Comparing Ray Tracing Based MU–CoMP–MIMOChannel Predictions with Channel Sounding

MeasurementsRichard Fritzsche ∗, Jens Voigt #, Carsten Jandura ∗, and Gerhard Fettweis ∗

∗Dresden University of Technology, Vodafone Chair for Mobile Communications Systems, D-01062 Dresden, Germany#Actix GmbH, D-01067 Dresden, Germany

{richard.fritzsche, carsten.jandura, fettweis}@ifn.et.tu-dresden.dejens.voigt@actix.com

Abstract— MIMO technology is ready for deployment in com-mercial cellular networks in the very near future. Thus, the needof incorporating this technology into radio network planning andoptimization rises dramatically for network operators. The mainquestion to answer is how accurate MIMO channel models reflectthe real MIMO channel. A good tool to learn about MIMOchannel characteristics is channel sounding measurements. Adeterministic channel model already used in high-capacity urbanareas for network planning and optimization purposes is raytracing. In this contribution, we verify a ray tracing channel sim-ulator by means of channel sounding measurements in the 2.53GHz range by comparing simulated and measured eigenvaluecharacteristics for various Multi–User (MU) downlink scenariosin a CoMP (Coordinated Multi-Point) environment.

I. INTRODUCTION

Due to promising spectral efficiency enhancements, MIMOtechnology will be introduced in next generation mobile com-munication systems. For adequate planning and optimizationof cellular networks an accurate channel modeling is neces-sary. A deterministic technique in single link channel predic-tion is ray tracing. The adaptability of ray tracing for MIMOchannel modeling got little attention in previous research,especially in the case of cooperative network structures andMU scenarios. Comparisons for SISO and SU–MIMO werepresented in e.g. [1], [2], and [3].

Our comparison of channel sounding measurement and raytracing simulation is based on the evaluation of the MIMOchannel matrix H ∈ CM×N , where N and M denote thenumber of transmit and receive antennas, respectively. Thematrix elements are obtained from the channel impulse re-sponse hm,n(k) ∈ C, where k denotes the sample index inthe time domain.

Considering a cellular network with multiple antennas ateach base station sector, index n can represent an antennaelement of a uniform linear array (ULA), a single columnsector antenna, where the alternative sectors are placed at thesame base station (SEC — sectorial) or a single column sectorantenna, where the alternative sectors are places at differentbase stations (NET — network), also known as CoMP. Atthe receiver side the index m can denote an element of anantenna array, assigned to a single user (SU) or one of multiple

users equipped with single antenna terminals (MU). The SU–MIMO cases were already analyzed in [3] using the samemeasurements and evaluation methodology. The MU–MIMOcases presented in this paper are illustrated in Fig. 1.

Fig. 1. A classification of the three proposed MU–MIMO channel types,where BS and MS denote base station and mobile station, respectively. Onlyin the MU–ULA–MIMO case two–column sector antennas are used.

This paper is organized as follows. The measurement cam-paign is described in Section II, while in Section III the raytracing simulator is introduced. We discuss our analysis inSection IV and present the results in Section V, before thepaper is concluded in Section VI.

II. CHANNEL SOUNDING MEASUREMENT CAMPAIGN

This work is based on channel sounding measurements,performed in August 2008 at downtown Dresden, focusingthe 2.53 GHz range. The campaign was arranged in termsof a cellular network structure with three base stations andthree sectors per base station, using one– and two–columncross polarized sector antennas, depending on the base station,see Fig. 2 (a) and [4]. As mobile station a uniform circulararray with eight dual polarized patch antennas was mountedonto the measurement car’s roof, see Fig. 2 (b). During the

(a) Transmitter (b) Receiver

Fig. 2. Antennas at the base station (a) and the mobile station (b).

campaign, Nw = 29 routes (dashed green lines between twogreen points in Fig. 3) were measured using a RUSK channelsounder [5]. Every 5.2 ms a snapshot was recorded, consistingof a channel impulse response (sampled with K = 273 tapsand the sampling interval ∆τ = 46.9 ns) for each of the 192(96) links between a base station and the receiver array, wherenumbers in brackets refer to one–column sector antennas.

