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3D Channel Model Extensions and Characteristics Study for Future Wireless Systems
Research Paper / Feb 2014


3D Channel Model Extensions and Characteristics

Study for Future Wireless Systems


Meilong Jiang, Mohsen Hosseinian, Moon-il Lee, Janet Stern-Berkowitz

{meilong.jiang, mohsen.hosseinian, moonil.lee, janet.stern}


InterDigital, Inc., USA


Abstract—This work introduces a complete framework for

three-dimensional (3D) channel extension based on two-

dimensional (2D) channel models. In the 3D channel modeling,

besides the azimuth angles, the multipath components of a

receive-transmit pair are determined by elevation angles, corre-

lations between elevation and azimuth, and the 3D configurations

of a user equipment’s (UE) location and velocity. The 3D channel

characteristics for an active antenna system (AAS) are studied in

terms of aggregated array gain and channel covariance matrix.

The 3D channel model is generated and examined through

Monte Carlo simulations and a comparison of fixed vertical

beamforming and adaptive vertical beamforming is presented.

The comparison shows that adaptive vertical beamforming can

potentially provide up to 8dB improvement in coupling loss.

In addition, it is shown that for line-of-sight (LoS) the 3D

channel covariance matrix can be decoupled into two independent

covariance matrices with reduced sizes that effectively leads

to reduced feedback overhead. For non-line-of-sight (NLoS),

the correlation-based Kronecker model technique can be used

to generate the 3D channel matrix with reduced complexity

compared to the geometry-based technique.




The channel model for system-level simulations applied in

the 3rd Generation Partnership Project (3GPP) is a geometry-

based stochastic channel model [1]. Geometry-based mod-

elling of the radio channel enables separation of propagation

parameters and antenna configurations (geometries and radi-

ation patterns). Channel realizations are generated by sum-

ming contributions of rays (plane waves) with specific small-

scale parameters like delay, power, angle-of-arrival (AoA) and

angle-of-departure (AoD). The current 3GPP channel model

considers the departure and arrival of multipath components in

azimuth angles only. Similarly, the beamforming and multiple

input multiple output (MIMO) schemes adopted in long term

evolution (LTE) and LTE-Advanced were designed to support

antenna configurations that are capable of adaptation in az-

imuth only. Although an elevation antenna radiation pattern

has been defined in 3GPP [1] and the elevation antenna gain in

LoS direction is partially considered in the channel generation,

the current 3GPP channel model has omitted small scale angles

of arrival and departure in the elevation domain. Hence, it is

in fact a 2D channel model.


Recently, there has been significant interest in enhancing

system performance through the use of active antenna systems

(AAS) [3]. Unlike traditional passive antennas, the complete

RF transceiver chain, including analog-to-digital converter

(ADC), digital-to-analog converter (DAC), low noise amplifier


(LNA), power amplifier, and electrical tilt phase shifter are

integrated into each antenna element in AAS. This way the am-

plitude and phase of each antenna element can be dynamically

adjusted to provide adaptive control over both the elevation

and the azimuth dimension. The increased control over the

elevation dimension enables a vast variety of new schemes

that provide improvement in system performance. To name a

few, schemes such as sector-specific elevation beamforming

and user-specific elevation beamforming are made possible by

having control over the elevation dimension.


In addition, small cell networks [4] have been advocated

as an efficient solution to further boost system performance

through cell densification and traffic offloading. In multifloor

scenarios the location of a UE may be at the same level

as, or even higher than, the small cell base-station antenna,

since the height of a small cell base-station antenna is usually

a few meters. This provides another reason why channel

characteristics in the elevation domain need to be considered.


The existing 2D channel models proposed in 3GPP [1]

and International Telecommunication Union (ITU) [2] are not

sufficient to study the schemes and evaluate the performance

for AAS and small cells. Therefore it is necessary to introduce

a full 3D channel model and investigate its spatial channel



In this work, we first identify the modifications needed to

extend an existing 2D 3GPP channel model to a complete 3D

channel. Then the 3D channel characteristics are analyzed in

terms of aggregated array gain and channel covariance matrix.

