoD The cross-correlation matrix has been expanded to 7-dimension from5-dimension in the 2D channel model In the stage of3GPP Release 12 (R12) three scenarios have been definednamely urban microcell with high UE density (3D-UMi)urban macrocell with high UE density (3D-UMa) and urbanmacrocell with one high-rise per sector and 300m intersitedistance (ISD) (3D-UMa-H) Based on the procedure inFigure 3 the 3D channelmodel of rectangle antenna array hasbeen given based on measurements The related parameterstheir distributions and the cross-correlation matrix for the3D channelmodel have been concluded in the technical spec-ification [11] Next we will discuss the modeling procedurebriefly according to [11 12 36 37]

The large-scale propagation of the 3D MIMO channelconsists of both the path loss and shadow fading The pathloss model has to be classified into outdoor and outdoor-to-indoor (O2I) models in consideration of the differentpropagation environments [11] The illustration of path lossfor both outdoor and O2I can be simply depicted in Figure 4In the outdoor scenarios the path loss is the function of thecarrier frequency 119891

0 distance 119889

3D between the eNB and theUE break point distance 119889bp the height of UE ℎUE and theheight of eNB ℎeNB namely

PLOD = 119891OD (1198910 1198893119863 119889bp ℎUE ℎeNB) (13)

As for the O2I scenarios three items constitute the path lossnamely basic path loss PLOD related to 119889

3119863-out and 1198893119863-in

which is similar to the outdoor scenario the loss throughwallPLTW and the indoor loss PLIN = 05119889

2119863-in namely

PLO2I = PLOD + PLTW + PLIN (14)

The shadow fading 120585119899is dependent on the cluster 119899 which

follows log-normal distribution namely

119891120585119899(119909) =

120599

119909

1

radic21205871205902

sh119899

expminus(120599 ln119909)2

21205902

sh119899 120599 =

10

ln 10

(15)

The correlation between adjacent shadow fading values canbe characterized as 119877(Δ119909) = expminus|Δ119909|119889cor where 119889cor isthe correlation distance related to the propagation environ-ments

Generally the propagation channel contains several clus-ters (119899 = 1 2 ) with different delay 120591

119899and power factors

Each cluster contains some rays (119898 = 1 2 119872) withthe same delay However in the 3D channel model the twostrongest clusters are spread into three subclusters with fixeddelay offset 0 5 and 10 ns The other related delays anglesand power can be generated by the given distributions andsome measured parameters in [11]

When the double polarization array is adopted at the eNBas shown in Figure 5 the 119899th cluster of the fast fading channelfrom the 119904th antenna of the eNB to the 119906th antenna of the UEin the NLoS scenario can be expressed as follows [11 12 2436 37]

119867119906119904119899

(119905) = radic119875119899

119872

sum

119898=1

[

119865119903119909119906120579

(120579119899119898EoA 120593119899119898AoA)

119865119903119909119906120593

(120579119899119898EoA 120593119899119898AoA)

]

119879

times[[

[

119890119895Φ120579120579

119899119898 radic120581minus1

119899119898119890119895Φ120579120593

119899119898

radic120581minus1

119899119898119890119895Φ120593120579

119899119898 119890119895Φ120593120593

119899119898

]]

]

times [

119865119905119909119904120579

(120579119899119898EoD 120593119899119898AoD)

119865119905119909119904120593

(120579119899119898EoD 120593119899119898AoD)

]

times 1198901198952120587(119903

119879

119903119909119899119898sdot1198891199031199091199061205820+119903

119879

119905119909119899119898sdot1198891199051199091199041205820+V119899119898119905)

(16)

where 119875119899is the power normalized factor such that the power

of all clusters equals one Φ120579120579119899119898

Φ120579120593

119899119898 Φ120593120579

119899119898 Φ120593120593

119899119898 are four

random initial phases of different polarisation combinationsfor the 119898th ray of the 119899th cluster and 120581

119899119898is the cross

polarisation power ratio 119865119903119909119906120579

and 119865119903119909119906120593

are the patternsof the 119906th receiver antenna in the direction of the sphericalbasis vectors 120579 and 120593 respectively Similarly 119865

119905119909119904120579and 119865

119905119909119904120593

are the same for the 119904th transmit antenna The spherical unitvector 119903

119909119899119898can be given as

119903x119899119898 =[[

[

cos 120579119899119898Eoy cos120593119899119898Aoy

cos 120579119899119898Eoy sin120593119899119898Aoysin 120579119899119898Eoy

]]

]

(17)

where ldquo119909 = 119905119909 119910 = 119860rdquo and ldquo119909 = 119903119909 119910 = 119863rdquo representthe spherical unit vectors for receiver and transmitter respec-tively 119889

