3D MIMO Channel Model based on Field Measurement ... - IEEE Xplore

IEEE WCNC'14 Track 1 (PHY and Fundamentals)

3D MIMO Channel Model based on Field Measurement Campaign for UMa Scenario Qinglin Luo

Feng Pei, Jianhua Zhang

Min Zhang

Alcaltel-Lucent Shanghai Bell Shanghai, China, 201206 [email protected]

Beijing University of Posts and Telecommunications, Beijing, China, 10000 peifeng, [email protected]

Alcatel-Lucent Swindon, United Kindom [email protected]

Abstract—This paper reports the methodology and results from our latest field measurement campaign for characterizing the 3-dimensional (3D) MIMO channel, particularly in the elevation domains, in a typical urban macro (UMa) environments in Beijing, China. Stochastic channel model parameters are obtained based on the high-resolution multi-path parameter estimates. In addition, a distance dependent elevation angular spread model is proposed based on field observations. These works enables the realistic evaluation of 3D MIMO system performance and extends the applicability of the ITU SCM models in 3D MIMO system study.

I. I NTRODUCTION There has been significant interest in enhancing the system performance through the use of antenna systems that have a two-dimensional array structure both in the elevation and azimuth dimensions. The new array structure provides more spatial degree of freedom in both elevation and azimuth domains [1]. Additional spatial degree of freedom in the elevation domain enables more advanced MIMO technologies such as vertical vectorization, 3-dimensional (3D) beamforming, or even full-dimensional MIMO (FD-MIMO) [2]. In order to evaluate the possible technical enhancement of 3D-beamforming and FD-MIMO, a new channel model is required that enables us to simulate both the horizontal and vertical channel characteristics with different user locations and heights. Existing ITU channel model [3] is a good starting point for 3D channel model study. In the ITU model, the horizontal behavior of a wireless channel is well studied and parameterized based on a large amount of field measurements data. But the vertical dimension is ignored. The WINNER projects including WINNER II [5] and WINNER+ [4] considered the elevation characteristics of a radio channel based on literature survey rather than extensive field measurements. Hence, the model they provided is considered to be incomplete and some of the recommended parameter values proves to be inaccurate. For example, in the WINNER+ project[4], the cross-correlation matrix of large scale parameters (LSPs) is non-positive definite and using it in simulations will cause unexpected errors. Literatures [6][7] also reported field measurement results such as elevation angular spread (EAS). However, the literatures focus on one or several aspects of the 3D characteristics, and did not provide a comprehensive set of parameters and

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their value recommendations, thus cannot be used in 3D MIMO system level evaluations. In this paper, we present a full set of model parameters from field measurements in Beijing and derive some elevation models for urban macro (UMa) line-of-sight (LOS) and non-line-of-sight (NLOS) environments. We investigated both the transmitter and the receiver side angular characteristics including their distribution functions and the parameters for the functions abstracted from measurement data. We provide the procedure for generating the angular angles in simulations based on the models and parameters. Furthermore, we observed obvious distance dependency phenomenon in the measuring of the elevation spread under UMa scenario and thus propose a model for characterizing such a behavior. The remainder of the paper is organized as follows. In Section II, we describe the measurement setup and system configurations. In Section III, the post processing methodology is presented. We report the measurement results in Section IV and the procedure for generating elevation angles in Section V. In Section VI, we study the distance dependency of elevation angular spread and propose a model based on our field observations. The paper is concluded in Section VII. II. M EASUREMENT S ETUP AND C ONFIGURATIONS We used PropSound channel sounder developed by Elektrobit of Finland as our basic measurement equipment. It was designed to enable realistic radio channel measurements in both the time and spatial domains. It is a Direct-Sequence Spread Spectrum (DSSS) system consisting of a transmitting and a receiving equipment. The transmitter sends BPSK modulated Pseudo-Noise (PN) codes over the air to the receiver, and the receiver stores the received and demodulated bits on the hard disk as raw I/Q data. Both the transmitter and the receiver are equipped with a high-order antenna array. Time Domain Multiplexing (TDM) with high speed electrical switching are implemented for sounding the antenna element channels separately. Transceivers are switched one by one at both ends and the switching cycle is kept small enough to satisfy the condition of the radio channel coherence time. In order to collect raw data with the 3D spatial signatures, a three dimension omni-directional array (ODA) with 56 antenna elements configured as 28 dual-polarized patches (±45◦ ) was installed at the receiver side, while a uniform planner array

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Fig. 1.