The 3D channel generation is validated through extensive

simulations which examine various small scale and large

scale channel parameters. Finally, a performance comparison

between fixed vertical beamforming and adaptive vertical

beamforming in 3D channel is provided which shows that AAS

system provides up to 8dB improvement in coupling loss.


The remainder of the paper is organized as follows. In

section II, the methodologies and major steps for the 3D

channel extension are introduced. In section III, 3D channel

characteristics are studied in terms of aggregated array gain

and channel covariance matrix. In section IV, simulation re-

sults are presented for various 3D channel parameters. Finally

concluding remarks are made in section V.





This section elaborates the steps and methodologies for gen-

erating a complete 3D channel model. 3D channel modeling




has been discussed in projects such as WINNER II [5] and

WINNER+ [6] as well as academic publications [7]. In [5],

the general 3D channel extension steps were outlined for the

WINNER II channel model. Later on a set of elevation related

parameters based on measurements and literature surveys

were provided in WINNER+ [6]. In this paper, we use the

3GPP 2D channel model [1] as baseline. Then, using similar

methodologies and measurement parameters defined in [5],

[6], we extend the existing 3GPP 2D channel to a 3D channel.

We implement and validate the 3D channel model for two main

channel scenarios, urban macro-cell (UMa) and urban micro-

cell (UMi). Some improvements in polarization and also in

correlation of large scale parameters (LSP) are suggested. For

example, the cross-correlation values of the seven LSPs as

defined in [5] and [6] result in a non-positive definite cross-

correlation matrix. This prohibits Cholesky factorization of

the cross-correlation matrix that is required during channel

generation. We apply an approximation method [8] to obtain

the closest positive definite cross-correlation matrix.


The channel generation process can be divided into three

stages [1]. In the first stage, the propagation scenario is

selected and the network layout as well as the antenna

configuration are determined. In the second stage, large-scale

and small-scale parameters are defined. In the third stage,

channel impulse responses are calculated. The 3D channel

model generation follows the same major steps as existing

2D channel generations. The changes needed for 3D channel

extension are summarized in Table I. The other steps remain

the same as those in the existing 2D channel generation [1].


In terms of LSPs and their cross-correlation generation,

we have initially 5 LSPs in the 2D channel model, namely

delay spread (DS), azimuth spread of departure angles (ASD),

azimuth spread of arrival angles (ASA), Ricean K-factor (KR)

and shadow fading (SF). Two new LSPs, i.e. elevation spread

of departure angles (ESD) and elevation spread of arrival

angles (ESA), are added to capture the angular spreads in the

elevation domain. Additionally, the Doppler shift component

needs to be updated in the channel coefficient generation by

considering UE mobility in the elevation direction.


The final channel coefficient for the n-th cluster (consisting

of a number of rays) of any receive-transmit element pair (u, s)

at the t-th time sample can be expressed as a summation of

M rays within the cluster, as given by (1) for the NLoS case.

It can be seen that the channel coefficient is a function of 3D

antenna patterns, polarization coupling, array phase offsets and

Doppler phase shift. The small scale elevation angles as well

as 3D geometries are factored into the components.


In (1), u is the receive antenna index and s the transmit

antenna index. Pn gives the power of cluster n calculated

assuming a single slope exponential power delay profile.

Frx,u,V and Frx,u,H are the antenna radiation patterns at

receive (rx) element u for vertical (V ) and horizontal (H)

polarizations, respectively.















are the


random initial phases for each ray m of each cluster n and

for four different polarization combinations {vv, vh, hv, hh}.