119903119909119906is the location vector of the 119906th receiver antenna

119889119905119909119904

is the location vector of the 119904th transmit antenna and 1205820

is the wavelength Doppler frequency119891119899119898

= 119903119879

119903119909119899119898sdotV1205820with

V = V sdot [cos 120579V cos120593V cos 120579V sin120593V sin 120579V]119879


Elevation spread at departure (ESD)

Elevation spread at arrival (ESA)

Set scenario network and antenna parameters

Assign propagation condition (NLOSLOS)

Calculate path loss

Azimuth of departure (AoD) Azimuth spread at departure (ASD)Subpath offset of AoD

Elevation of departure (EoD)Subpath offset of EoD Lognormal shadowing (SF)

Path delays Delay spread (DS)Average path powersAzimuth of arrival (AoA) K factorSubpath offset of AoA

Elevation of arrival (EoA) Azimuth spread at arrival (ASA)Subpath offset of EoA

Draw random initial phases

Generate channel coefficient

Apply path loss and shadowing

Figure 3 The procedure of 3D channel model [11 12]

Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB

Figure 4 Illustration of path loss [11]

As for the LoS scenario the fast fading with a main pathcan be written as follows [11 12 24 36 37]

H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593

(120579LoSEoA 120593LoSAoA)]

119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)

where 120575(sdot) and119870119877are the indicative function and Rice factor

respectivelyIf only the vertical polarization is adopted in LoS or NLoS

scenarios the 2 times 2 polarisation matrix in (16) and (18) canbe replaced by exp(119895Φn119898) and only vertically polarizationpattern is applied [11 12]

According to the above procedures of channel modelingwe can generate the realistic channel coefficients to evaluatethe three aforementioned scenarios However the channelmodel is not precise for simulations since the nonstationaryphenomenon has not been reflected [19] Moreover thechannel models of other scenarios and antenna array config-urations have to be given in order to extend the applicationsof massive MIMOTherefore the properties and modeling of3DMIMO channel still need to be further investigated


eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593

Figure 5 Illustration of coordinate [11 12]

5 Conclusion

Massive MIMO has been regarded as one of efficient waysto improve both spectrum efficiency and energy efficiencyfor the broadband wireless communication systems As thefirst step to evaluate the performance of any communicationsystems the channelmodels formassiveMIMOare necessaryto be investigated which is the main concern of this paperAccording to the ability of array to radiate the signals theantenna array configurations are classified into 2D and 3Dantenna arrays Generally the linear antenna array is 2Dantenna array and the rectangle spherical and cylindricalantenna array belong to 3D antenna array From studyingthe current measurement results of different configurationsit can be found that the linear antenna array gives rise tothe nonstationary phenomenon and near-field effect The 3Dantenna array has lower angular resolution yet it can resolvein both azimuth and elevation Increasing the number ofantennas at eNB can decorrelate different user channels

At present CBSMs aremainly used to analyze the theoret-ical performance of massive MIMO due to its simplificationThere are three kinds of simplified CBSMs widely used fordifferent objectives namely iid Rayleigh channel modelcorrelation channel model and mutual coupling channelmodel The channel model reflecting both the nonstationaryphenomenon and spherical wave effect has been establishedfor the linear antenna array based on the cluster model Theimproved 3D channel model of rectangle antenna array hasbeen proposed in 3GPP in order to evaluate three kinds ofscenarios However the channel models of other antennaarray configurations and scenarios have to be supplementedand the nonstationary property for spherical cylindricaland rectangular antenna array needs further measurementsTherefore the channel model of massive MIMO is still anopen topic which needs much more investigation for itsimprovements in the next steps

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the China Natural ScienceFunding (61271183) Program for New Century ExcellentTalents inUniversity (NCET-11-0600)National KeyTechnol-ogy RampD Program of China under Grant 2013ZX03003005and National High Technology Research and DevelopmentProgram of China (2014AA01A705)

References

[1] Z Hasan H Boostanimehr and V K Bhargava ldquoGreen cellularnetworks a survey some research issues and challengesrdquo IEEECommunications Surveys ampTutorials vol 13 no 4 pp 524ndash5402011

[2] D Feng C Jiang G Lim L J Cimini Jr G Feng and G Y LildquoA survey of energy-efficient wireless communicationsrdquo IEEECommunications Surveys amp Tutorials vol 15 no 1 pp 167ndash1782013

[3] Y Chen S Zhang S Xu and G Y Li ldquoFundamental trade-offson green wireless networksrdquo IEEE Communications Magazinevol 49 no 6 pp 30ndash37 2011

[4] G Y Li Z Xu C Xiong et al ldquoEnergy-efficient wireless com-munications tutorial survey and open issuesrdquo IEEE WirelessCommunications vol 18 no 6 pp 28ndash35 2011

