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Theory, Techniques and Validation ofOver-the-Air Test Methods for Evaluating

the Performance of MIMO User Equipment

Application Note

Abstract

Several over-the-air (OTA) test methods have been proposed to characterizethe radiated performance of multiple input multiple output (MIMO) devices.Knowing that antenna gain and spatial correlation are important factors tosystem performance, it has become necessary to include OTA testing of MIMOantenna performance. This paper will discuss three predominant OTA test meth-ods including the two-stage OTA method, the multiple test probe OTA methodand the reverberation chamber method. In some test configurations, the probeantennas are connected to a wireless channel emulator, such as the AgilentN5106A PXB, to emulate real-world multipath environments. In addition, thispaper will discuss two types of MIMO channel models, the correlation-basedand geometry-based models, and show how antenna and spatial characteristicsat the MIMO transmitter and receiver can be separated into independent terms.Separating antenna gains and spatial characteristics allow the practical imple-mentation of accurate OTA measurement systems using commercially availabletest instrumentation. This paper will also show measurements of spatial correla-tion and system capacity taken from commercial MIMO devices, and compari-sons will be made using several OTA methods. It is assumed that the reader isfamiliar with basic concepts of MIMO technologies and additional backgroundcan be found in the References section [1], [2], [3]. Additional information on the3GPP MIMO channel models can also be found in References [4].

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Traditional conducted test methods fortesting the performance of single inputsingle output (SISO) devices is typicallyachieved with a system comprised of abase station (BS) signal generator anda wireless channel emulator directlycabled to the device under test (DUT).The channel emulator typically provides aselection of channel models that faithfullyreproduce a wireless signal propagationenvironment based on time-domain fad-ing, Doppler spreading and path loss ofthe BTS signals. These test systems areideally suited for characterizing the SISOmobile subscriber (MS) or user equipment(UE) under controlled and repeatable con-ditions without the antennas influence.Many test specifications, including 3GPP

TS 34.114 [5], also require OTA testing ofSISO devices in order to include antennaeffects during the measurements. SISOOTA testing performed in an anechoicchamber actively measures the total radi-ated power (TRP) and total radiated sen-sitivity (TRS) [6] of the UE. The SISO testis mainly used to test the antenna gainand the sensitivity of the receiver due toantenna gain and UE self interference.The SISO test does not require a fadingchannel. It is known that this type oftesting is not sufficient for characterizingthe performance of MIMO UE, and OTA

testing of MIMO antenna systems mustinclude a model of the spatial correlationeffects between antenna elements andinteraction with the surrounding multipathenvironment. While the basic measure-ment equipment used in SISO OTA testsystems can also be included in a MIMOOTA test system, additional equipmentmeasurement techniques and improvedchannel models will be required to accu-rately represent the spatial characteristicsof the multipath and the MIMO antennacharacteristics.

In any wireless system, a signalpropagating through a terrestrial channelcan arrive at the destination along anumber of different paths, referred to asmultipath. Each path can be associatedwith a time delay and a set of spatialangles, one angle at the transmitter andone at the receiver. For example, Figure1a shows a simplified diagram of a 2x2MIMO system operating in a multipathenvironment. Between the Tx1 and Rx0antenna pair, the figure shows a direct

line-of-sight (LOS) path and several othernon-LOS (NLOS) paths. Each transmitand receive antenna pair would ideallyhave an uncorrelated set of multipathcharacteristics depending on the antennaspacing and polarizations. The multipathcharacteristics arise from scattering,reflection and diffraction of the radiatedenergy by objects in the surroundingenvironment. The various propagationmechanisms influence the channelsspatial characteristics, signal fading,Doppler and path loss. At each receiveantenna, multipath propagation results inboth a time spreading, referred to as delayspread, and spatial spreading as transmit-ted signals follow unique transmissionpaths from the BS to the UE antennas

arriving at different angles with differentpath losses. At the receive antenna, eachpath can be associated with an angle ofarrival (AoA) as measured relative to thearray normal. These signal paths are alsoassociated with an angle of departure(AoD) as the transmitted signals leavethe BS antenna and enter the channel.The AoDs are measured relative to thenormal of the transmit antenna array. Thespatial characteristics of the wirelesschannel are modeled using a spatialdistribution referred to as power anglespectrum (PAS). As MIMO performance

is strongly influenced by spatial correla-tion introduced by the PAS and antennacharacteristics, it is extremely importantto measure MIMO devices using an OTAtest system that can accurately emulaterealistic channels and include the effects

of angular spread, direction of arrival,antenna gain, antenna spacing and anten-na polarization. For example, as shown inFigure 1b, the antenna patterns for Rx0and Rx1 exhibit peak gains separatedby 180 degrees. The difference betweenantenna patterns as a function of anglemay help to de-correlate the signalsarriving at each receive antenna, thereforeit is important to include the antennacharacteristics in any MIMO channelmodel and associated OTA test system inorder to get an accurate measurement ofthe MIMO UE performance.

As in all test systems, a balance must beachieved between the accuracy of theMIMO OTA measurement approach and

the speed and complexity of the overalltest system. It may also be beneficialthat the MIMO OTA test system supportbackward compatibility to SISO operation.Three predominant OTA test methodsexamined in this application note includethe two-stage OTA method, the multipletest probe method and the reverberationchamber method. The goal of this applica-tion note is to introduce the test require-ments, channel models available for OTAtesting, equipment configuration and OTAchamber requirements. Also includedare the channel model implementation

measurements and validation using thedifferent OTA test methods. The nextsection begins with an introduction of thedesired figures of merit (FOM) measuredin order to determine a good MIMOdevice from a bad device.

Figure 1. (a) Diagram of a simple wireless 2x2 MIMO configuration and (b) associated

antenna gain pattern for the two MS/UE antennas.

Rx1

MS/UE

Rx0

Tx1

Tx0

BS

(a) 2x2 MIMO system (b) Antenna gain patterns

30

45

9090

180

0

+

Antenna Rx0 gainAntenna RX1 gain

Introduction

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Traditionally, the performance of 2G and3G systems, such as those with SISOconfigurations, are assessed with speci-fied test parameters or figures of merit(FOMs). These FOMs include maximumtransmit power and receive sensitivity andend-to-end system bit error rate (BER)or frame error rate (FER). These mea-surements can be performed with testequipment cabled directly to the UE orcan be over-the-air to include the effectsof antenna radiation and antenna interac-tion with the UE. With the introduction ofMIMO, the antenna design and associ-ated gain pattern become fundamental tothe performance of the MIMO system asmultipath and low correlation betweenmultiple antennas provide the potential

capacity increase over traditional SISOtechniques.

The proposed list of FOMs for MIMO OTAtesting, as defined by 3GPP, is shown inTable 1[6]. The FOMs include OTA andantenna radiation test parameters formeasuring the performance of the UEin realistic environments. The FOMs arecategorized as active and passivetesting. Active device testing includesOTA measurements with an active trans-mitter. The transmitted signal is typicallydelivered by a BS signal emulator such as

the Agilent E6621 wireless test set. Activetesting may or may not include the emula-tion of multipath signal fading. Passivetesting includes characterization of theMIMO antenna radiation. These measure-ments can be taken directly on the MIMOantenna array or from the UE when theequalizer response signal is availablefor characterizing the individual antenna

element performance of the MIMO array.Passive testing does not require an activeBS emulator or channel fading emulator.Passive antenna characterization mayalso include the use of a specific anthro-pomorphic mannequin (SAM) phantomhead to measure the proximity effectsbetween the human head model and theMIMO UE antenna array.

The predominant FOM for characterizingMIMO UE performance is MIMO through-put. This active end-to-end throughputmeasurement attempts to emulate arealistic user experience by testing thedata capacity under the influence of sig-nal fading and in a modeled environmentwith spatial variation. Organizations, such

as the 3GPP, COST 2100 and CTIA developstandardized channel models that includethe effects of path loss, shadow fading,delay spread, power delay profile (PDP),PAS, AoD, AoA and angle spread orazimuth spread (AS) in a variety of wire-less environments including urban andsuburban types. Modeling and emulatingthe spatial variations, including PAS andAS, and their effect on MIMO throughputwill be discussed in more detail later inthis application note.