κ defines the cross-polarization power ratio in linear scale

assuming the same value for vv/vh and hh/hv. Ftx,s,V and

Ftx,s,H are the antenna radiation patterns for transmit (tx)


element s. ϕn,m and φn,m are respectively the azimuth angle

of arrival (AoA) and the azimuth angle of departure (AoD) for

the m-th ray at the n-th cluster. ϑn,m and θn,m are respectively

the elevation angle of arrival (EoA) and the elevation angle of

departure (EoD) for the m-th ray at the n-th cluster. ϕ¯n,m

is the arrival spherical unit vector with azimuth angle ϕn,m

and elevation angle ϑn,m. φ¯n,m is the departure spherical unit

vector with azimuth angle φn,m and elevation angle θn,m.

r¯rx,u is the location vector of element u of the UE antenna

array. r¯tx,s is the location vector of element s of the eNodeB

(eNB) antenna array. [·] denotes the dot product of two vectors.


Specifically, ϕ¯n,m and φ¯n,m are respectively given by


ϕ¯n,m =


⎣ cosϑn,m cosϕn,mcosϑn,m sinϕn,m




⎦ , φ¯n,m =


⎣ cos θn,m cosφn,mcos θn,m sinφn,m


sin θn,m


⎦ .


For simplicity, we assume 2D planar arrays placed in the

YZ plane at both eNB and UE with the first element placed

at the origin (0, 0, 0) and equal antenna separation along the

Y-axis and Z-axis. The location vectors of the transmit and

receive elements, r¯tx,s and r¯rx,u are respectively given by


r¯tx,s =


⎣ xs = 0ys = nsds


zs = hB +msds


⎦ , r¯rx,u =


⎣ xu = 0yu = nudu


zu = hU +mudu


⎦ ,


where ns is the element index in a row of the transmit antenna

array and nu the element index in a row of the receive

antenna array. ms is the element index in a column of the

transmit antenna array and mu the element index in a column

of the receive antenna array. ds and du are respectively the

transmit and receive antenna separations (usually set as half

wavelength). We assume the same antenna separation for both

vertical and horizontal dimensions. hB denotes the height

(from the ground) of the eNB and hU the height of the UE.

We also assume hB � ds and hU � du.


The Doppler frequency component υn,m, which character-

izes the temporal fading, depends on angles of arrival at the

UE and the UE velocity vector and is calculated as


υn,m =

ϕ¯n,m · υ¯








(cos θυ cosϑn,m cos (ϕn,m − φυ) + sin θυ sinϑn,m) ,


where υ¯ is the velocity vector of the UE with speed υ;

φυ and θυ are the azimuth and elevation angles of the

UE’s velocity, respectively. Vector υ¯ can be given by υ¯ =

|υ¯| [ cos θυ cosφυ cos θυ sinφυ sin θυ ] .


In the LoS case, the channel coefficients can be obtained by

adding a single line-of-sight ray and scaling down the NLoS

components. The LoS channel coefficients can be expressed

as (2). In (2), δ (·) is the Dirac’s delta function and KR the

Ricean K-factor. ϕ¯LoS and φ¯LoS are spherical unit vectors

based on LoS departure and arrival angles. υLoS is the Doppler

frequency depending on LoS arrival angles and UE speed

vector. {ΦvvLoS, ΦhhLoS} are the random initial phases for the

LoS path for polarization combinations {vv, hh}.




Table I: Modifications required for 3D channel extension

Steps in TR 36.814 [1] Annex

B that require modifications


TR 36.814 [1] Annex B Full 3D channel generation


Step 1 Give 2D locations of eNB and UE, compute LoS

azimuth departure angle φLOS and LoS azimuth arrival

angle ϕLOS .

Give antenna pattern as defined in [2].


Give 3D locations of eNB and UE, compute LoS azimuth

angle of departure φLoS , LoS azimuth angle of arrival

ϕLoS , LoS elevation angle of departure θLoS , LoS

elevation angle of arrival ϑLoS .

Give AAS antenna pattern as defined in [10].


Step 4 Generate correlated large scale parameters, i.e., DS,



Generate correlated large scale parameters, i.e., DS, ASA,



Step 7 Step 7: Generate arrival angles ϕ and departure angles

φ. (For azimuth only)


Step 7a: Generate azimuth angle of departure φn,m and

azimuth angle of arrival ϕn,m.