Fig. 3. Overview of the measurement campaign at downtown Dresden. BS1 isequipped with two-column antennas, BS2 and BS3 with one-column antennas.

TABLE IPARAMETERS FROM MEASUREMENT CAMPAIGN

Parameter SettingCenter Frequency 2.53 GHzBandwidth (B) 21.25 MHzTransmit Power 44 dBmTime Windows 12.8 µsSamples (K) 273Base Stations / Sectors 3 / 3Antennas (Tx) XX-POL (BS1), X-POL (BS2, BS3)Antennas (Rx) PUCA 8Inter Site Distance ≈ 750 mMeasurement Route 8800 mAverage Rx Velocity 4.2 m/sSnapshots per Route ≈ 450.000

Thus 12 (6) transmitter elements (Ns = 3 sectors withNt = 2 (1) antenna columns and Nq = 2 polarizationdirections per column) sent to 16 receiver elements (Nd = 8patch antennas with Np = 2 polarization directions per patch).For other measurement parameters refer to Table I. Fromchannel sounding measurements (symbolized by M) we obtainthe channel impulse response

hM

(k, νp, νq, νm, νn, µr, νw, νb) , (1)

where the arguments denote:

k — sample index in time domainνp — polarization component at receiver sideνq — polarization component at transmitter sideνm — receiver patch (at UE)νn — transmitter element (at BS)µr — snapshotνw — measurement routeνb — base station

According to the channel sounding data structure weconstitute

νn = (νs − 1)Nt(νb) + νt, (2)

where νs and νt indexes the sector and the antenna column,respectively. The number of available columns depends on thebase station:

Nt(νb) =

{2 for νb = 1

1 for 2 ≤ νb ≤ 3(3)

The measured channel impulse response includes complexAdditive White Gaussian Noise n ∼ CN (0, σ2

n). For noisereduction, each sample k that does not fulfill the constraint

|hM

(k, νp, νq, νm, νn, µr, νw, νb) |2 > σ2n (4)

is excluded from any further evaluation. To estimate the noisepower threshold σ2

n, we applied the algorithm presented in[6]. To abstract from polarization effects, one polarizationcomponent at the transmitter is selected, while both receivedpolarization components are added. Applying this to (1), we

obtain the channel impulse response

hM (k, νm, νn, µr, νw, νb) =∑νp

hM

(k, νp, 1, νm, νn, µr, νw, νb) ,(5)

which is used for the analysis in Section IV.

III. RAY TRACING CHANNEL SIMULATION

The used ray tracing simulator reproduces the propagationpaths from a transmitter to a receiver through a 3D environ-ment based on a ray launching approach. Transmitters aresimulated as points placed into the 3D environment. Aroundthese points ray tubes are generated with a predefined angle ofaperture. The rays are weighted with the complex value fromthe 3D antenna pattern of its transmitter. A 3D topographicaldatabase is accessed to determine the nearest obstacle in thecurrent propagation direction of a ray. Once the ray hits anobstacle the algorithm includes the radio wave propagationeffects specular reflection, diffraction, and diffuse scatteringin its ongoing calculation based on the known algorithms ofGeometrical Optics, the Uniform Theory of Diffraction, andthe Effective Roughness approach [7]. See [3] for a discussionof the importance of certain ray tracing model features andfurther details of our models. A ray is traced until its powerfalls below a specified noise level. For our simulations thesmallest noise level estimated from measurements is applied(see Section II). Further simulation parameters are listed atTable II. Receivers are modeled by horizontal square planeswith a lateral size of arx = 10 m having complex antennapatterns. If a ray hits a receiver plane, it is registered at thereceiver. When the simulation is finished all registered raysare concluded to create a channel impulse response for eachtransmitter-receiver pair.