[5] G Auer V Giannini C Desset et al ldquoHow much energy isneeded to run a wireless networkrdquo IEEE Wireless Communi-cations vol 18 no 5 pp 40ndash49 2011

[6] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2013

[7] A Ghrayeb and T M Duman Coding for MIMO Communica-tion System John Wiley amp Sons New York NY USA 2007

[8] T Marzetta ldquoNoncooperative cellular wireless with unlimitednumbers of base station antennasrdquo IEEE Wireless Communica-tions vol 9 no 11 pp 3590ndash3600 2010

[9] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[10] F Tufvesson ldquoVery largeMIMOsystems ICASSP tutorialmdashpartII propagation aspects of very large MIMOrdquo in Proceedings ofthe 37th IEEE International Conference on Acoustics Speech andSignal Processing (ICASSP rsquo12) 2012

[11] ldquoTechnical specification group radio access networkstudy on 3Dchannel model for LTE (Rel 12)rdquo 3GPP TR- 36873 V111 2013

[12] Y-H Nam B Ng K Sayana et al ldquoFull-dimension MIMO(FD-MIMO) for next generation cellular technologyrdquo IEEECommunications Magazine vol 51 no 6 pp 172ndash179 2013

[13] ldquoRequirements candidate solutions and technology roadmapfor lte rel-12 onwardrdquo 3GPP RWS-120010 2012

[14] ldquoTechnologies for Rel-12 and onwardrdquo 3GPPRWS- 120021 2013[15] ldquoViews onRel-12 and onwards for LTE andUMTSrdquo 3GPPRWS-

120006 2013


[16] B M Hochwald T L Marzetta and V Tarokh ldquoMultiple-antenna channel hardening and its implications for rate feed-back and schedulingrdquo IEEETransactions on InformationTheoryvol 50 no 9 pp 1893ndash1909 2004

[17] S Payami and F Tufvesson ldquoChannel measurements andanalysis for very large array systems at 26GHzrdquo in Proceedingsof the 6th European Conference on Antennas and Propagation(EuCAP rsquo12) pp 433ndash437 Prague Czech Republic March 2012

[18] X Gao O Edfors F Rusek and F Tufvesson ldquoLinear pre-coding performance in measured very-large MIMO channelsrdquoin Proceedings of the 74th IEEE Vehicular Technology Conference(VTC rsquo11) pp 1ndash5 Budapest Hungary September 2011

[19] X Gao F Tufvesson O Edfors and F Rusek ldquoMeasuredpropagation characteristics for very-large MIMO at 26GHzrdquoin Proceedings of the 46th IEEE Asilomar Conference on SignalsSystems and Computers (ASILOMAR rsquo12) pp 295ndash299 PacificGrove Calif USA November 2012

[20] J Hoydis C Hoek T Wild and S ten Brink ldquoChannelmeasurements for large antenna arraysrdquo in Proceedings of the9th IEEE International Symposium on Wireless CommunicationSystems (ISWCS rsquo12) pp 811ndash815 Paris France August 2012

[21] ldquoC-RAN the road towards green radio access networkrdquo TechRep China Mobile Research Institute 2012

[22] ldquoActive antenna system utilizing the full potential of radiosources in the spatial domainrdquo Tech Rep Huawei 2012

[23] C-XWang and SWu ldquoMassiveMIMOchannel measurementsand modeling advances and challengesrdquo submitted to IEEEWireless Communion Magazine

[24] Z Zhong X Yin X Li and X Li ldquoExtension of ITU IMT-advanced channel models for elevation domains and line-of-sight scenariosrdquo in Proceedings of the 78th IEEE VehicularTechnology Conference (VTC rsquo13) pp 1ndash5 Las Vegas Nev USASeptember 2013

[25] J Hoydis S ten Brink and M Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[26] H Yin D Gesbert M Filippou and Y Liu ldquoA coordinatedapproach to channel estimation in large-scale multiple-antennasystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 31 no 2 pp 264ndash273 2013

[27] C Masouros M Sellathurai and T Ratnarajah ldquoLarge-scaleMIMO transmitters in fixed physical spaces the effect oftransmit correlation and mutual couplingrdquo IEEE Transactionson Communications vol 61 no 7 pp 2794ndash2804 2013

[28] B Clerckx C Craeye D Vanhoenacker-Janvier andCOestgesldquoImpact of antenna coupling on 2 times 2MIMO communicationsrdquoIEEE Transactions on Vehicular Technology vol 56 no 3 pp1009ndash1018 2007

[29] C Masouros J Chen K Tong M Sellathurai and T Rat-narajah ldquoTowards massive-MIMO transmitters on the effectsof deploying increasing antennas in fixed physical spacerdquo inProceedings of the Future Network and Mobile Summit pp 1ndash102013

[30] C A Balanis AntennaTheory Analysis and Design JohnWileyamp Sons Hoboken NJ USA 2012