Additional active FOMs include the TRP,

TRS, channel quality indicator (CQI),and block error rate (BLER). The TRPand TRS performance metrics verify thepeak throughput as well as cell edgeperformance. The TRP and TRS aremeasured without channel fading. TheTRP is a measure of how much power theUE radiates and is defined as the integralof the power transmitted over the entire

radiation sphere. The TRS is related tothe power available at the antenna outputsuch that a receive sensitivity threshold isachieved for each antenna polarization.Characterizing the performance of MIMOantennas is predominately performedusing passive testing. Passive testingevaluates antenna efficiency, mean effec-tive gain (MEG), antenna gain imbalance,spatial correlation and MIMO capacity.These passive FOMs are calculatedusing measured spatial antenna patternsobtained from traditional anechoicchamber test methods. For example, theMIMO capacity can be estimated usingthe measured antenna patterns andthe selected multipath channel model.Together these parameters are used to

calculate the ideal channel coefficientsand related capacity based solely on thespatial properties without including theeffects of DSP and baseband processingin the UE. Although passive measurementmethods alone cannot directly providethe total end-to-end OTA performance ofthe UE, combining these separate passivemeasurements with a MIMO channelemulator can quickly yield similar resultsachievable by other more complex OTAtest systems.

MIMO Figures of Merit

Table 1. List of FOMs for MIMO OTA measurement

Category I II III IV VFOMs MIMO throughput

(VRC)

TRP

TRS

CQI

BLER (FRC)

MIMO throughput

(FRC)

Antenna efficiency

MEG

Gain imbalance

Spatial correlation

MIMO capacity

Requirements MIMO T-put > X Mbps TRP > +X dBm

TRS < X dBm

CQI > X

BLER < X %

T-put > X Mbps

Efficiency > X dB

MEG > X dBi

Imbalance < X dB

Correlation < X

Capacity > X bps/Hz

Subject OTA OTA OTA MIMO antennas MIMO antennas

Methodology Active

(with fading)

Active Active

(with fading)

Passive/Active Passive

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Modeling the Spatial Characteristicsof the Multipath Channel

The multiplexing capacity gainsachievable by using multiple anten-nas at both the transmitter (Tx) andthe receiver (Rx) have generated so

much interest in recent years thatmost modern wireless communica-tion systems have options for MIMOimplementations including the802.11n WLAN, 802.16 WiMAX and3GPP LTE. The capacity increase isobtained by the potential de-correla-tion between the channel coefficientsintroduced by the rich multipathenvironment establishing severalparallel subchannels between thetransmit antenna array and receivearray [7]. However, system capacity is

greatly reduced once the subchannelsbecome highly correlated to the pointwhere fully correlated subchannelsresult in a capacity degradation tothat of a single subchannel as foundin a SISO system. Traditional methodsfor modeling wireless channels, suchas power delay profile (PDP) andDoppler spectrum, can accurately rep-resent the multipath effects in a SISO

system, but improved channel modelsare required for MIMO systems. Theshortcoming of traditional modelsis that they typically do not include

spatial effects introduced by antennagain, antenna position, antenna polar-ization and UE movement within themultipath environment. To accuratelymodel and test the performance of aMIMO UE, it is necessary to includethe spatial characteristics of theenvironment and the antenna arrays.

When developing simulation andtest strategies for characterizingthe performance of the MIMO UEunder realistic channel conditions, it

becomes important to develop chan-nel models that accurately emulate aspatially rich multipath environment.These spatial models, including cor-relation effects, can be implementedin their exact form or approximatedwithin the system simulation or targettest system. There are two basictypes of channel models currentlybeing studied for LTE OTA testing.

The first model uses a stochasticor correlation-based channel modelof the multipath environment. Thiscorrelation-based model is a good fit

for the two-stage OTA method whichcombines the spatial properties of themultipath with the spatial propertiesof the BS and UE antenna arrays. Thesecond method is a geometry-basedchannel model, such as the spatialchannel model (SCM) [4], that usesray-tracing techniques approximatethe multipath environment. TheSCM technique is a good fit to themultiple test probe OTA test method,where the SCM is emulated withmultiple probe antennas positioned

within a large anechoic chamber. Theaccuracy in the SCM approximation isdirectly related to the number of testprobes implemented in the OTA testsystem. The geometry-based SCMcan also be implemented in the two-stage OTA test method with a largereduction in system complexity.

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Correlation-based channel model

A simplified multipath channel withina 2x2 MIMO system is shown in

Figure 2. In this case, the base stationuses a two-element array for trans-mitting two data streams from the Tx0and Tx1 antennas. The BS antennaarray boresight is defined normalto the array and will be used as thereference point for determining theAoD from this array. In this example,the UE also contains two antennaelements and, similarly, its array bore-sight is defined as normal to the UEarray and will be used as a referencefor determining the AoA. The UE can

also be moving relative to the BS withvelocity (v) as shown in Figure 2.

The multipath environment in thisexample contains two groupings ofmultiple reflections or scattererscalled clusters. A cluster is associ-

ated with a tight grouping of spatialangles around the BS and/or UE.The cluster can be representativeof a large building with high archi-tectural detail creating radio wavescattering from around the structure.Rather than attempt to include eachreflected signal path and its associ-ated AoD and AoA in the channelmodel, a statistical model can be cre-ated that includes the mean AoD andmean AoA for each cluster as wellas an associated AS representing the

distribution of angular power abouteach mean.

Cluster n in Figure 2 shows transmis-sion path n connecting the BS arrayto the UE array. Path n leaving the BShas a mean AoD of n,AoD, and an AS

of n,AoD. At the UE, this path has anAoA of n,AoA, and an AS of n,AoA. Atypical BS would have a narrow ASdue to the fact that the BS antennaarray is located at a high elevationand away from most scatterers. Incontrast, the UE is located at lowelevation near a large number of localscatterers, resulting in a wide AS.

Figure 2. MIMO system showing an antenna array at both the BS and UE. Multipath reflections and/or scatterers are grouped into

individual clusters and modeled as a single path with an associated angular spread.

Cluster n

Cluster n+1

Rx1

Rx0

V

Tx0

Tx1

n, AoDn, AoA

n, AoD n + 1, AoA

n, AoA

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The distribution of the signal power

as a function of angle for each cluster

can be characterized with a probability

density function (PDF) [3]. The PDF is

modeled using a Laplacian, Gaussianor uniform distribution. The distribu-

tion is selected based on the type of

multipath channel to be modeled. For

example, the spatial power distribution

for an outdoor urban environment will

often be modeled using a Laplacian

distribution. The standard deviation

of the PDF is the angular spread (AS),

sometimes referred to as azimuth

spread and usually defined in the

horizontal or azimuth plane. The array

PAS is a combination of PDFs from

all the associated clusters, and isdisplayed as the average power at the

antenna as a function of angle. This

total angular power, integrated over

360 degrees in azimuth, is normalized

to a value of one. Figure 3a shows a

simulated PAS at the receive antenna

array for a multipath channel having

two large clusters, n and n+1, similar

to the configuration shown in Figure2. The PAS contains two distinctive

peaks arriving at angles n,AoA and

n+1,AoA. These angles are relative to

the antenna array boresight. A similar-

looking PAS is found at the transmit

antenna array for the associated

departure angles. For this channel,

the receive array PAS is best modeled

using a truncated Laplacian PDF as

shown in Figure 3b [3]. The mean

AoAs for the modeled PDF coincide

with the cluster peaks of the original

PAS. The standard deviations, n,AoAand n+1,AoA, can be independently opti-

mized for each cluster. In theory, each

antenna element in the receive array

would have a slightly different PAS,

but, in practice, especially for outdoor

channels, the clusters are positioned

relatively far from the array, making

the AoAs approximately equal, so the

same PAS can be assigned to eachantenna element. The elements in the

transmit array will also be assigned the

same PAS, though the PAS distribu-

tions are usually quite different at the

transmitter and receiver arrays. A more

complex model would be required for a

MIMO system having cross-polarized

antenna elements. In this case, a

different PAS may be required for each

element in the cross-polarized antenna

array. The PAS using truncated PDFs

will be included in the correlation-

based channel model and implementedas one option in the two-stage OTA

test system.

Figure 3. (a) PAS at the receive antenna array for a multipath channel having two clusters (b) equivalent PAS model using the truncatedLaplacian PDF.

(a) Actual PAS

Angle of arrival (deg.) Angle of arrival (deg.)

180

Po

wer

Po

wer

Clustern + 1

Clustern

+180 180 n+1, AoA

n+1, AoA

n, AoA

n, AoA +180

(b) Modeled PAS

Clustern + 1

Clustern

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Figure 4. Approximation of a Laplacian PAS using 20 equal-amplitude sub-paths.

Figure 5. Geometry-based representation of the Tx PAS and Rx PAS using five sub-paths

relating to cluster n.