Step 7b: Generate elevation angle of departure θn,m and

elevation angle of arrival ϑn,m.


Step 8 Random coupling of rays within clusters Random coupling of rays within clusters (azimuth departure

vs azimuth arrival; elevation departure vs. elevation arrival;

azimuth arrival vs. elevation arrival).


Step 10 Generate channel coefficients for each cluster n and

each receive-transmit element pair (u, s), eq. (20)

(NLoS) and (21) (LoS) in 36.814.


Generate channel coefficients for each cluster n and each

receive-transmit element pair (u, s), as given in (1) for

NLoS and in (2) for LoS.


HNLoSu,s,n (t) =






UE antenna pattern in 3D︷ ︸︸ ︷[

Frx,u,V (ϕn,m, ϑn,m)

Frx,u,H (ϕn,m, ϑn,m)


]T coupling between polarizations with random phases︷ ︸︸ ︷[













n,m ejΦ





] eNB antenna pattern in 3D︷ ︸︸ ︷[

Ftx,s,V (φn,m, θn,m)

Ftx,s,H (φn,m, θn,m)



· ej2πλ−1(ϕ¯n,m·r¯rx,u)︸ ︷︷ ︸ ·


UE array phase offset



−1(φ¯n,m·r¯tx,s)︸ ︷︷ ︸ ·


eNB array phase offset


ej2πυn,mt︸ ︷︷ ︸

Doppler phase shift




HLoSu,s,n(t) =




KR + 1

HNLoSu,s,n (t)


+ δ (n− 1)



KR + 1



Frx,u,V (ϕLoS , ϑLoS)

Frx,u,H (ϕLoS , ϑLoS)


]T [




LoS 0


0 ejΦ




] [

Ftx,s,V (φLoS , θLoS)

Ftx,s,H (φLoS , θLoS)



· ej2πλ−1(ϕ¯LoS·r¯rx,u) · ej2πλ−1(φ¯LoS ·¯rtx,s) · ej2πυLoSt (2)


For a spatial channel with N clusters (i.e. resolvable mul-

tipath components) for both LoS and NLoS, the final 3D

channel in time domain can be expressed as


H(N)LoSu,s (t) =





H(N)LoSu,s,n (t). (3)




A. Aggregated Array Gain with AAS

In an AAS, the amplitude and phase of each element can


be dynamically adjusted to form a beam in desired directions

with controlled beamwidth. We now study the 3D channel

characteristic in terms of aggregated array gain for AAS. We

consider both fixed and adaptive vertical beamforming.


For an antenna array, the aggregated array gain is jointly

determined by the antenna radiation pattern and array factor.

An antenna radiation pattern is defined as the combined gain

of the horizontal pattern and the vertical pattern. As given in

[10], the combined 3D antenna/element pattern in an AAS, for

azimuth angle φ and elevation angle θ, can be expressed as


AE (φ, θ) = GE,Max−min {− [AE,H (φ) +AE,V (θ)] , Am} ,


where horizontal antenna pattern AE,H (φ) is given by


AE,H (φ) = −min









, Am



and vertical antenna


pattern is given by AE,V (θ) = −min













The horizontal and vertical half-power beamwidths, ϕ3dB and

θ3dB , respectively, are both 65 degrees. In addition, maximum

attenuations are set as Am = 30dB and SLAV = 30dB.

The elevation angle θ is defined between 0◦ and 180◦ (90◦

represents the direction perpendicular to the array) and the

azimuth angle ϕ is defined between −180◦ and 180◦. GE,Max

is the maximum directional gain of the radiation element (in

dB), which is assumed to be 8 dBi.