[31] X Gao F Tufvesson O Edfors and F Rusek ldquoChannel behav-ior for very-large MIMO systems-initial characterizationrdquo inProceedings of the Joint Workshop on Small Cell CooperativeCommunications (COST IC1004 rsquo12) 2012

[32] E H Aggoune ldquoA non-stationary wideband channel model forlarge MIMO communication systemsrdquo

[33] A Ghazal C-XWang H Haas et al ldquoA non-stationaryMIMOchannel model for high-speed train communication systemsrdquoin Proceedings of the 75th IEEE Vehicular Technology Conference(VTC rsquo12) pp 1ndash5 Yokohama Japan June 2012

[34] T Aulin ldquoA modified model for the fading signal at a mobileradio channelrdquo IEEE Transactions on Vehicular Technology vol28 no 3 pp 182ndash203 1979

[35] K Kalliola H Laitinen P Vainikainen M Toeltsch J Laurilaand E Bonek ldquo3-D double-directional radio channel character-ization for urbanmacrocellular applicationsrdquo IEEETransactionsonAntennas and Propagation vol 51 no 11 pp 3122ndash3133 2003

[36] J Meinila P Kyosti L Hentila et al ldquoD53 WINNER+final channel modelsrdquo Wireless World Initiative New RadioWINNER 2010

[37] ldquoWINNER II interim channel modelsrdquo IST-WINNER 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Table 1 Features of massive MIMO

Feature Main reason

Advantages

High spectrum efficiency [6 9] Large multiplexing gain and array gainHigh energy efficiency [6 9] Radiated energy can be concentrated on UEHigh reliability [9] Large diversity gain

Efficient linear precoderdetector [9] Favorable propagation condition for iid Rayleighchannel

Weak interuser interference andenhanced physical security [6] Orthogonal UE channels and extremely narrow beam

Simple scheduling scheme [16] Channel harden phenomenon averages out the fastfading

Robust to individual element failure [6] Large number of antenna array elements

Disadvantages

Pilot contamination [8] Limited orthogonal pilots as of bounded coherentinterval and bandwidth

High signal processing complexity [9] Large number of antennas and multiplexing UE

Sensitive to beam alignment [6] Extremely narrow beam is sensitive to UE moving orantenna array swaying

Poor broadcast channel [6] Be blind to UE positions

In Release 11 (R11) specified by the 3rd generation partner-ship project (3GPP) the MIMO technique can only radiatethe beam in horizontal dimension as of the fixed down tilt ofantenna array In order to well exploit the vertical angular res-olution of signal propagation different kinds of the antennaarray configurations such as the rectangular spherical andcylindrical antenna array deployments have been studied in3GPP [13ndash15]With theseMIMO antenna array deploymentsthe eNB can adaptively adjust both azimuth and elevationangles of signal propagation In other words the radiatedMIMO signals can be controllable in the three-dimension(3D) space and thus called as 3D MIMO In order toenhance the system capacity 3DMIMO should employ moreantennas And massiveMIMO should adopt the rectangularspherical or cylindrical antenna array configurations for thepractical system considering the space of antennas arrayTherefore 3D MIMO with a large number of antennas canbe regarded as one of practical forms of massive MIMO

Up to now massive MIMO has been paid much attentionto by both academic and industry organizations There arelots of works done for massive MIMO such as performanceanalysis remedies for alleviating pilot contamination andchannel estimation The channel model is fundamental fortheoretical analysis as well as for performance evaluationof massive MIMO system Therefore this paper mainlyinvestigates the state of the art of the channel models for themassive MIMO system The configuration of antenna arrayas the critical factor deciding the characteristics of massiveMIMO channels is first presented briefly Based on the givenantenna array configurations the current measured activitiesof massive MIMO channels are studied for working out themain properties of massive MIMO channels which are thebasis for the precise channelmodelsWith the newpropertiestwo kinds of channel models namely correlation-basedstochastic models (CBSMs) and geometry-based stochasticmodels (GBSMs) are presented for the massive MIMO in

consideration of both the theoretical analysis and realisticsystem evaluation

The remainder of this paper is organized as followsSection 2 discusses antenna array deployments of massiveMIMO In Section 3 measurement results of massive MIMOchannel are mainly investigated In Section 4 both theCBSMs and GBSMs of massive MIMO are studied Finallywe conclude the paper in Section 5

2 Antenna Array Configuration

The antenna array structures roughly undergo three phaseswith the development of technique in manufacturing Inthe traditional passive antenna array the radiofrequencycircuit is usually connected to the physical antennas throughthe radiofrequency cable Subsequently in order to reducethe loss induced by the radiofrequency cable and save thecost of installation and maintenance the remote radio unit(RRU) separated from the baseband unit (BBU) has beenwidely adopted [21] The digital baseband signals generatedfrom the BBU are sent to the RRUs through the opticalfiber The radiofrequency circuit is as close as possible tothe physical antennas Furthermore active antenna arraysystem without radiofrequency cable may be made which ishelpful to the realization of themassive antenna array [22] Inactive antenna array both the radiofrequency circuits and theantenna elements are integrated into one circuit board whichis an important milestone for the development of antennaarray