Geometry-based channelmodel using sum-of-sinusoids

technique

An approximate model to the previ-ously discussed angular distributionscan be developed using sub-paths toproduce the desired power spectrumassociated with each cluster [8]. Theproposed model is based on the sum-of-sinusoids technique that uses a setof sub-paths with predefined angularspacing and equal power level toproduce the desired PDF distribution.Figure 4 shows an approximationto a Laplacian distribution using20 equal-amplitude sub-paths. Byapproximating the distribution with alarge number of sub-paths, a Rayleighfading statistic can also be achievedas a function of time. Maintainingequal power for each sub-path willprevent any single sub-path fromdominating the distribution and there-by producing Rician fading. There isa tighter grouping of sub-paths nearthe peak of the Laplacian distributionto place more power at the center ofthe distribution. The angular spacings

are optimized to achieve a desiredstandard deviation or angular spread(AS). As the required AS widens, thesub-paths spread out further in angleand begin to approach a uniformdistribution where the sub-paths areall equally spaced in angle. This sum-of-sinusoids model can be definedwith even or odd number of sub-pathsapproximating the desired PAS distri-bution. Reference [8] has a procedurefor calculating the appropriate anglesfor each sub-path.

The sub-path model, implementedas a geometry-based model in anOTA test system, will include a set ofunique rays connecting the transmit

and receive antennas. Figure 5 showsa simplified geometry-based modelusing a distribution of sub-paths toapproximate a Laplacian PAS at thetransmit antenna array and an associ-ated grouping of sub-paths to model aLaplacian PAS at the receive antenna

array. Figure 5 is simplified for clarityby showing only a single cluster, n,and five sub-paths connecting trans-mit antenna array to receive antenna

array. For the simplified case, themean AoD for transmit antenna arrayis AoD and the mean AoA for receiveantenna array is AoA. The sub-pathangular distributions are referencedto these AoD and AoA values.

Angle (deg.)

Power

Sub-pathapproximation

+

Laplacian PAS

PASAoD

n, AoD

n, AoA

LOS

Tx1

Tx0

Rx1

Rx0

PASAoA

Sub-path 5

Sub-path 5

Sub-path 4

Sub-path 4

Sub-path 3

Sub-path 3

Sub-path 2

Sub-path 2

Sub-path 1

Sub-path 1

Cluster n

+ n, AoA +

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The 3GPP has developed a technicalspecification for modeling the spatialcharacteristics of MIMO channelsbased on this ray-tracing or geometry-

based approach. The model is definedas the SCM [4]. The SCM providesmathematical channel models foruse in link-level and system levelsimulations of outdoor environments.This simulation model emulatessmall scale fading including effectsof shadowing, path loss and inter-cell interference. The basic modeldefines three types of multipathenvironments namely the suburbanmacro, urban macro and urban micro.These models can be used with

any antenna array configuration inorder to simulate the MIMO systemperformance. All the SCM modelsassume a multipath channel with sixclusters, defined by their mean AoDand AoA, with each cluster comprisedof 20 equal-powered sub-paths usedto approximate the associated PASdistribution.

Depending on the type of environ-ment, the 3GPP SCM specifiesPAS distributions for Laplacian and

uniform PDFs. PAS distributions aremodeled in the horizontal, or azimuth,plane as most outdoor scenariostypically experience little change in

elevation characteristics. The SCMdefines unique PAS distributionsfor all three multipath environmentswith individual sub-paths having aspecified angular spread relative tothe clusters mean AoD and AoA. Forexample, Table 2 shows the relativeangular positions for the 20 sub-pathsrequired to model a single path hav-ing a 5 degree AS at the BS and a 35degree AS at the UE operating withinan urban microcell environment.

As defined in the 3GPP SCM, theangular spread for individual pathsare fixed during simulations, but theAoDs, AoAs and time delays for eachpath are random variables for eachiteration. The SCM procedure requiresnumerous iterations, or drops, toprovide a statistical average of theMIMO performance. During a drop,which may cover several frames ofa MIMO transmission, the spatialand delay characteristics remainfixed but the channel coefficients

may undergo fast fading due to anyrelative motion of the UE. In this case,the channel coefficients are modifieddue to changing phase characteristics

for each sub-path in the simulation.Additional information regardingthe SCM environmental parametersfor the SCM drop are provided inreference 3GPP TR 25.996 [4]. The3GPP SCM will be the basis for OTAtesting. As discussed in the next sec-tion, when using a reduced numberof sub-paths, Rayleigh fading is notfully developed and, as a result, thepower in each sub-path will requirea separate process to introduce timefading. For example, a channel fader,

such as the Agilent N5106A PXB,will be required to introduce Rayleighfading to each sub-path.

Table 2. PAS sub-path AoD and AoA angular offsets for an urban micro environment [4]

Sub-path #(m)

Angular offset for a 5-degAS at BS (degrees)

Angular offset for a 35-degAS at UE (degrees)

1, 2 0.2236 1.5649

3, 4 0.7064 4.9447

5, 6 1.2461 8.7224

7, 8 1.8578 13.0045

9, 10 2.5642 17.9492

11, 12 3.3986 23.7899

13, 14 4.4220 30.9538

15, 16 5.7403 40.1824

17, 18 7.5974 53.1816

19, 20 10.7753 75.4274

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Geometry-based channel modelusing quantized PAS

In many cases, when implementing

an OTA test system using geometry-based channel models such as the3GPP SCM, it may not be practical toinclude a large number of sub-pathsin the sum-of-sinusoids technique.Unfortunately, reducing the numberof sub-paths may not only reduce theaccuracy of the PAS approximationbut also has a secondary effect ofaltering the Rayleigh fading statisticsin time. As previously discussed, thesum-of-sinusoids technique producesboth the proper angular distribution

as well as Rayleigh fading in timewhen the number of sub-paths islarge. Greatly reducing the numberof sub-paths in an OTA test system

will require additional techniques toproperly create Rayleigh fading.

Assuming that time fading will beintroduced to each sub-path by othermeans, an alternate approximationto the PAS distribution can be madeusing a smaller number of sub-pathsthat effectively quantize the PASamplitude and angular distribution.For example, Figure 6 shows thedesired Laplacian PAS distributionand a quantized representation

using three sub-paths with unequalamplitudes. The angular placementof the sub-paths and their associatedamplitudes must be optimized to

properly model the PAS distributionand fading characteristics whenthese three signals are combined atthe receive antenna. Not shown inFigure 6, is the requirement that eachsub-path be independently faded asa function of time in order to properlyemulate the multipath channel. Asdescribed later in this applicationnote, a channel emulator such as theAgilent N5106A PXB can be used tointroduce sub-path fading in the OTAtest system.

Figure 6. Quantized approximation of a Laplacian PAS using three unequal powered sub-paths.

Angle (deg.)

Power

Quantized PAS

+

Laplacian PAS

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Spatial Correlation Effects on MIMO Capacity

As mentioned previously, the capac-ity increase in a MIMO system isobtained when low correlation existsbetween the multiple paths of the

wireless channel. A rich multipathenvironment would ideally result inuncorrelated spatial characteristicsat each antenna element. The PASis just one spatial characteristic thatmay introduce channel correlation.Correlation between antenna ele-ments in an array will also have adetrimental effect on the multiplexingcapacity of the MIMO system.

It can be shown that the antenna-to-antenna spacing at either the

transmitter and/or receiver has astrong relationship to the overallspatial correlation [3]. For example,if two omni-directional receiveantennas with the same polarizationwere placed in very close physicalproximity, there would most likely bea high degree of correlation at theoutputs of these two antenna ele-ments, even in the presence of a richmultipath environment. Unfortunately,many portable MIMO devices tendto be physically small, thus limitingthe antenna separation to less than

a wavelength. An alternate solutionto achieve the low spatial correlationbetween two closely spaced anten-nas is to cross polarize the antennas,

or, in other words, position theantenna polarizations in orthogonalor near orthogonal orientations [3].Additionally, low correlation may beachieved with pattern diversity inthe antenna gains at the BS and/orUE. Figure 7a shows the simulatedantenna gain pattern for each receiveantenna element in a two-elementdipole array. Figure 7a also showsthe AoA for six signals arriving fromclusters positioned in the surroundingenvironment. It is expected that the

difference between the two antennagain patterns may improve thecapacity of the MIMO system whencompared to a system having anten-nas with omni-directional patterns.For example, Figure 7b shows thesimulated capacity for a 2x2 MIMOsystem using this two-element dipolearray in the presence of a channelwith a single cluster having a BS AoDof 50 degrees and AS of 2 degrees,and the UE having an AoA of 67.5degrees and AS of 35 degrees. Asshown in Figure 7b, the capacity is

higher when there is pattern diversitybetween the UE antenna elementsas compared to the omni-directionalcase. The capacity found in this

example was simulated using thecorrelation-based model implementedwith a Laplacian PAS distribution andantenna patterns shown in Figure 7a.The dipole antenna patterns weremodeled using the Agilent electro-magnetic solver EMPro. The capacitywas calculated using the correlationcoefficients determined by the AgilentN5106A PXB channel emulator. ThePXB can calculate the channel coef-ficients from selected channel modelsand arbitrary antenna patterns. The

PXB calculations can use either thecorrelation-based or geometry-basedchannel models. By providing amethod to separate the PAS fromthe antenna patterns, MIMO systemperformance can be quickly evaluatedusing a variety of antenna arrays,even before the BS and UE antennasare built. The next section of theapplication note includes the math-ematics for calculating the spatialcorrelation matrix by separating theantenna patterns from the spatialproperties of the channel.