Transmitter antenna (left) and receiver antenna (right)

Fig. 3.

View of Sector A from the transmitter

Fig. 4.

View of Sector B from the transmitter

TABLE I BASIC CONFIGURATION FOR 3D MIMO CHANNEL MEASUREMENT Parameter

Fig. 2.

Measurement scenarios and routes

(UPA) with 32 elements configured as 16 dual-polarized patches (±45◦ ) was used at transmitter side, as shown in Fig. 1. The receiver was placed on a trolley which was moved with pedestrian speed during the measurements. Both the horizontal and the vertical separations between two adjacent antennas are half wavelength. The down-tilting of the transmitting antenna array is approximately 9◦ . The configurations of the measurement system are summarized in Table I: The measurement campaign was carried out in Beijing. As shown in Fig. 2, the measurement scenario is located at a university campus. Surrounding buildings are high-rise buildings as shown in the below photos. The transmitters are installed on the top of a 7-floor teaching building. The height of the transmit antennas is 30.8 meters, much higher than the surrounding buildings in the measurement area. Two measurement sectors are planned as shown in Fig. 4 and Fig. 3. In sector A, measurement routes 1,2,4 are LOS, and others are NLOS. In sector B, measurement routes 6,7,8,9,11,12,13 are LOS, and others are NLOS. The trolley moves at the speed of about 3 km/h. It can be observed that this measurement scenario is close

Value

Carrier(GHz)

3.5

Bandwidth(MHz)

100

Code lengths

63

Transmit antenna type

Uniformed panel array UPA (32 Elements)

Receive antenna type

Cylinder Omni-directional array (56 Elements)

Power

2W

Transmit antenna

Azimuth

−180◦ ∼ 180◦

Angle range

Elevation

−55◦ ∼ 90◦

Receive antenna

Azimuth

−70◦ ∼ 70◦

Angle range

Elevation

−70◦ ∼ 70◦

to the definition of Urban Macro (UMa) scenario specified in the WINNER modeling [4]. III. P OST P ROCESSING A. Elevation Parameter Definition After the acquisition of the raw IQ data, we first calculate the channel impulse responses (CIR) and then derive channel parameters from the CIRs using the Spatial-Alternating Generalized Expectation-maximization (SAGE) algorithm [8]. SAGE is an extension of the expectation-maximization (EM) algorithm with fast convergence. It is one of the most widely used channel parameter extraction algorithms due to its high

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accuracy and availability for the estimation of parameters for almost every type of antenna array. It takes a set of CIR measurements, i.e., a snapshot, as input and output the per-path estimates of channel parameters for paths within the snapshot. The derived parameters include the azimuth of departure (AoD), azimuth of arrival (AoA), elevation of departure (EoD), elevation of arrival (EoA), propagation delay, Doppler shift, and polarization channel power matrix. For the 3D MIMO channel model, two elevation angular parameters are introduced to characterize the spatial transmission of wireless signals in elevation domain: • the elevation angle of departure (EoD) • the elevation angle of arrival (EoA) They are defined as the angle between the median propagation direction of the signals to a receiver and the LOS direction from the transmitter to the receiver. Correspondingly, two new elevation angular spreads need to be introduced to characterize the second order characteristics of the elevation angles: • the elevation angular spread of departure (ESD) • the elevation angular spread of arrival (ESA) The angular spread is defined as the root-mean-square (RMS) errors of the EoDs within a snapshot. Note that since the azimuth channel has been well studied in the literatures and standardized by ITU, we do not intend to propose any change to it. The purpose of measuring azimuth parameters is to evaluate the correlations between azimuth and elevation parameters. B. Derivation of Elevation Angles Assume that the SAGE algorithm outputs the per-path elevation angles xi and the polarization power matrix Pp (xi ), p = {HH, HV, V H, HH} where H and V denote the horizontal and vertical polarization, respectively. We first obtain the power angular spectrum (PAS) by combining the power of different polarizations of a path, e.g., P (xi ) = Pp (xi ) (1) p={HH,HV,V H,HH}

where xi is the per-path elevation angle (EoD or EoA) from SAGE output, p is the polarization pair index, and Pp (xi ) is the per-polarization channel power. Then the first order moment (mean value) of elevation angle (EoD or EoA) can be written as, x ¯=

L i=1

xi

P (xi ) L P (xi )