As shown in Figure 1 there are several typical antennaarray configurations for massive MIMO systems that islinear antenna array spherical antenna array cylindricalantenna array rectangular antenna array and distributedantenna array [6] The linear array is an example of one-dimension (1D) antenna array which generally propagates


Spherical

Cylindrical

Linear

Distributed

Rectangular


















Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

MS2

MS3

MS1

eNB






4 Channel Model






CBSM








G = HD12 (1)

whereD = diag1205731 1205732 120573


matrix and120573119896= 120601119889minus120572





2




1 h2 h


namely ℎ119899119896



1

119873G119867G asymp D 119873 ≫ 119870 (2)


1

119873h119867119894h119895asymp

0 119894 = 119895

1 119894 = 119895(3)


1

119873

1003817100381710038171003817g1198961003817100381710038171003817

2

asymp 120573119896 119896 = 1 2 119870 (4)



h119896= R119896k119896 119896 = 1 2 119870 (5)


119896steering


119863119896)



R119896=

1

119863119896

[a (1205791198961) a (120579

1198962) a (120579

119896119863119896)] (6)

where 120579119896119894


a (120579119896119894) = [1 119890

(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879

(7)




a (120579119896119894 120601119896119894)

= vec [1 119890(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879


(8)

where 120579119896119894

and 120601119896119894





h119896= ZR119896k119896 119896 = 1 2 119870 (9)




119863119896)


Z = (119885119860+ 119885119871) (Γ + 119885

119871I)minus1 (10)

with

Γ =

[[[[[[

[

119885119860

119885119872

0 sdot sdot sdot 0

119885119872

119885119860

119885119872

sdot sdot sdot 0

0 119885119872

119885119860

sdot sdot sdot 0

d d


119872119885119860

]]]]]]

]

(11)

where 119885119860 119885119871 and 119885



119872 The


Σ119873= 119864 [HH119867] = 119870ZRR119867Z119867 (12)

where R = [R1R2 R



119873otimes I119870)











0 distance 119889




3119863-out and 1198893119863-in


2119863-in namely




119891120585119899(119909) =

120599

119909

1

radic21205871205902

sh119899

expminus(120599 ln119909)2

21205902

sh119899 120599 =

10

ln 10

(15)






119867119906119904119899

(119905) = radic119875119899

119872

sum

119898=1

[

119865119903119909119906120579

(120579119899119898EoA 120593119899119898AoA)

119865119903119909119906120593

(120579119899119898EoA 120593119899119898AoA)

]

119879

times[[

[

119890119895Φ120579120579

119899119898 radic120581minus1

119899119898119890119895Φ120579120593

119899119898

radic120581minus1

119899119898119890119895Φ120593120579

119899119898 119890119895Φ120593120593

119899119898

]]

]

times [

119865119905119909119904120579

(120579119899119898EoD 120593119899119898AoD)

119865119905119909119904120593

(120579119899119898EoD 120593119899119898AoD)

]

times 1198901198952120587(119903

119879

119903119909119899119898sdot1198891199031199091199061205820+119903

119879

119905119909119899119898sdot1198891199051199091199041205820+V119899119898119905)

(16)



Φ120579120593

119899119898 Φ120593120579

119899119898 Φ120593120593

119899119898 are four




and 119865119903119909119906120593


119905119909119904120579and 119865

119905119909119904120593


119909119899119898can be given as

119903x119899119898 =[[

[

cos 120579119899119898Eoy cos120593119899119898Aoy


]]

]

(17)



119889119905119909119904



= 119903119879

119903119909119899119898sdotV1205820with







Calculate path loss









Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB



H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593


119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)






eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Spherical

Cylindrical

Linear

Distributed

Rectangular


















Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

MS2

MS3

MS1

eNB






4 Channel Model






CBSM








G = HD12 (1)

whereD = diag1205731 1205732 120573


matrix and120573119896= 120601119889minus120572





2




1 h2 h


namely ℎ119899119896



1

119873G119867G asymp D 119873 ≫ 119870 (2)


1

119873h119867119894h119895asymp

0 119894 = 119895

1 119894 = 119895(3)


1

119873

1003817100381710038171003817g1198961003817100381710038171003817

2

asymp 120573119896 119896 = 1 2 119870 (4)



h119896= R119896k119896 119896 = 1 2 119870 (5)


119896steering


119863119896)