Figure 7. (a) Antenna pattern diversity operating in a multipath channel with six clusters. (b) MIMO capacity versus SNR using a dipole

antenna array and an omni-directional antenna array having a single multipath cluster.

(a) Antenna pattern and cluster AoAs (b) Capacity vs. SNR

Antenna Rx0 gainAntenna RX1 gain

AoA #6

AoA #3

Channelcapacity(Bits/s/Hz)

SNR (dB)

AoA #5

AoA #4

AoA #1 3 5 10 15 20

4

5

6

7

8

9

Idealomni-directional

array

Dipole array

AoA #2

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Modeling the capacity andspatial correlation of the

multipath channel

The instantaneous capacity of anMxN receive antenna MIMO systemcan be expressed as the followingequation:

Where IN is the N-by-N identitymatrix, is the average receive signalto noise ratio (SNR), (.)H is thecomplex conjugate transpose, andH is the normalized channel matrixwhich includes the spatial correlationeffects of PAS and antenna gainpatterns. Modeling a MIMO systemusing the geometry-based SCMmethod allows the individual channel

coefficients of H to be calculateddirectly by summation of the multiplesub-path characteristics between thepairs of transmit and receive anten-

nas. In this case, the spatial effects ofantenna gain can be handled by asso-ciating the AoAs and AoDs for eachsub-path with the angular distributionof the gain pattern.

Obtaining the MIMO capacity usingthe correlation-based method firstrequires a calculation of the spatialcorrelation matrix, R, in order tocalculate the channel matrix, H, andassociated capacity. It will be shownthat the spatial correlation matrix of

the channel can be separated into atransmitter correlation matrix and areceiver correlation matrix.

While both the correlation-based andgeometry-based methods are onlyapproximations to the desired MIMOchannel, it is important to understand

the assumptions and mathematicsused in each technique. The fol-lowing sections of this applicationnote will review the mathematical

techniques that allow separationof the spatial properties from theantenna characteristics. Separatingthe spatial and antenna propertiesallows the channel models to beimplemented in a practical OTA testsystem. Comparisons will be madebetween practical implementations ofseveral OTA measurement systemsusing either a correlation-based or ageometry-based model. As shown inthe examples below, the two-stageOTA test method allows direct com-

parison between these two channelmodels while operating with thesame hardware configuration.

CMIMO= log2 [det(IN + HHH)] (1)

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Correlation-based model usingindependent spatial propertiesat the transmitter and receiver

As the capacity of a MIMO system

substantially depends on the spatial

correlation between individual transmit

and receive branches, the spatial

correlation matrix, R, is often a desired

metric that provides an intuitive under-

standing of the systems operation.

Under certain assumptions, the spatial

correlation matrix at the transmitter

side, RTX, can be separated from the

spatial correlation matrix at the receiver

side, RRX

, allowing the complete spatial

correlation matrix, R, to be calculated

using the following equation:

Where tr{.} is the trace of the matrix

and is the Kronecker product. The

Kronecker assumption has the advan-

tage that the entries in the complete

spatial correlation matrix can be

separated into the transmitter side and

receiver side [9].

The spatial correlations at the transmit-

ter and receiver can be independently

determined based on the PAS and

antenna gain patterns at the respective

antenna arrays. For example, using a

simplified 2x2 MIMO model where the

antenna element patterns, G(), are

identical at the transmitter, the calcu-

lated transmit correlation coefficient

between transmit antenna element

1 and transmit antenna element 2 is

found using the following equation:

Where d is the physical d istance

between transmit antenna elements,

PASTx() is the power azimuth spectrum

at the transmitter having a set of trun-

cated Laplacian, uniform or GaussianPDFs, GTx() is the antenna element

pattern at the transmitter which is

assumed identical for each, and is the

carrier wavelength.

A similar equation can be used todetermine the correlation coefficientat the receiver array. For this simpli-fied example, it is assumed that theantenna element patterns at thereceiver are identical, though thepatterns between the transmitter

and receiver could be different.The receive correlation coefficientbetween receive antenna element1 and receive antenna element 2 isfound using the following equation:

As shown in equations (3) and (4),

the correlation coefficients at the

transmitter and receiver are directly

related to the multiplication of the PAS

and the associated antenna gain. As a

result, independent measurements of

transmitter antenna gain and receiver

antenna gain can be used to calculate

the respective correlation coefficients.

The correlation coefficients can then

be used to determine the correlation

matrix at the transmitter and receiverusing the following equation:

Where (.)* is the complex conjugate.The complete channel correlationmatrix, R, would be calculated usingequation (2). The simplified expres-

sions for correlation coefficients (3)and (4) assumed that the elementpatterns were the same at eachlocation. If the element patterns weredifferent, such as the case shownin Figure 7a, then the equations forcorrelation coefficients would needto be modified to include the effectsof different antenna gain patterns.This technique is also robust enoughto include the effects of antennapolarization. The spatial correlationmatrices provide insight into the level

of correlation to the signals leavingthe transmit antenna array and thesignals arriving at the receive arrayindependently. As such, the spatialcorrelation matrices are often used tocompare the performance of differentOTA measurement techniques asshown later in this application note.

Continuing with the Kroneckerassumption described above, thechannel matrix can then be approxi-mated using the following equation:

Where (.)T is the matrix transpose andG is an N x M random matrix withzero-mean i.i.d. complex Gaussianentries. In general, the Kroneckerassumption will result in a lessaccurate model of the short-term timevariation of wideband channels [9] for

arbitrary polarization angles. Agilenthas developed a proprietary algorithmthat improves the accuracy of theKronecker assumption when calculat-ing the spatial correlation matrix andchannel matrix using the correlation-based method in a two-stage OTAmeasurement.

RX,12=

j2 sin ()de PASRX ()GRX()d

PASRX ()GRX()d

(4)

TX,12=

j2 sin ()de PASTX ()GTX()d

PASTX ()GTX()d (3)

RTx= [ ]1 TX,12(TX,12)* 1 (5)

RRx= [ ]1 RX,12(RX,12)* 1 (6)

(7)= RRX G (RTX)T1

tr{RRX}

R= RTX RRX1

tr{RRX}(2)

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Geometry-based model usingindependent spatialand antenna gain parameters

When using the geometry-based

channel model, such as the SCM, the

channel matrix is calculated from the

summation of numerous sub-paths

associated with separate clusters

placed in the channel. The geometry-

based model, also called a double direc-

tional channel model, does not explicitly

specify the locations of the individual

clusters, but rather the angular direc-

tions of the sub-paths. Geometry-based

modeling of the radio channel also

allows separation of spatial parameters

and antenna patterns. As shown in the

correlation-based method, separation of

the spatial and antenna characteristics

will simplify calculation of the channel

and correlation matrices. For the 3GPP

SCM downlink, the received signal at

the UE consists of six time-delayed

paths from the transmitter. Each path

consists of 20 sub-paths in an SCM

simulation. As previously described,

having 20 sub-paths results in a highly

accurate representation of the PASusing the sum-of-sinusoids technique.

A simplified calculation for the coef-ficient of the mth sub-path within thenth cluster is shown in Figure 8. Thecoefficient calculation is based on thegeometry shown in Figure 5 for a 2x2MIMO system. The following calcula-tion is associated with antenna pairTx1 and Rx1. There would be a similarcalculation for each antenna pairbetween all combinations of transmit

and receive antennas.

The angle n, m, AoDis defined as theAoD for the mth sub-path of the nthcluster, n, m, AoA is the AoA for thissub-path, G(n, m, AoD) is the BS antenna

gain at angle n, m, AoD, G(n, m, AoA) is theUE antenna gain at angle n, m, AoA, n, mis the phase of the mth sub-path of thenth cluster and k = 2/. The geom-etry-based model and associatedcalculation in Figure 8 shows that theantenna gains and the angular param-eters are separable. This simplifiedcalculation assumes no time variationas a result of propagation delay andUE motion, and no attenuation effectsdue to path loss and shadowing. Amore complete expression including

antenna polarization effects, loss andmotion is included in reference [10].