We now introduce the array factor F for a single column

uniform linear array (ULA) placed in the Z-axis. From tradi-

tional antenna theory [9], it is known that the array factor of

an array depends on the spacing and weighting of the array

elements. F is defined as


F = W · V, (4)


where V denotes the phase shift due to element placement in




the array and can be expressed as V = [v1, v2, · · · , vK ]T and


vk = exp



−2πi (k − 1) ds



cos (θ)



, k = 1, 2, . . .K. (5)


K is the number of antenna elements in a ULA. ds denotes the

antenna separation and θ the direction of departure signal in

elevation dimension. W is the designed beamforming weight

vector that determines the side lobe levels and electrical

downtitling direction. W is given by


W = [w1, w2, . . . , wK ]

T .


For simplicity, the amplitude of the weighting vector is

assumed to be identical for each radiation element. The phase

of the weighting vector is used to implement electrical steering

and is dependent on the required vertical steering angle. For

example, to form a beam pointing to a down-tilt direction

θetilt, the beamforming weights ωk can be obtained by


wk =







2πi (k − 1) ds



cos (θetilt)



, k = 1, 2, . . .K.



Correspondingly, the aggregated array gain AA (φ, θ) with a

fixed beamforming (towards a fixed town-tilt direction θetilt)

for a ULA in dB scale can be expressed as


AA (φ, θ) = AE (φ, θ) + 10 log10











⎦ . (7)


We now consider a UE specific beamforming for the 3D chan-

nel, known as adaptive vertical beamforming, which adaptively

points the vertical beam towards an optimal θ which is the

strongest receive direction of each UE. Since there is only

one column of antenna elements in the ULA, we need only

consider the vertical beamforming. The optimal UE specific

beamforming weights woptk can be obtained by


woptk =







2πi (k − 1) ds



cos (θ)





k = 1, 2, ...,K. (8)

By using vk from (5) and woptk from (8) in (7), the aggregated

array gain AA (φ, θ) for the adaptive vertical beamforming can

be expressed as


AA (φ, θ) = AE (φ, θ) + 10 log10K. (9)

The aggregated array gain in (9), therefore, represents the

optimal, i.e., maximum aggregated array gain for the desired

user, which is achievable by UE-specific adaptive vertical

beamforming when the optimal weights in (8) are used. The

above ULA analysis can be readily extended to the multi-

column uniform rectangular array (URA) case.


B. 3D Channel Covariance Matrix

We now derive the 3D channel covariance matrix for a URA.


We assume a URA placed in the YZ plane at the eNB with

the first element located at the origin (x = 0, y = 0, z = 0).

The transmit array has S = K×L antenna elements spanning


K rows along the Z-axis and L columns along the Y-axis with

equal element spacing ds. Each antenna element can be labeled

by s or (l, k) where s = (k− 1)L+ l, for k = 1, ...K and l =

1, ...L. So the location (x, y, z) of each antenna element (l, k)

can be expressed as: x(l,k) = 0, y(l,k+1) = y(l,k), y(l+1,k) =

y(l,k) + ds, z(l+1,k) = z(l,k) and z(l,k+1) = z(l,k) + ds, ∀ l, k.


We first derive the 3D channel covariance matrix in the

LoS case. Without applying any beamforming weights, the

3D channel characteristic is determined only by the element

radiation patten, antenna spacing and propagation of each ray

path. In the LoS case, for the two adjacent vertical antenna

elements (s and s + L) from the same column, the channel

coefficients between receive-transmit pairs (u, s) and (u, s +

L), i.e., Hu,s(t) and Hu,s+L(t), have the following property,


Hu,s+L(t) ≈ Hu,s(t)e(−j 2πλ ds cos θ), (10)

where Hu,s(t) is given by (3). θ is the angle of departure

in elevation domain. This property can be easily obtained by

applying the Ricean factor KR → +∞ in (2) for strong LoS

and the fact that amplitude gains of Hu,s(t) and Hu,s+L(t)

(represented by the second row in (2)) are almost the same

because the amplitude gain depends on LoS angles only and

the polarization initial phase is independent of the transmit

elements. Thus the difference between Hu,s(t) and Hu,s+L(t)

can be captured by the phase shift due to propagation.