R119896=

1

119863119896

[a (1205791198961) a (120579

1198962) a (120579

119896119863119896)] (6)

where 120579119896119894


a (120579119896119894) = [1 119890

(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879

(7)




a (120579119896119894 120601119896119894)

= vec [1 119890(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879


(8)

where 120579119896119894

and 120601119896119894





h119896= ZR119896k119896 119896 = 1 2 119870 (9)




119863119896)


Z = (119885119860+ 119885119871) (Γ + 119885

119871I)minus1 (10)

with

Γ =

[[[[[[

[

119885119860

119885119872

0 sdot sdot sdot 0

119885119872

119885119860

119885119872

sdot sdot sdot 0

0 119885119872

119885119860

sdot sdot sdot 0

d d


119872119885119860

]]]]]]

]

(11)

where 119885119860 119885119871 and 119885



119872 The


Σ119873= 119864 [HH119867] = 119870ZRR119867Z119867 (12)

where R = [R1R2 R



119873otimes I119870)











0 distance 119889




3119863-out and 1198893119863-in


2119863-in namely




119891120585119899(119909) =

120599

119909

1

radic21205871205902

sh119899

expminus(120599 ln119909)2

21205902

sh119899 120599 =

10

ln 10

(15)






119867119906119904119899

(119905) = radic119875119899

119872

sum

119898=1

[

119865119903119909119906120579

(120579119899119898EoA 120593119899119898AoA)

119865119903119909119906120593

(120579119899119898EoA 120593119899119898AoA)

]

119879

times[[

[

119890119895Φ120579120579

119899119898 radic120581minus1

119899119898119890119895Φ120579120593

119899119898

radic120581minus1

119899119898119890119895Φ120593120579

119899119898 119890119895Φ120593120593

119899119898

]]

]

times [

119865119905119909119904120579

(120579119899119898EoD 120593119899119898AoD)

119865119905119909119904120593

(120579119899119898EoD 120593119899119898AoD)

]

times 1198901198952120587(119903

119879

119903119909119899119898sdot1198891199031199091199061205820+119903

119879

119905119909119899119898sdot1198891199051199091199041205820+V119899119898119905)

(16)



Φ120579120593

119899119898 Φ120593120579

119899119898 Φ120593120593

119899119898 are four




and 119865119903119909119906120593


119905119909119904120579and 119865

119905119909119904120593


119909119899119898can be given as

119903x119899119898 =[[

[

cos 120579119899119898Eoy cos120593119899119898Aoy


]]

]

(17)



119889119905119909119904



= 119903119879

119903119909119899119898sdotV1205820with







Calculate path loss









Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB



H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593


119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)






eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

MS2

MS3

MS1

eNB






4 Channel Model






CBSM








G = HD12 (1)

whereD = diag1205731 1205732 120573


matrix and120573119896= 120601119889minus120572





2




1 h2 h


namely ℎ119899119896



1

119873G119867G asymp D 119873 ≫ 119870 (2)


1

119873h119867119894h119895asymp

0 119894 = 119895

1 119894 = 119895(3)


1

119873

1003817100381710038171003817g1198961003817100381710038171003817

2

asymp 120573119896 119896 = 1 2 119870 (4)



h119896= R119896k119896 119896 = 1 2 119870 (5)


119896steering


119863119896)



R119896=

1

119863119896

[a (1205791198961) a (120579

1198962) a (120579

119896119863119896)] (6)

where 120579119896119894


a (120579119896119894) = [1 119890

(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879

(7)




a (120579119896119894 120601119896119894)

= vec [1 119890(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879


(8)

where 120579119896119894

and 120601119896119894





h119896= ZR119896k119896 119896 = 1 2 119870 (9)




119863119896)


Z = (119885119860+ 119885119871) (Γ + 119885

119871I)minus1 (10)

with

Γ =

[[[[[[

[

119885119860

119885119872

0 sdot sdot sdot 0

119885119872

119885119860

119885119872

sdot sdot sdot 0

0 119885119872

119885119860

sdot sdot sdot 0

d d


119872119885119860

]]]]]]

]

(11)

where 119885119860 119885119871 and 119885



119872 The


Σ119873= 119864 [HH119867] = 119870ZRR119867Z119867 (12)

where R = [R1R2 R



119873otimes I119870)











0 distance 119889




3119863-out and 1198893119863-in


2119863-in namely




119891120585119899(119909) =

120599

119909

1

radic21205871205902

sh119899

expminus(120599 ln119909)2

21205902

sh119899 120599 =

10

ln 10

(15)






119867119906119904119899

(119905) = radic119875119899

119872

sum

119898=1

[

119865119903119909119906120579

(120579119899119898EoA 120593119899119898AoA)

119865119903119909119906120593

(120579119899119898EoA 120593119899119898AoA)

]