The channel coefficient for the nthcluster between Tx1 and Rx1 is thesummation of all the M sub-paths,where M is the total number ofsub-paths in the sum-of-sinusoidsapproximation, typically set to 20. Thecomplete channel coefficient for allN paths connecting Tx1 and Rx1 isthe summation of coefficients for allindividual clusters as shown below:

The number of clusters, N, is six inthe 3GPP SCM. The complete chan-nel matrix, H, for this simplified 2x2MIMO system is then related to eachcombination of transmit to receiveantenna pairs using the followingequation:

Having the complete channel matrix,

the calculation of the spatial correlation

matrix, R, is defined in reference [11]

as:

Here E{ } is the expected value. Thecalculation in equation (10) doesnot require the Kronecker product todetermine the correlation matrix butstill allows separation of the spatialproperties and the antenna gains asshown in Figure 8. As mentioned,the above-simplified expression forchannel matrix, H, does not includethe effects of time due to motion and

path delay. The actual time variantimpulse response for the MIMO chan-nel would have the form of H(t;),as shown in reference 3GPP TdocR4-091949 [10].

It will be shown when implementingthe SCM in the multiple test probeOTA test system, that a reduction inhardware complexity and cost can beachieved using a smaller number ofsub-paths at the expense of potentialuncertainty in the measurements.When implementing the SCM modelin the two-stage OTA system, all sixpaths, each with 20 sub-paths, can beeasily implemented within the AgilentN5106A PXB at a greatly reducedsystem cost and complexity.

hn, m(tx1, rx1) =

G(n, m, AoD)e G(n, m, AoA)e e

jkdtx sin (n, m, AoD) jkdRx sin (n, m, AoA) jn, m

(8)H(tx1, rx1)= hn, m (tx1, rx1)N

n=1

M

m=1

(9)H = H(tx0, rx0) H(tx0, rx1)

H(tx1, rx0) H(tx1, rx1)

(10)R = E {vec (H) vec (H)H}

Figure 8. Simplified calculation for the coefficient of the mth sub-path within the nth cluster.

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OTA Testing of MIMO Devices

Testing the radiated performance ofMIMO devices in a repeatable andcontrollable environment is verychallenging. Conducted tests can be

defined to measure the performanceof MIMO receivers, however, testsmay not emulate real life conditionsif the effects of antenna and spatialradiation are not included as part ofthe test. The purpose of OTA testingis to include the radiated characteris-tics of the multipath channel and theMIMO antenna during the measure-ment process. OTA testing can beused to identify whether the MIMOantenna design has acceptable per-formance over a wide variety of mul-

tipath environments. One challengeto OTA testing is to select a multipathchannel model that can be imple-mented in a practical measurementsystem without loss in accuracy. Ofthe two channel models discussed,correlation-based and geometry-based, several measurement configu-rations are available that approximatethese models and effectively measurethe radiated performance of theMIMO UE. It will be shown that dif-ferent OTA measurement techniqueswill have approximately the sameperformance and the selection of theOTA test system should be based onthe complexity, flexibility and cost tothe end-user.

In the ideal case, testing MIMOdevices would be as simple as testingSISO devices, but as discussed above,the MIMO performance is closelytied to the antenna performance andthe channels spatial characteristics,

thus making MIMO OTA testing muchmore challenging and potentiallycomplex. For example, the standard-ized OTA test method for a SISOdevice is conceptually simple, result-ing in a set of basic measurementsincluding antenna gain, TRS and TRP[5]. As shown in Figure 9, a typicalconfiguration for measuring a SISOantenna gain includes an anechoicchamber and a vector network ana-

lyzer (VNA), such as the Agilent PNASeries or ENA Series analyzers. Theantenna gain can easily be measuredusing the VNA when a direct connec-

tion to the UE antenna is available.For this configuration, a knownreference antenna and an associ-ated calibration procedure would berequired to remove path loss fromthe transmission measurement. Fora UE without internal access to theantenna, the UE could be placed in atest mode that supports capturing I/Qdata or a channel estimate associ-ated with the received signal. In thisconfiguration, the VNA is replacedwith a BS emulator when measuring

receive gain and a signal analyzer fortransmission gain. An Agilent E6621ABS emulator and N9020A MXA signalanalyzer can be used in this environ-ment. As the antenna gain is usuallyexpressed as a function of spatialangle, the azimuth and elevationgain performance is measured whilephysically rotating the UE. Also, whenpolarization effects are required, theUE antenna or the reference antennacan be rotated by 90 degrees.

When measuring the TRS of theUE receiver, a BS emulator is con-nected to the reference antennaand a separate connection is madeto the baseband control of the UEin order to measure bit-error-rate(BER), frame-error-rate (FER) and/orreceived power level. When measur-ing the TRP from the UE transmitter,a link antenna is connected to theBS emulator to independently controlthe operation of the UE while a signal

analyzer is used to measure thetransmitted power at the referenceantenna. The TRS and TRP are typi-cally averaged as the UE is physicallyrotated over various elevation andazimuth orientations to include theeffects of antenna gain. In somecases, the UE is attached to a SAMphantom to measure the proximityeffects to a human test model. Inaddition, these active measurements

can include time-varying effects ofa multipath channel by including achannel fader such as the AgilentN5106A PXB baseband generator and

channel emulator.

An important point concerning theaccuracy of the anechoic chambermeasurement is that while theanechoic material is typically con-structed of pyramidal RF absorbers,the sum of all non-ideal internalreflections from these absorbersand surrounding support structuresand test cables must be lower thanthe desired signal, otherwise theseundesired reflections will decrease

the accuracy of the radiated measure-ments. An anechoic chamber isdesigned to optimize a small areaaround the DUT with minimal internalreflections. This area is called thequiet zone of the anechoic chamber.This quiet zone is typically a functionof the chamber size and operatingfrequency and is usually optimizedso that the DUT would completelyfit inside this area for the highestmeasurement accuracy. When mea-suring large DUTs or a DUT againsta SAM phantom, the physical sizeof the chamber and associated quietzone must be considered. Ideally, thequiet zone is positioned far enoughaway from any reference or probeantenna in order to approximate afar-field or plane-wave propagation ofthe radiated test signals. The far-fieldapproximation would simulate theexpected operating environment forthe DUT.

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The test methodologies and metricsfor a SISO OTA measurement cannotbe directly extended to a MIMOOTA test system if the interactionsbetween channel and antennacharacteristics are to be included. Forthe MIMO antenna, not only will thereceived power imbalance at eachantenna influence the performance,but also the spatial correlations. Aspreviously discussed, the correlationdepends on antenna parameters,such as gain, element spacing andelement polarization as well as PASparameters such as AoA, AoD and

AS. The major challenge for MIMOOTA performance testing is to find ameasurement method that includesthe radiated performance of theMIMO antenna while operating ina realistic multipath environment.As previously shown, both thecorrelation-based and geometry-based models allow the antenna gainand the channels spatial propertiesto be independently determined and

used to estimate the MIMO capacity.This technique will provide a usefulmethod for measuring the OTA perfor-mance of a MIMO device.

Various systems and methods havebeen proposed to generate realisticpropagation environments for MIMOOTA testing. Three of the major testmethodologies will be addressedin the following sections of thisapplication note. One of the methodsrequires a reverberation chamber togenerate a rich propagation environ-ment [6], but this technique is limited

to uniform PAS. A second methodrequires multiple probe antennas sur-rounding the UE inside the anechoicchamber and, together with channelemulation, can achieve a variety ofmultipath conditions [6]. The issuewith the multiple test probe OTAmethod is that the number of probeantennas and RF channel emulatorsrapidly becomes very large in orderto achieve good accuracy. Add in the

capability for polarization diversity,and the resulting OTA test systemmay be very complex and costly. Thethird method is an extension over tra-ditional antenna gain measurementswhere the radiated performance ofthe MIMO antenna is first measuredusing a standard anechoic chamber.The second step in this methodcombines the measured OTA antennaperformance with the desired channelmodel using a channel emulator suchas the Agilent N5106A PXB. Thedesired FOMs for the MIMO UE arethen determined using a conducted

measurement having a direct con-nection between the UE and theemulator. This two-stage OTA method[6] is described in the next section ofthis application note.

Figure 9. Basic OTA test configuration for measuring antenna gain, TRS and TRP of SISO

and MIMO devices.

LinkantennaQuiet

zone

Referenceantenna

Testchamber

TRS

TRP

Anechoicmaterial

SISO or MIMO DUT

VNA

BER, FER

power

BS

emulator

BSemulator

Signalanalyzer

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MIMO OTA testing using thetwo-stage method

The two-stage OTA method is designed

to provide an accurate and cost effec-tive MIMO OTA measurement system

by combining the benefits of traditional

anechoic chamber radiated measure-

ments with the flexibility of a fading

channel emulator, such as the Agilent

N5106A PXB. The two-stage method

is based on the knowledge that the

antenna characteristics can be inde-

pendently measured and then math-

ematically combined with the desired

channel characteristics in the Agilent

N5106A PXB channel emulator. As

shown in equations (3) and (4) for the

correlation-based model, the respective

antenna gains at the transmitter and

receiver are independent factors in the

determination of the spatial correlation

coefficients and the associated channel

coefficients. A similar approach is

found when using the geometry-based

model. As shown in equation (8), the

antenna gain can also be introduced as

an independent parameter in the deter-

mination of channel coefficients. One

benefit to the two-stage method is thateither channel model, correlation-based

or geometry-based, can be produced

by the PXB channel emulator. By

measuring both models using the same

hardware and measured antenna gain

patterns, it is possible to compare the

MIMO performance using both channel

models. Details for implementing the

two-stage OTA method follow.