C. Derivation of Elevation Spreads We use the circular angular spread method to calculate the elevation angular spread and avoid the ambiguity of angles due to the modula of 2π, similar as the approach in [9]. Let xi (δ) denote the elevation angle of path i with a shift of δ from xi , then the minimum root-mean-square (RMS) value of all the shifted angles is an estimate of the angular spread, denoted by σx , i.e., ⎛ ⎞ L 2 σx = min ⎝ (xi (Δ) − x ¯i ) f (xi )⎠ (4) Δ

where

⎧ ⎨ 2π + (xi (Δ) − xi ) (xi (Δ) − xi ) xi (Δ) − x = ⎩ 2π − (xi (Δ) − xi )

if (xi (Δ) − xi ) < −π if |xi (Δ) − xi | ≤ π if (xi (Δ) − xi ) > π (5) The searching step of Δ can be determined according to the precision of the measurement system. We set it to 2 degrees in our measurement. IV. M EASUREMENT R ESULTS

A. Distribution of EoA and EoD Fig. 5 and Fig. 6 shows the EoD and EoA power angular spectrum (PAS, equal to the probability angular spectrum if using normalized power as probability) in UMa LOS and NLOS conditions for some selected field channel measurement snapshots. In the figures, a truncated Laplacian distribution is used to fit the probability density of the raw data, p(x) =

√ 1 e− 2πσx

(ϕ−μ)2 2σ 2

TABLE II ROOT-M EAN -S QUARE (RMS) FITTING ERROR COMPARISON

Fitting Function

where L is the number of paths in the snapshot under processing. x ¯i is also called the power-weighted mean of the elevation angle. The elevation angle of the snapshot can be expressed by where Med{Ai , Bi } denotes taking median value of {Ai } after being sorted according to the values of {Bi }.

(6)

) is recommended in [[3]] for fitting azimuth angles in UMa scenario. For comparing the goodness-of-fit of the two distributions, we calculate the mean fitting errors of both Gaussian and Laplacian distribution for all the snapshots under LOS and NLOS scenario and presented in the following table.

(2)

(3)

x 1 −| σ | 2σ e

From the figures it can be observed that the power angular spectrum of EoD and EoA are well fitted by the Laplacian distribution. Truncated Gaussian distribution (p(ϕ) =

i=1

x = Med{xi , P (xi )}, i = 1...L

i=1

Laplace Gaussian

Elevation Angle

RMS Fitting Errors LOS

NLOS

EoD

0.48

0.54

EoA

0.46

0.42

EoD

0.51

0.62

EoA

0.44

0.43

It can be observed that Laplace generally provides better fitting than Gaussian except for the LOS EoA case where Laplace performs slightly worse.

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The EoD distribution in UMa (Compared with Laplace fitting)

Fig. 7.

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The EoA distribution in UMa (Compared with Laplace fitting)

n=1

n=1

Pn

where n is the path index and Pn is the path power. ϕ¯ is also called power-weighted mean value of ϕ. The mean of ϕ¯ of all snapshots in either LOS or NLOS from our measurement are reported in the following table. TABLE III P OWER WEIGHTED MEAN OF ELEVATION ANGLES Elevation Angle

Power-weighted Mean (◦ ) LOS

NLOS

EoD

0.04

0.1

EoA

1.88

1.51

Fig. 8.

In [3][4] and [5], the mean of azimuth angles are assumed to be zero. This is reasonable for the azimuth angles because the reflection and diffraction experienced by the azimuth rays from both sides of the LOS direction are generally symmetrical. However, due to the single-side reflection and diffraction from the earth ground or from rooftop, the mean angle of the elevation rays may shift away from zero or LoS direction. The first-order moment mean value of EoD and EoA can be defined by: L Pn ϕ¯ = ϕn · L (7)

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ESD distribution in UMa

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ESA distribution in UMa

B. Distribution of ESA and ESD The distributions of ESD in UMa LOS and NLOS are shown in Fig. 7 and the distributions of ESA of LOS and NLOS are shown in Fig. 8. The raw data are fitted by a lognormal function, (log10 x−μ)2 (8) 2σ 2 p(x) = √ 1 e− 2πσx

From the figures it can be observed that the ESD and ESA are well fitted by the lognormal distribution. (x−μ)2

1 Normal distribution (p(x) = √2πσx e− 2σ2 ) is usually also used for the angular spread fitting. For comparing the goodness-of-fit of the two distributions, we calculate the mean fitting errors of both Lognormal and Normal distribution for all the data under LOS and NLOS scenario and presented in Table IV. It can be observed that Lognormal generally provides better fitting than Normal. The mean value μ and standard deviation σ of ESD and ESA assuming lognormal distribution are listed in Table V.