119879

times[[

[

119890119895Φ120579120579

119899119898 radic120581minus1

119899119898119890119895Φ120579120593

119899119898

radic120581minus1

119899119898119890119895Φ120593120579

119899119898 119890119895Φ120593120593

119899119898

]]

]

times [

119865119905119909119904120579

(120579119899119898EoD 120593119899119898AoD)

119865119905119909119904120593

(120579119899119898EoD 120593119899119898AoD)

]

times 1198901198952120587(119903

119879

119903119909119899119898sdot1198891199031199091199061205820+119903

119879

119905119909119899119898sdot1198891199051199091199041205820+V119899119898119905)

(16)



Φ120579120593

119899119898 Φ120593120579

119899119898 Φ120593120593

119899119898 are four




and 119865119903119909119906120593


119905119909119904120579and 119865

119905119909119904120593


119909119899119898can be given as

119903x119899119898 =[[

[

cos 120579119899119898Eoy cos120593119899119898Aoy


]]

]

(17)



119889119905119909119904



= 119903119879

119903119909119899119898sdotV1205820with







Calculate path loss









Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB



H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593


119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)






eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












CBSM








G = HD12 (1)

whereD = diag1205731 1205732 120573


matrix and120573119896= 120601119889minus120572





2




1 h2 h


namely ℎ119899119896



1

119873G119867G asymp D 119873 ≫ 119870 (2)


1

119873h119867119894h119895asymp

0 119894 = 119895

1 119894 = 119895(3)


1

119873

1003817100381710038171003817g1198961003817100381710038171003817

2

asymp 120573119896 119896 = 1 2 119870 (4)



h119896= R119896k119896 119896 = 1 2 119870 (5)


119896steering


119863119896)



R119896=

1

119863119896

[a (1205791198961) a (120579

1198962) a (120579

119896119863119896)] (6)

where 120579119896119894


a (120579119896119894) = [1 119890

(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879

(7)




a (120579119896119894 120601119896119894)

= vec [1 119890(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879


(8)

where 120579119896119894

and 120601119896119894





h119896= ZR119896k119896 119896 = 1 2 119870 (9)




119863119896)


Z = (119885119860+ 119885119871) (Γ + 119885

119871I)minus1 (10)

with

Γ =

[[[[[[

[

119885119860

119885119872

0 sdot sdot sdot 0

119885119872

119885119860

119885119872

sdot sdot sdot 0

0 119885119872

119885119860

sdot sdot sdot 0

d d


119872119885119860

]]]]]]

]

(11)

where 119885119860 119885119871 and 119885



119872 The


Σ119873= 119864 [HH119867] = 119870ZRR119867Z119867 (12)

where R = [R1R2 R



119873otimes I119870)











0 distance 119889




3119863-out and 1198893119863-in


2119863-in namely




119891120585119899(119909) =

120599

119909

1

radic21205871205902

sh119899

expminus(120599 ln119909)2

21205902

sh119899 120599 =

10

ln 10

(15)






119867119906119904119899

(119905) = radic119875119899

119872

sum

119898=1

[

119865119903119909119906120579

(120579119899119898EoA 120593119899119898AoA)

119865119903119909119906120593

(120579119899119898EoA 120593119899119898AoA)

]

119879

times[[

[

119890119895Φ120579120579

119899119898 radic120581minus1

119899119898119890119895Φ120579120593

119899119898

radic120581minus1

119899119898119890119895Φ120593120579

119899119898 119890119895Φ120593120593

119899119898

]]

]

times [

119865119905119909119904120579

(120579119899119898EoD 120593119899119898AoD)

119865119905119909119904120593

(120579119899119898EoD 120593119899119898AoD)

]

times 1198901198952120587(119903

119879

119903119909119899119898sdot1198891199031199091199061205820+119903

119879

119905119909119899119898sdot1198891199051199091199041205820+V119899119898119905)

(16)



Φ120579120593

119899119898 Φ120593120579

119899119898 Φ120593120593

119899119898 are four




and 119865119903119909119906120593


119905119909119904120579and 119865

119905119909119904120593


119909119899119898can be given as

119903x119899119898 =[[

[

cos 120579119899119898Eoy cos120593119899119898Aoy


]]

]

(17)



119889119905119909119904



= 119903119879

119903119909119899119898sdotV1205820with







Calculate path loss









Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB



H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593


119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)






eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











a (120579119896119894 120601119896119894)

= vec [1 119890(1198952120587119889120582) sin 120579119896119894 119890(1198952120587(119873minus1)119889120582) sin 120579119896119894]119879


(8)

where 120579119896119894

and 120601119896119894





h119896= ZR119896k119896 119896 = 1 2 119870 (9)




119863119896)