The first stage in the two-stage OTA

method requires measurements of the

antenna array gain pattern with theUE placed inside a standard anechoic

chamber as shown in Figure 10. The

array gain can be passively measured

using a VNA, such as the Agilent PNA

Series or ENA Series analyzers, when

direct access to the UE antenna ports

is available. When antenna ports are

not available, the UE array gain can be

actively measured using a BS emulator,

and a UE capable of providing I/Q

data or channel estimates. During UE

transmit array gain measurements, the

BS emulator can be connected to a

link antenna, as shown in Figure 9, As

in the SISO case, the chamber shouldbe equipped with a positioner, making

it possible to perform full 3-D far-field

pattern measurements for both the

transmit and receive antenna arrays.

The reference antenna should also be

capable of measuring two orthogonal

polarizations either through physical

movement of a linearly-polarized

antenna or through a pair of cross-

polarized antennas. For the MIMO

pattern testing, the equipment and

chamber requirements are the same as

that of a SISO antenna measurement.Once the antenna patterns are mea-

sured, they can be used by the channel

emulator to reproduce the UE antenna

influence during the second stage of

MIMO testing.

The second stage in the two-stage OTA

method requires a conducted test of the

UE using a BS emulator and a channel

emulator, such as the Agilent N5106A

PXB. The channel emulator combines

the actual measured or simulated 2D

or 3D antenna gains with the selected

MIMO channel model. The model can

be based on either the correlation orgeometry approximations of a rich mul-

tipath environment. The lower portion

of Figure 10 shows the measurement

configuration for this second stage of

UE testing. In this figure, a 2x2 MIMO

system is measured using a four-chan-

nel fading emulator. In general, as the

number of fading channels in the emu-

lator equals the number of transmitters

times the number of receivers at the

UE, the two-stage OTA method is one of

the most cost effective techniques. The

output from the two-stage method mayinclude BER, FER, channel coefficients

and correlation coefficients. From these

metrics the channel capacity can also

be calculated. It should be noted that

the two-stage method is capable of

characterizing a MIMO device for all the

FOM requirements previously shown in

Table 1 [12].

Figure 10. Test configuration using the two-stage OTA method for a 2x2 MIMO

device. Stage 1 requires measurements of array gain and Stage 2 combines the gain

measurements with the channel model in a conducted performance test.

Quietzone

Referenceantenna

Antenna

patterns

BSemulator

Channelemulator

BSemulator

MIMODUT

Conducted

Stage 1

Stage 2

BER, FER,H, R

MIMODUT

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There are several considerationsrequired when implementing thetwo-stage OTA method. The firstconsideration is related to the correla-

tion-based model and the associatedKronecker product used to separatethe transmitter correlation matrixfrom the receiver correlation matrixas shown in equation (2). Agilent hasfound that for real antenna patterns,the Kronecker assumption is not typi-cally valid and thus becomes an issuewhen attempting to combine theantenna patterns with channel model.Agilent has developed a unique corre-lation matrix calculation for arbitraryantenna patterns under multipath

channel conditions that improves theaccuracy of the Kronecker approach.Another consideration in the two-stage MIMO OTA method is that thefar field UE antenna patterns can beaccurately measured in order to fullycapture the mutual coupling betweenthe multiple antenna elements. Thiscan be accomplished with carefulcalibration of the anechoic chambertest system. One last consideration inthe two-stage OTA method concernsthe physical connection to the UEreceiver ports during the conductedtest stage. The UE must have thecapability to bypass the antennas andprovide a cabled connection to thechannel emulator as shown in Figure10. While this technique is especiallyattractive during the developmentphase of the UE, by allowing theability to quickly measure the MIMOperformance with various antennaconfigurations, it assumes that thereis minimal interaction between inter-

nal spurious emissions from UE radiohardware and the MIMO antennaarray.

As a comparison between acorrelation-based channel model andthe equivalent geometry-based modelusing only the two-stage OTA test

system, Table 3 shows the resultingcorrelation coefficients for the twochannel models. The MIMO systemused vertically polarized omni-direc-tional antennas at the BS array with asingle cluster modeled as a LaplacianPDF and AS of 2 degrees. The UEarray consisted of vertically polar-ized dipole antennas with antennapatterns shown in Figure 7a and asingle Laplacian PDF with AS of 35degrees. The antenna separation atthe BS and UE are two wavelengths

and 0.225 wavelengths respectively.

The geometry-based SCM modelimplemented 20 sub-paths for thesingle cluster and 50 drops were usedto provide a statistical average of the

matrix coefficients. The mean AoDand AoA were changed for each dropand randomly distributed over 360degrees. As shown in Table 3a and3b, the correlation coefficients forthe respective transmit and receiveantenna pairs are very close in value.Table 3c shows the differencesbetween these matrices. Most ofthe values in Table 3c are negative,which means that the correlationcoefficients from the SCM model areslightly lower than the correlation-

based channel coefficients.

Table 3a. Channel correlation matrix from SCM

Tx0-Rx0 Tx0-Rx1 Tx1-Rx0 Tx1-Rx1Tx0-Rx0 1.0000 0.6670 0.9519 0.6687

Tx0-Rx1 0.6670 1.0000 0.6496 0.9550

Tx1-Rx0 0.9519 0.6496 1.0000 0.6672

Tx1-Rx1 0.6687 0.9550 0.6672 1.0000

Table 3b. Channel correlation matrix from correlation-based model

Tx0-Rx0 Tx0-Rx1 Tx1-Rx0 Tx1-Rx1Tx0-Rx0 1.0000 0.7050 0.9547 0.6721

Tx0-Rx1 0.7050 1.0000 0.6721 0.9547

Tx1-Rx0 0.9547 0.6721 1.0000 0.7050

Tx1-Rx1 0.6721 0.9547 0.7050 1.0000

Table 3c. Difference between SCM and correlation-based model (Table 3a Table 3b)

Tx0-Rx0 Tx0-Rx1 Tx1-Rx0 Tx1-Rx1Tx0-Rx0 0 -0.0380 -0.0027 -0.0034

Tx0-Rx1 -0.0380 0 -0.0225 0.0003Tx1-Rx0 -0.0027 -0.0225 0 -0.0378

Tx1-Rx1 -0.0034 0.0003 -0.0378 0

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To create a measurement exampleof the MIMO capacity as a functionof the UE orientation using the two-stage OTA test method, a commercial

MIMO USB dongle was connectedto a pair of dipole antennas. Themeasured antenna pattern for eachelement is shown in Figure 11a. Theantenna patterns were also measuredagainst a SAM phantom with theresults shown in Figure 11b. It isnoted that there are large changes to

the measured dipole patterns in thepresence of the SAM head model andit is expected that this will greatlyaffect the MIMO performance. The

two-stage OTA method implementedthe rural macro SCM running insidethe Agilent N5106A PXB channelemulator [13]. The antenna patternswere incorporated into the channelmodel and the MIMO capacity wasestimated with the UE rotated over180 degrees in 10 degree steps. The

measured MIMO capacity is shown inFigure 11c, illustrating that the SAMphantom not only has a large influ-ence on the antenna gain patterns,

but also on the measured capac-ity as a function of UE orientation.Additional measurement examples forspatial correlation and channel capac-ity using the two-stage OTA methodwill be compared to the multipletest probe OTA method later in thisapplication note.

Figure 11. (a) Measured antenna patterns for a 2-element dipole array using the two-stage OTA method, (b) measured antenna pattern

for the same array in the presence of a SAM phantom and (c) measured 2x2 MIMO capacity using these two arrays at the UE.

12.0

11.5

11.0

10.5

10.0

9.5

9.0

8.5

0 20 40 60 80

Dipole array with SAM

Orientation (deg)

(c) Measured capacity using two-stage method

(b) Dipole array with SAM

90

0.4

0.2

MS antenna #2

MS antenna #1

0.6

0.860

30

0

330

300

270240

210

180

150

120

(a) Dipole array

90

0.4

0.2

MS antenna #2

MS antenna #1

0.6

0.860

30

0

330

300

270

240

210

180

150

120

Channelcapacity(b/s/Hz) Dipole array

100 120 140 160 180

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Figure 12. Test configuration for the multiple test probe OTA method using an anechoic chamber and channel emulator. Probe antennasare grouped to emulate the desired AoA and associated AS.