C. Cross-correlation between Parameters Cross-correlation parameters between the two large scale parameters (ESA and ESD) and the other five large scale parameters (delay, angle of departure (AoD), angle of arrival

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TABLE IV C OMPARISON OF FITTING FUNCTIONS Fitting Function

Elevation Angle

Normal LogNormal

TABLE VII T HE CLUSTER PARAMETERS

RMS Fitting Errors

CESD[◦ ]

NLOS

LOS

14

9

11

EoD

1.09

1.04

NLOS

16

6

8

EoA

0.5

0.59

EoD

1.09

1.13

EoA

0.5

0.81

root-mean-square (RMS) spread (now equal to the angular spread) σϕ σ ln(Pn / max(Pn )) (9) ϕn = ϕ C

Lognormal distribution

ESA (log10 [◦ ])

CESA[◦ ]

LOS

TABLE V M EASUREMENT RESULTS OF ESD AND ESA PARAMETERS

ESD (log10 [◦ ])

Cluster Num

LOS

NLOS

μ

1.08

1.01

σ

0.54

0.54

μ

1.14

1.24

σ

0.84

0.9

(AoA), Shadow Fading standard deviation, Ricean K-factor [3]) are also added into the model. Table VI gives the measurement results of these cross-correlations. We also listed the WINNNER+ recommended values for the C2 (urban macrocell) scenario [4] side by side with our measurement results in the table for comparison. TABLE VI C ROSS - CORRELATIONS OF E LEVATION PARAMETERS Measurement results

WINN+ C2

LOS

NLOS

LOS

NLOS

ESD vs. SF

0.07

0.07

0

0

ESA vs. SF

0.21

0.21

-0.8

-0.8

ESD vs. K

0.2

NA

0

NA

ESA vs. K

-0.08

NA

0

NA

ESD vs. DS

-0.33

-0.37

-0.5

-0.5

ESA vs. DS

-0.22

-0.17

0

0

ESD vs. ASD

0.4

0.64

0.5

0.5

ESA vs. ASD

-0.27

-0.1

0

-0.4

ESD vs. ASA

-0.38

-0.25

0

0

ESA vs. ASA

0.41

0.02

0.4

0

ESD vs. ESA

-0.16

-0.02

0

0

In (9), σϕ is generated from the lognormal random generator with parameters in Table V, constant C is a scaling factor related to the total number of clusters and can be determined by using Table A1-4 of [3] and the number of clusters reported in Table VII. Pn is determined by Step 6 of [3]. In the LOS case, constant C is dependent also on Ricean K-factor. Additional scaling of angles is required to compensate the effect of LOS peak addition to the angular spread. As a working assumption, the heuristic scaling constant of (15) of [3] can be reused for elevation angles. For introducing randomness on above or below the LOS, a positive or negative sign is assigned to the angles by multiplying a random variable Xn with uniform discrete distribution among the set of {−1, 1}. The component of Yn ∼ N (0, σϕ /5) is further added to introduce random variation. The component of LOS direction ϕLOS is added due to user dropping. It is proposed that an offset angle ϕ¯ is added to the final EoA or EoD to account for the non-zero mean offset angles. Therefore the final EoA or EoD for the n-th path can be generated as below, ϕn = Xn ϕn + Yn + ϕLOS + ϕ¯

(10)

Note that Yn + ϕ¯ may be substituted by Yn ∼ N (ϕ, ¯ σϕ /5). ϕ¯ is determined from Table III. In the LOS case, substitute (10) by (11) to enforce the first cluster to the LOS direction ϕLOS ϕn = Xn ϕn + Yn − (Xn ϕ1 + Y1 − ϕLOS )

(11)

Finally, the per-ray offset angle cE is added for generating the mth ray within the cluster ϕn,m = ϕn + cE αm

(12)

where cE is the cluster-wise RMS elevation spread of elevation angles (cluster ESD or cluster ESA) in Table VII, and αm is determined from Table A1-5 of [3].