For a UE with U receive antennas and an eNB with S

transmit antennas (2D planar array), the U×S MIMO channel

matrix H can be partitioned into K sub-matrices given by


H =


H¯k=1 , . . . , H¯k=K







H¯k =



H1,(k−1)L+1 H1,(k−1)L+2 ... H1,(k−1)L+L

H2,(k−1)L+1 H2,(k−1)L+2 ... H2,(k−1)L+L


... ... ... ...

HU,(k−1)L+1 HU,(k−1)L+2 ... HU,(k−1)L+L




for k = 1, ...,K and each H¯k has the matrix size U × L.

Using (10), the channel matrix H can be rewritten as


H =


H¯k=1, . . . , H¯k=K



= vT ⊗ H¯k=1,


where v is a K×1 Vandermonde column vector given by v =[

1, e−j


λ ds cos θ , ..., e−j


λ (K−1)ds cos θ



. ⊗ denotes the


Kronecker product operation and T the transpose operation.

Now we obtain the transmit covariance of H, RH ∈ CS×S ,



RH = E





= E





)⊗ (H¯Hk=1H¯k=1)} = Rv⊗RH¯k=1 ,(11)

where Rv denotes the covariance matrix of v and RH¯k=1 is the

covariance of the first submatrix H¯k=1. Therefore, the transmit

covariance of a LoS U × S MIMO channel can be decoupled

into two independent covariance matrices with reduced sizes

(L×L and K ×K ). Note that Rv has rank 1 and it depends

on antenna separation ds and the LoS elevation angle only.




This feature can be utilized to determine an efficient transmit

scheme with reduced feedback overhead for LoS MIMO [11].


The covariance matrix (i.e. spatial correlation matrix) for

NLoS 3D MIMO channel has been discussed in [12]. For a

practical channel model such as the geometry-based stochastic

model defined in section (II), there is no closed-form expres-

sion for the covariance matrix due to the complex AoA/AoD

and EoD/EoA distributions. However, when assuming the an-

gles of arrival and departure are independent due to significant

local reflections, namely spatial separability, such as in indoor

or in-vehicle environments, the covariance matrix R of the 3D

MIMO channel can take the following Kronecker form [12]


R = E[vec(H)vec(H)T ] = RBS ⊗RMS ,

where RBS and RMS are the covariance matrices at the

eNB and the UE, respectively. vec denotes the vectorization

operation. We can simplify the generation of the 3D MIMO

channel, H, using the covariance matrix R; the channel

can be generated from H = unvec(R 12 vec(HW )). unvec

denotes the reverse operation of vec. HW is a U × S matrix

with complex Gaussian elements and R can be obtained

by numerical simulations or from measurement results. This

feature can be used to generate a 3D channel with much lower

complexity compared to the geometry-based method and is

especially useful for link level simulations in 3D MIMO when

the spatial separability assumption applies.



We provide simulation results that verify the 3D channel


by examining several important small scale parameters (EoA

and EoD) and large scale parameters (ESA and ESD). We also

present simulation results for coupling loss, which is defined

as the signal power loss between eNB and UE including all

non fast-fading attenuations. Both UMa and UMi channels are

considered. The general UMa and UMi settings are compliant

with [1], [2]. The AAS antenna settings are taken from the

3GPP RAN4 technical report [10]. Additional elevation related

parameters for 3D channel generation can be found in [5], [6].


A. Small Scale Parameters

Figure 1 shows the CDF distribution for EoA for both


UMa and UMi channels. As expected for both LoS and NLoS

cases EoA is fairly uniformly distributed and centered at 90◦.

Arrivals higher than 140◦ happen rarely, which indicates less

reflection from the ground to the receive antenna at the UE.


Figure 2 depicts the CDF distribution for EoD for both UMa

and UMi. As seen for both LoS and NLoS cases almost 65%

of departures happen at angles greater than 90◦. Only about

35% of departures are less than 90◦ among which the majority

happen between 60◦ and 90◦. These results are expected as the

height of the transmit antenna at the eNB for these scenarios

is much higher than the receive antenna at the UE.