MIMO OTA testing usingmultiple test probes

A second OTA test method using

an anechoic chamber includes alarge set of probe antennas placedwithin the chamber and positionedaround the MIMO DUT. The multipletest probe OTA method attempts toemulate the receive-side AoA and AScharacteristics that would be radiatedfrom several multipath clusters. Thespatial characteristics from the BS,such as AoD and AS, are emulatedusing a channel emulator such as theAgilent N5106A PXB and associatedMXG signal generators connected to

the multiple test probes. This OTAmethod approximates a MIMO chan-nel using a geometry-based channelmodel such as the 3GPP SCM.

Figure 12 shows the configurationof the multiple test probe OTA testsystem using an anechoic chamberwith eight probe antennas placeduniformly around the MIMO UE. Eachprobe antenna emulates a sub-pathin the geometry-based cluster model.Several test probes are often groupedto approximate the AS of a singlecluster. The probes are excited atdifferent angular positions around theUE to emulate a specific AoA. Whileradiation from the probes approxi-

mate the OTA signals arriving at theUE, individual channel emulators arecabled to each probe to emulate theeffects of BS spatial correlation, path

delay, path fading and Doppler. If dualpolarized antenna measurements arerequired, the number of probe anten-nas and channel emulators woulddouble. Figure 12 shows a BS emula-tor and a channel emulator, such asthe Agilent N5106A PXB, configuredto create the faded test signals foreach sub-path, as well as a set ofAgilent MXG signal generators toupconvert the faded baseband signalsto the required RF carrier frequency.

Quiet zone

Probeantennas

BER, FERpower

Channelemulator

Signal Gen.

Signal Gen.

Signal Gen.

Signal Gen.

Signal Gen.

Signal Gen.

Signal Gen.

Signal Gen.

BSemulator

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There are several challenges facing

OTA test methodologies that attempt

to fully emulate multipath fading

using multiple probe antennas within

an anechoic chamber. As previouslymentioned, geometry-based approxi-

mations to a MIMO channel can be

implemented using either a sum-of-

sinusoids technique or a quantized PAS

with unequal amplitude sub-paths. Due

to practical concerns over equipment

complexity, lengthy calibration and test

times, as well as potential high cost, a

reduced number of test probes is often

preferred, resulting in the use of the

quantized PAS approximation for the

channel model. When approximating

the PAS with a limited number of testprobes, the probe spacing and power

levels need to be optimized in order to

achieve a realistic test environment.

System simulations have shown that a

reasonably accurate test method can be

achieved with a reduced number of test

probes. For example, a simulation using

three test probes grouped together to

represent one cluster in the channel

model showed that the simulated

channel characteristics are very close

to the theoretical model that used 20

sub-paths. In this case, the simulated

and theoretical channel characteristics

were compared for spatial correlation

coefficient, Rayleigh statistics and

fade depth [14]. It will be shown that

measured results using three test

probes will not be as accurate as the

simulations, possibly due to sensitivity

to errors in chamber calibration and

probe location. Measured throughput

data using this configuration will be

provided later in this application note

along with comparisons to the two-stage OTA method.

Another challenge to implementing

the multiple test probe OTA method

includes optimization of the anechoic

chambers quiet zone. It is also known

that the size of the quiet zone can

be increased with the introduction of

additional test probes. The size of the

quiet zone should be approximately one

wavelength when testing UE handsets

but would need to increase to approxi-

mately four wavelengths when testing

laptops or a handset attached to a SAM

phantom [15]. In this case, the chambermay be physically larger using the

multiple test probe OTA method than a

chamber required for traditional SISO

and the two-step OTA method.

Agilent has measured the throughput

of a commercially available MIMO

device using the multiple test probe

OTA method having a single cluster

channel model with a Laplacian PAS

and AS of 35 degrees at the UE. Figure

13a shows the test configuration using

four probe antennas, representingfour sub-paths, at a 40 degree angular

spacing, and centered on the desired

AoA. Using a simulation for this specific

test configuration, the relative power

levels across the four probes were

optimized to match the statistics of a

theoretical model based on the 20-path

sum-of-sinusoids approach. As the

total power level over all antennas is

normalized to one, the simulated power

levels resulted in a relative power of

0.13 for antennas #1 and #4 and 0.37

for antennas #2 and #3. Figure 13b

shows the angular and power distribu-

tion for each sub-path in the quantized

PAS implementation. It should be noted

that the signals applied to each probe

have independent Rayleigh fading

statistics created using a four-channel

Agilent N5106A PXB fading emulator

and four MXG upconverters. The test

system was calibrated using a known

reference antenna to account for varia-

tion in the path loss as a function of

angle for each test probe. The MIMODUT was an 802.11n network card with

two antennas. The TCP/IP throughput

was measured as a function of angle

at three power levels over the range of

-34 dBm to -14 dBm. Figure 14 shows

the measured throughput for this single

cluster channel as the DUT was rotated

over 360 degrees in the horizontal plane

at 30 degree increments. As shown in

the figure, the measured throughput is

sensitive to AoA and power level. As

expected, the measured results show

that throughput can be quite high whenthe received power level, and associ-

ated SNR, is also high at each MIMO

antenna. During the testing phase,

it was discovered that the statistical

average for throughput converged

only when a very large number of

measurement points were taken for

each position of the DUT. It should be

noted that, for the same fading model

(sum of sinusoids), the measurement

times are comparable between the

multiple test probe OTA method and the

two-stage OTA method. It should also

be noted that the setup and calibration

time of the anechoic chamber using

the multiple test probe OTA method is

typically 1-2 days while the chamber

calibration and antenna measurements

are complete in approximately 1 hour

using the two-stage OTA method.

Figure 13. Probe antenna angular configuration and relative antenna power weights to

approximate a single Laplacian PAS with AS of 35 degrees.

#2

4040

MIMODUT

(a) Probe antenna configuration (b) Laplacian approximation

Angle (deg.)

40

AoA#3

#4

60 20 +20 +60

#40.13

#10.13

#30.37

#20.37

#1 AoA

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A second set of throughput measure-ments using the configuration shownin Figure 15a was performed with achannel having two multipath clus-

ters. In this case, the four test probeswill be shared between the twoclusters. The relative cluster delay isset to 200 ns using the PXB channelemulator. As shown in Figure 15a, theAoA for each cluster is centered onprobe antennas #2 and #3, respec-tively. For this configuration, the ASfor each cluster is emulated usingthree probe antennas, and the powerweights are chosen to maintain a35 degree AS. The narrow spreadof the AoA requires that two of the

probes, #2 and #3, combine signalsfrom both clusters. The test probesrelative angular positions and powerweights are shown in Figure 15b. Inthis configuration, probe antennas#1-#3 are associated with AoA1 andhave relative power weighting of 0.26,0.48 and 0.26 respectively. Probes#2t-#4 have the same relative powerdistribution.

The measured throughput for thesame MIMO device is shown inFigure 16. When the power level isset to -14dBm, the two-cluster chan-nel model achieves a much higherthroughput than single cluster model,confirming that a richer multipathchannel will improve the MIMO per-formance. When the power level isreduced to -24 dBm and -34 dBm, theresults for the two-cluster channelare very similar to the single clusterchannel model, but with slightlylower throughput for the two-cluster

channel. The difference betweenthe measurements is due to theuncertainty of the TCP/IP throughputestimates. At these lower powerlevels, the receiver SNR is too low forMIMO multiplexing to be effective,and switching to beamforming and/or other antenna diversity techniquesmay improve the system performance.

Figure 14. Measured throughput for commercial MIMO device using for single cluster channel.

Figure 15. Probe antenna angular configuration and relative antenna power weights to

approximate a two-cluster Laplacian PAS with AS of 35 degrees.

Figure 16. Measured throughput for commercial MIMO device using a two-cluster channel

with relative 200 nsec excess delay.

Power = 14 dBm

Throughput(Mbps)

Orientation (degree)

00

2

4

6

8

10

12

14

16

18

20

50 100 150 200 250 300 350

Power =24 dBm

Power =34 dBm

Power = 14 dBm

Through

put(Mbps)

Orientation (degree)

00

5

10

15

20

25

30

50 100 150 200 250 300 350

Power = 24 dBm Power =34 dBm

#2

4040

MIMODUT

(a) Probe antenna configuration (b) Laplacian approximation

Angle (deg.)