Z = (119885119860+ 119885119871) (Γ + 119885

119871I)minus1 (10)

with

Γ =

[[[[[[

[

119885119860

119885119872

0 sdot sdot sdot 0

119885119872

119885119860

119885119872

sdot sdot sdot 0

0 119885119872

119885119860

sdot sdot sdot 0

d d


119872119885119860

]]]]]]

]

(11)

where 119885119860 119885119871 and 119885



119872 The


Σ119873= 119864 [HH119867] = 119870ZRR119867Z119867 (12)

where R = [R1R2 R



119873otimes I119870)











0 distance 119889




3119863-out and 1198893119863-in


2119863-in namely




119891120585119899(119909) =

120599

119909

1

radic21205871205902

sh119899

expminus(120599 ln119909)2

21205902

sh119899 120599 =

10

ln 10

(15)






119867119906119904119899

(119905) = radic119875119899

119872

sum

119898=1

[

119865119903119909119906120579

(120579119899119898EoA 120593119899119898AoA)

119865119903119909119906120593

(120579119899119898EoA 120593119899119898AoA)

]

119879

times[[

[

119890119895Φ120579120579

119899119898 radic120581minus1

119899119898119890119895Φ120579120593

119899119898

radic120581minus1

119899119898119890119895Φ120593120579

119899119898 119890119895Φ120593120593

119899119898

]]

]

times [

119865119905119909119904120579

(120579119899119898EoD 120593119899119898AoD)

119865119905119909119904120593

(120579119899119898EoD 120593119899119898AoD)

]

times 1198901198952120587(119903

119879

119903119909119899119898sdot1198891199031199091199061205820+119903

119879

119905119909119899119898sdot1198891199051199091199041205820+V119899119898119905)

(16)



Φ120579120593

119899119898 Φ120593120579

119899119898 Φ120593120593

119899119898 are four




and 119865119903119909119906120593


119905119909119904120579and 119865

119905119909119904120593


119909119899119898can be given as

119903x119899119898 =[[

[

cos 120579119899119898Eoy cos120593119899119898Aoy


]]

]

(17)



119889119905119909119904



= 119903119879

119903119909119899119898sdotV1205820with







Calculate path loss









Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB



H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593


119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)






eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













0 distance 119889




3119863-out and 1198893119863-in


2119863-in namely




119891120585119899(119909) =

120599

119909

1

radic21205871205902

sh119899

expminus(120599 ln119909)2

21205902

sh119899 120599 =

10

ln 10

(15)






119867119906119904119899

(119905) = radic119875119899

119872

sum

119898=1

[

119865119903119909119906120579

(120579119899119898EoA 120593119899119898AoA)

119865119903119909119906120593

(120579119899119898EoA 120593119899119898AoA)

]

119879

times[[

[

119890119895Φ120579120579

119899119898 radic120581minus1

119899119898119890119895Φ120579120593

119899119898

radic120581minus1

119899119898119890119895Φ120593120579

119899119898 119890119895Φ120593120593

119899119898

]]

]

times [

119865119905119909119904120579

(120579119899119898EoD 120593119899119898AoD)

119865119905119909119904120593

(120579119899119898EoD 120593119899119898AoD)

]

times 1198901198952120587(119903

119879

119903119909119899119898sdot1198891199031199091199061205820+119903

119879

119905119909119899119898sdot1198891199051199091199041205820+V119899119898119905)

(16)



Φ120579120593

119899119898 Φ120593120579

119899119898 Φ120593120593

119899119898 are four




and 119865119903119909119906120593


119905119909119904120579and 119865

119905119909119904120593


119909119899119898can be given as

119903x119899119898 =[[

[

cos 120579119899119898Eoy cos120593119899119898Aoy


]]

]

(17)



119889119905119909119904



= 119903119879

119903119909119899119898sdotV1205820with







Calculate path loss









Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB



H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593


119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)






eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Calculate path loss









Outdoor

Indoor

hUE

hUE

d3D-in

d3D-out

d2D-ind2D-out

d 3D

d2D

dbp

heNB



H119906119904119899

(119905) = radic1

119870119877+ 1

H119906119904119899

(119905) + 120575 (119899 minus 1)radic119870119877

119870119877+ 1

times

119872

sum

119898=1

[119865119903119909119906120579

(120579LoSEoA 120593LoSAoA)119865119903119909119906120593


119879

119890119895ΦLoS

times [1 0

0 minus1] [

119865119905119909V120579 (120579LoSEoD 120593LoSAoD)

119865119905119909V120593 (120579LoSEoD 120593LoSAoD)

]

times 1198901198952120587(119903

119879

119903119909LoS sdot1198891199031199091199061205820+119903119879

119905119909LoS sdot1198891199051199091199041205820+VLoS119905)

(18)






eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










eNB

x

x

z

z

120579

n

120593y

y

UE

120579

120593


5 Conclusion





Acknowledgments


References















120006 2013


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Massive MIMO Channel Models: A...

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