D. Number of clusters The number of clusters, azimuth and elevation spread of arrival and departure spread in a cluster are given in Table VII. V. P ROCEDURE FOR G ENERATING E LEVATION A NGLES Based on the above measurements and observations, if the composite PAS of all clusters is modelled as Laplace the EoD or EoA can be determined by applying the inverse Laplacian function below with the cluster power parameter Pn and the

VI. S TUDY OF D ISTANCE D EPENDENCY OF E LEVATION PARAMETERS In reality, the wireless signals propagated from the transmitter to the receiver may be blocked or reflected by surrounding objects including buildings, trees, hills, etc., with random sizes and locations. The impact of these objects is modeled as large scale shadowing effect in conventional 2D channel model. When the channel is extended from 2D to 3D, the impact of

175


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and different distance ranges in NLOS condition. Table VIII indicates that both the ESD and ESA generally decrease with the increase of distance. 8( Į

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TABLE VIII T HE RELATION BETWEEN AS AND THE DIFFERENT DISTANCE IN NLOS

8(

CONDITION

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Fig. 9.

Ground reflection of elevation rays under 3D channel model

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143-163m

214-240m

304-335m

ESD([o]) ESA([o])

13.55 29.74

9.33 13.7

8.61 13.77

VII. C ONCLUSION

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Distance

In this paper, we present the field measurement methodology and report the results for the elevation parameters of the 3D MIMO channel under an UMa scenario. Based on the results, we propose to use Laplace distribution to model the EoD and the EoA under UMa and recommend to use corresponding parameters in future 3D MIMO performance evaluations. We also observed the distance dependency of the angular spread parameters based on the field observations which agrees well with our expectation.

ACKNOWLEDGMENT

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This work is funded by the Chinese national major and longterm project under the item of next generation of broadband wireless and mobile communications (2013ZX03003007)

Fig. 10. Relation between AS (in degree) and distance in UMa LOS scenarios

the earth ground on the propagation of elevation rays should be properly modeled. Fig. 9 illustrates the ground reflections of the elevation rays in LOS case. It can be observed that as the UE moves away from the eNB, the angle (α) between the LOS and the reflection direction becomes smaller. Based on this observation, we expected that the ESA would decrease with the increase of the distance between the transmitter and receiver. Fig. 10 shows the measured angular spreads versus the distance in LOS condition. From the figure it can be seen that both the ESD and the ESA change with the increase of the distance between the mobile terminal and the base station. Particularly, the ESA shows obvious dependency on the distance. For distances larger than 100m, the linear fit of the ESA decrease with a rate of about 0.013 degrees/meter. This agrees well with our expectation. For distances less than 100m, the ESA is observed to become relatively small. Our explanation is that the measurement equipments (i.e., the trolley, the bottom of the receiving antennas, etc) may block some rays with large α angle, thus the ESA becomes small. In the NLOS condition, the continuous measurement of ESAs along the propagation path is not possible in the field. Thus, the measurement data are not continuously available with increasing distance. We perform averaging on the measurement samples in different distance ranges (143-163m, 214240m, 304-335m). Table VIII gives the relation between AS

R EFERENCES [1] J. Koppenborg, H. Halbauer, S. Saur and C. Hoek, ”3D beamforming trials with an active antenna array”, Smart Antennas (WSA), 2012 International ITG Workshop on, March 2012, p110 -114. [2] 3GPP, RP-122034, ”Study on 3D-channel model for elevation beamforming and FD-MIMO studies for LTE”. [3] Guidelines for evaluation of radio interface technologies for IMTAdvanced (12/2009), ITU-R, M.2135-1 Std. [4] WINNER+ Final Channel Models, WINNER+ Deliverable, V1.0.0 2010.6.30. [5] WINNER II Channel Models, D1.1.2 V1.2, IST-4-027756 WINNER II Deliverable, V1.1 2007.9.30. [6] K.Kalliola, H. Laitinen, P. Vainikainen, M. Toeltsch, J. Laurila, and E. Bonek,”3-d double-directional radio channel characterization for urban macrocellular applications”, IEEE Trans. On Antennas and Propagations, vol. 51, no. 11, nov.2003 [7] J.Medbo, H. Asplund, J.-E. Berg, and N. Jalden,”Directional channel characteristics in elevation and azimuth at an urban macrocell base station,” in Antennas and Propagation (EUCAP), 2012 6th European Conference on, Mar 2012, pp. 428-432. [8] Fleury B H, Tschudin M, Heddergott R, et al, ”Channel parameter estimation in mobile radio environments using the SAGE algorithm”, IEEE Journal on Selected Areas in Communications, 1999, 17, page 434450. [9] 3GPP, Spatial channel model for MIMO simulations, TR 25.996 V6.1.0, Sep. 2003.

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