TABLE IIPARAMETERS FOR RAY TRACING

Parameter SettingsRelative Permittivity (Real Part) 4.0Effective Roughness (see [7]) 0.3Scattering Directivity (see [7]) 4.0Ray Tube Aperture Angle 1Max. Number of Reflections per Ray ∞Max. Number of Diffractions per Ray 2

A. Single Antenna Channel Impulse Response

The direct result of the ray tracing channel simulator (de-noted by S) is the fully polarimetric (polarization–dependent)channel impulse response

hS

(τ, νp, νq) =∑l

al(νp, νq)e−j2πfcτlδ(τ − τl), (6)

where al(νp, νq) is the complex attenuation from polarizationcomponent νq at the transmitter to polarization componentνp at the receiver and τl is the delay of path l. fc denotesthe carrier frequency. According to (5) we abstract frompolarization effects by selecting a transmitter polarization andadding the resulting polarization components at the receiver:

al =

2∑νp=1

al(νp, 1). (7)

B. Multiple Antenna Channel Impulse Response

At the transmitter we use ULAs with a distance betweenthe antenna elements of 0.6 λ. Because of the approximatedbuilding structures in our 3D environment model, a separateplacement of transmitters and receivers with a distance ofseveral centimeters is less reasonable in a ray launching model.Hence, the propagation paths from the array elements arereconstructed using a single transmitter placed in the center ofthe array, considering the phase shifts to the several antennaelements. Assuming an antenna array at both, the transmitterand the receiver, the generic impulse response for the SU–ULA–MIMO case can be written as, compare e.g. [8]:

hS

(τ, νm, νt) =∑l

alδ(τ − τl) · ...

exp{−j(2πfcτl + ∆γrxνm,l + ∆γtxνt,l)

}.

(8)

The path wise phase shift ∆γi,l between the array center andantenna element i can be calculated in general (applicable foruniform arrays) with

∆γi,l =−2πdiλ

cos(ϕi − ϕl), (9)

where the following conventions are considered (see Fig. 4):

di — distance between the array center and element iϕl — direction of path l according to the array centerϕi — direction of element i according to the array centerλ — carrier wave length

Fig. 4. Calculation of the phase shift at array element i based on path l atthe array center.

The discrete channel impulse response can be obtained bycumulating all paths within a sampling interval ∆τ

hS(k, νm, νt) =

∫ k∆τ

(k−1)∆τ

hS

(τ, νm, νt)dτ. (10)

According to (5), we write the simulated (S) channel impulseresponse as

hS (k, νm, νn, νr, νw, νb) , (11)

where the notation of Section II is used. Furthermore, νrdenotes the receiver plane index. The transmitter elements νnare obtained from (2).

IV. COMPARISON METHODOLOGY

The general comparison methodology is illustrated in Fig.5. The basic idea is to construct MIMO channel matrices fromthe channel impulse responses (5) and (11).

Fig. 5. Process to compare measured and simulated channel data.

A. Channel Construction

While transmitters can easily be placed in the 3D envi-ronment, receiver planes have to be located along the mea-surement routes. Because an established trade-off betweenacceptable simulation time and adequate simulation accuracyis obtained from arx = 10 m (compare [3]), about 450snapshots are placed inside the area of a receiver plane. Usingsnapshot position information (xµr , yµr , zµr ) obtained fromchannel sounding, the mapping of multiple snapshots to areceiver νr is formulated by the index set

M(νr) = {µr|xζ(νr−1)+1 ≤ xµr≤ dx(νr − 1)arx,

yζ(νr−1)+1 ≤ yµr≤ dy(νr − 1)arx},

(12)

where

ζ(νr) =

0 for νr = 0

maxµr∈M(νr)

µr for 1 ≤ νr ≤ Nr (13)

selects the snapshot with the largest index related to receiverνr. The instantaneous route direction is considered by

dx(νr) = sgn(xζ(νr) − xζ(νr−1)+1)

dy(νr) = sgn(yζ(νr) − yζ(νr−1)+1)(14)

At the simulation a receiver νr collects each wave fronthitting its plane. From M(νr) we want to find the snapshotthat received the most dominant of these wave fronts. Hence,

we select the snapshot with the highest power, compare againwith [3]. Based on (5) a selection function can be written as:

µr(νr) = argmaxµr∈M(νr)

∑k

∑νm

∑νn

|hM(k, νm, νn, µr)|2, (15)

disclaiming to explicitly note νw and νb. In the MU case thereceivers (users) have to be selected, i.e. two selected receiversshare the same resource. We consider random user selectionby successively selecting receivers from two predefined routes(see Fig. 6). To guarantee equal numbers of receivers, exces-sive planes from the longer route stay unconsidered. Becausesingle antenna terminals are assumed, we need to select areceiver patch from the circular array. According to (15) wechoose the patch with the highest received power:

νm(νr) = argmaxνm

∑k

∑νn

|hM(k, νm, νn, µr(νr))|2. (16)

Fig. 6. User selection and selection of corresponding snapshots.

B. MIMO Matrix Composition

We obtain the parameters νw, νs and νb from the specifiedscenarios using the function χ, where the numbers of in- andoutput parameters depend on the channel type (see Fig. 1). Weobtain the MIMO matrix elements

hMm,n(k, νr) = hM(k, νm(νr), νn(n), µr(νr), νw(m)νb) (17)

from (5) for the measured channel and

hSm,n(k, νr) = hS(k, νm(νr), νn(n), νr, νw(m)νb) (18)

from (11) for the simulated channel. In the ULA case, theparameters can be assigned using

[νw(m), νs] = χULA(m, νz) (19)

with νn(n) = (νs − 1)2 + n from (2) and νb = 1. νz denotesthe index of the selected scenario. Furthermore, we obtain

[νw(m), νb] = χSEC(m, νz) (20)

with νn(n) = (n− 1)Nt(νb) + 1 for SEC-MIMO and finally

[νw(m), νs(n), νb(n)] = χNET(m,n, νz) (21)

for NET-MIMO, where νn(n) = (νs−1)Nt(νb)+1. To reducethe channel impulse response to a single channel coefficient weconsider selection combining (select the sample with largestpower).

C. Channel Quality Metric

Because the performance of MIMO systems is stronglyrelated to its eigenvalue distribution, a widely-used metricto evaluate the channel matrix is its condition number. It isdefined as the ratio of the largest to the smallest eigenvalue.Because the considered channels only have two eigenvalues,we introduce the eigenvalue ratio, which we define as thelogarithmic inverse of the condition number:

reig = 10 · log10

(λ2

λ1

), (22)

where λ1 > λ2. To describe the deviation between simulatedand measured channels the eigenvalue ratio deviation is intro-duced

∆reig = rSeig − rMeig (23)

V. RESULTS

In this section, we present eigenvalue statistics for the dis-cussed MU–MIMO channel types, where the MIMO matricesare composed as described in Section IV-B. The usability ofMIMO for reig < −10 dB is typically not reasonable becausecapacity gains are small in comparison with lower complexSISO. From our analysis, we conclude that only 20 % of theanalyzed snapshots pass this criterion in our environment, seeFig. 7. However, we did not consider smart user selection,spatial filtering, and power control.

Fig. 7. Cumulative Distribution Function (CDF) of the measured eigenvalueratio for the three proposed MU channel types.

Fig. 8 shows a ∆reig which is similarly distributed for allthree channel types. The average deviation values are near0 dB, deviations |∆reig| > 10 dB are between 40 % and50 %.

VI. CONCLUSIONS

In this contribution, three MU–MIMO channel types wereanalyzed, comparing channel sounding measurements withray tracing simulations, based on a CoMP network structure.

Fig. 8. Comparison between simulation and measurement using the CDF ofthe eigenvalue ratio deviation.

It was shown that carefully performed ray tracing basedsimulations are useable as channel model for MU–MIMOchannel predictions. For a random selection of users only20 % of the analyzed points in our urban environment holdan eigenvalue ratio larger than -10 dB, which is an empiricalbound for spatial multiplexing usability.

ACKNOWLEDGMENT

The work presented in this paper was partly sponsored bythe German federal government within the EASY-C projectunder contracts 01BU0630 and 01BU0638.

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