B. Large Scale Parameters

Figures 3 and 4 show elevation angle spread CDF distri-


bution for arrival and departure, respectively. As shown, for

LoS, the angle spread is much narrower compared to NLoS

due to the presence of a strong line-of-sight path.


C. Coupling Loss

Figure 5 shows the CDF distribution for coupling loss (path


gain) for UMa channel for AAS antenna type A10 [10]. In

the fixed downtilt case, the beamforming coefficients wk are

chosen to electrically create a beam with a fixed downtilt angle

(θetilt = 12


◦). In the AAS adaptive case, the beamforming

weights are adaptively chosen to form a beam towards the

strongest receive direction in elevation for each UE. As shown,

with the adaptive vertical beamforming, the coupling loss

achieves as much as 5dB improvement for a wide range of

UEs compared to the AAS with fixed electrical downtilt.


Figure 6 compares the coupling loss for adaptive beamform-

ing and fixed downtilt for UMi channel. We assume all UEs

are outdoor UEs. Compared to fixed downtilt beamforming, a

3dB to 8dB improvement is observed for over 95% of UEs

when using adaptive vertical beamforming.



This paper introduces the methodology and required steps


for 3D channel extensions. Studies on 3D channel character-

istics reveal that higher array gain can be achieved by AAS

with adaptive beamforming. We show that the 3D channel

covariance matrix exhibits desirable features especially for the

LoS case, which can be used to reduce channel feedback

overhead. The full 3D channel model is implemented and

validated through extensive simulations. Simulation results

demonstrate expected CDF distributions for small scale and

large scale parameters. In addition, the 3D channel with UE-

specific adaptive beamforming is shown to achieve higher long

term channel path gain. The 2D channel model can only offer

fixed vertical beamforming, whereas the 3D channel model can

make adaptive vertical beamforming possible. This makes the

3D channel model a highly desirable enhancement for future

wireless systems.



[1] TR 36.814, “Further advancements for E-UTRA physical layer aspects”,


V9.0.0, 3GPP.


0 20 40 60 80 100 120 140 160 180























angle (degrees)














Figure 1: CDF distribution for UMa and UMi EoA




0 20 40 60 80 100 120 140 160 180























angle (degrees)














Figure 2: CDF distribution for UMa and UMi EoD


0 20 40 60 80 100 120 140 160 180























angle (degrees)














Figure 3: Distribution of ESA for UMa and UMi


0 5 10 15 20 25 30 35 40























angle (degrees)














Figure 4: Distribution of ESD for UMa and UMi


Figure 5: CDF of coupling loss (path gain) for UMa


Figure 6: CDF of coupling loss (path gain) for UMi


[2] ITU M.2135, “Guidelines for evaluation of radio interface technologies

for IMT-Advanced,” ITU-R, Dec. 2009.


[3] J. Koppenborg, et al., "3D beamforming trials with an active antenna

array," in 2012 International ITG Workshop on Smart Antennas (WSA),

pp.110-114, Mar. 2012.


[4] T. Nakamura, et al.,"Trends in small cell enhancements in LTE ad-

vanced," IEEE Commun. Mag., vol.51, no.2, pp.98-105, Feb. 2013.


[5] IST-WINNER II Deliverable 1.1.2 v.1.2, “WINNER II channel models,”

IST-WINNER2, Tech. Rep., 2007.


[6] D5.3: WINNER+ Final Channel Models, P. Heino, 2010.

[7] Z. Zhong, et al., “Extension of ITU IMT-A channel models for elevation


domains and line-of-sight scenarios,” VTC 2013, fall

[8] L. R. Schaeffer, “Modification of negative eigenvalues to create positive


definite matrices and approximation of standard errors of correlation esti-

mates,” Available:


[9] Constantine A. Balanis, “Antenna theory: analysis and design,” 3rd

Edition, John Wiley & Sons, Inc., 2005.


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