40

AoA

#3

#4

60 20 +20 +60

0.26

0.48

0.26

0.26

0.48#1

AoA1 AoA2

AoA

#10.26

#1

#2 #3

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MIMO OTA testing using areverberation chamber

A third OTA measurement technique

that has been proposed to evaluateMIMO performance operating in real-istic fading channels makes use of areverberation chamber. A reverbera-tion chamber is a large metal cavitywithout absorbers that is sized tosupport numerous cavity modes. Themodes are stirred with metallic platesthat rotate or move during the testingphase. Movement of the plates willcreate Rayleigh distributed signalpaths between reference antennasand the MIMO DUT. Figure 17 showsthe configuration for measuring theOTA performance of a 2x2 MIMO sys-tem using a reverberation chamberwith two wall antennas. The insideof the chamber is completely metallicand shielded from any extraneoussignals. The number of wall antennasis the same as the proposed numberof BS antennas. In Figure 17, thetwo BS antennas are connected toa BS emulator. Figure 17 also showsa single metallic mode-stirrer, but

often several stirrers are required tomove or rotate during OTA test. Inaddition, the MIMO UE may be placedon a rotating platform to improvethe chambers fading performance.The reverberation chamber andassociated mode-stirrers create athree-dimensional uniform Rayleighfading environment around the UE.The interaction between the BSantennas and the metallic cavity willinfluence antenna correlations. OTAmeasurements using a reverberation

chamber resulted in a higher MIMOcapacity when compared to thetwo-stage OTA method [16]. Thedifference may result from the factthat the reverberation chamberpresents a uniformly distributed PASin three-dimensions that is optimizedfor an indoor environment, especiallywhen compared to a channel that ismodeled for an outdoor environment.On the other hand, the reverberation

chamber is useful when evaluatingMIMO devices targeted for indoorenvironments where the spatialdistributions tend to result in three-

dimensional PAS distributions.

To improve the capability of thereverberation chamber OTA method,a channel emulator can be used tointroduce an increased power delayprofile (PDP), Doppler spectrum andspatial correlation at the BS antennas[6]. In this case, the basic measure-ment configuration is identical to theconfiguration shown in Figure 17, butthe Agilent N5106A PXB introduceschannel fading of the BS transmitted

signals. It should be noted that thecombined channel characteristics area convolution of the reverberationchambers multipath channel andthe channel created by the channel

emulator. In general, reverberationchambers tend to be physicallysmaller and lower cost than anechoicchambers. Since the channel is

isotropic, there is no need to rotatethe DUT during the test, thus the totalmeasurement time using a reverbera-tion chamber will be the shortest ofthe three OTA methods. Whenattempting to compare the measuredspatial correlation between differentOTA methods, the limited flexibilityin configuring the AoA and AS whenusing the reverberation chambermethod makes it difficult to comparethese results to the measurementsrecorded using other OTA systems.

However, the reverberation chamberhas demonstrated the ability to rank-order devices equipped with receivediversity according to their relativethroughput performance.

Figure 17. Test configuration for a 2x2 MIMO system using a reverberation chamber.

Quietzone

BSemulator

BER, FER,power

Mettalicwalls

MIMODUT

Modestirrer

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To compare the measured perfor-mance using the two-stage OTAmethod and the multiple test probeOTA method, a 2x2 MIMO system

is implemented using a two-clusterchannel model with Laplacian PASand AoAs at -27.2 and +27.2 degreesand AS of 35 degrees [17]. The two-stage method is configured using thesystem described in Figure 10 andthe multiple test probe method isconfigured using the system shownin Figure 12, but is implemented withonly four test probes as shown inFigure 15. For all measurements, theOTA test systems were configuredwith vertically polarized antennas.

In this case, the multiple test probemethod required twice the numberof PXB channels and signal genera-tors than the two-stage method. Ifboth vertical and horizontal antennapolarizations were required, then themultiple test probe method wouldrequire four times the number ofPXB fading channels and signalgenerators. When measuring bothpolarizations using the two-stagesystem, the only addition is to include

the measurement of vertical and hori-zontal antenna patterns during thefirst stage of test. It is this reducedsystem complexity and cost that

makes the two-stage OTA method anattractive solution when character-izing MIMO device performance.

For these measurement comparisons,the two-stage OTA method beginswith basic antenna pattern measure-ments of the two UE antennas testedover an angular range of 180 in azi-muth. The next step in the two-stagemethod is to combine the antennapatterns with the desired two-clusterchannel model inside the Agilent

N5106A PXB channel emulator. Thetwo-stage method implementedtwo different channel models: thefirst model where the PXB createsthe desired two-cluster multipathenvironment using a correlation-based Laplacian PAS and a secondmodel where the PXB implements ageometry-based SCM using a 20 sub-path sum-of-sinusoids approximation.

The multiple test probe OTA methodimplemented the two-cluster channelmodel using a quantized PAS mappedto four antennas positioned around

the UE as shown in Figure 15. For thismeasurement, the angular separationbetween test probes was set to54.4 degrees noting that Figure 15shows the separations at 40 degrees.The change in angular positionrequired a complete recalibration ofthe path loss and readjustment ofthe probe power levels in order toachieve reasonable approximationbetween the quantized PAS and thedesired SCM using 20 sub-paths. Asshown in Figure 15, each cluster is

approximated using three Rayleighfaded sub-paths [17]. Rayleigh fadingis created at each test probe usinga separate channel from the AgilentN5106A PXB. Also included is asimulation of a quantized LaplacianPAS model, as implemented in themultiple test probe system. Thistheoretical simulation is includedas a comparison between all threemeasured results.

Experimental Validation of the Two-Stageand Multiple Test Probe OTA Methods

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Figure 18. Real (a) and imaginary (b) components of the correlation coefficient between two UE antennas as a function of orientation angle.

Multi-probe SCMTheorectical SCM

Two-stage correlation

Orientation (degrees)

(a) Real part

Realpartofcorrelationcoefficient

1500.8

0.6

0.4

0.2

0.2

0.4

0.6

0

100 10050 500 150

Two-stageSCM

Multi-probe SCM

TheorecticalSCM

Two-stage correlation

Orientation (degrees)

(b) Imag. part

Imag.partofcorrelationcoefficient

1501

1

0.80.6

0.2

0

0.8

0.6

0.4

0.2

0.4

100 10050 500 150

Two-stageSCM

The real and imaginary componentsfor the measured and theoreticalspatial correlation between the twoUE antennas as a function of UE

orientation are shown in Figure 18.Comparing the test results betweenthe two models implemented inthe two-stage OTA method, thecorrelation coefficient terms usingthe geometry-based SCM are nearlyidentical to those using the correla-tion-based model implying that the

sum-of-sinusoids technique using 20sub-paths has similar measurementaccuracy to the correlation-basedmodel. The theoretical simulation of

the quantized Laplacian PAS havingthree Rayleigh faded sub-paths alsodemonstrates reasonable trackingto the measured results usingthe two-stage OTA system. Themeasurements using the multipletest probe OTA method shows thelargest discrepancy when compared

to the other results. It is probablethat the measurement accuracy usingthe quantized PAS approximationis sensitive to uncertainty in the

chamber calibration and probe loca-tion. Increasing the number of testprobes will improve the measurementaccuracy at the expense of greatersystem complexity and higher imple-mentation cost.

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The last set of measurementscompare the average throughput ofthe commercial two-antenna HSDPAMIMO network card using the two-

stage OTA method and the multipletest probe method. The throughputmeasurements were made with thecard configured for 1x2 diversityand Hset 3. The maximum possible

throughput in this configuration is2332kbps. Figure 19 shows that thetwo measurements are effectivelythe same. While it is unlikely that

throughput measurements will everbe identical using the same MIMOdevice tested under different OTAmethods, the important requirementis that the selected OTA system is

capable of determining a goodMIMO device from a bad one. Inaddition, the selected OTA test sys-tem will require a trade-off between

measurement speed, cost, systemcomplexity and realistic operatingconditions.

Figure 19. Comparison of the measured MIMO throughput using the two-stage OTA

method and the multiple test probe OTA method.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-80dBm -82dBm -84dBm -86dBm -88dBm -90dBm -92dBm -94dBm

kbps

Throughput comparison Dell E6400 Single cluster, AS=35, V=3km/h

Multiple Probe

Two Stage

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Conclusion

This application note outlined thechannel models and test methods formeasuring the performance of MIMOdevices in realistic environments

using over-the-air test conditions.Three predominant OTA methodswere described and test results werepresented. While the reverberationchamber method is one of the fastestand lowest-cost OTA measurementtechniques, it is limited to uniformlydistributed multipath channels. Themultiple test probe OTA method hasthe flexibility of emulating a varietyof multipath conditions and does notrequire access to the UE antennaports, however, this method can

become highly complex and costlyto implement especially when dual

polarized antenna measurementsare required. The multiple test probeOTA method also has the longestcalibration and measurement times

as well as the largest chamberrequirements of the three OTAsystems examined. The complexityand cost of the multiple test probesystem can be reduced when usinga smaller number of probe antennas,but system accuracy becomes sensi-tive to calibration and measurementerrors. The two-stage OTA methodcomes closest to emulating the fullmathematical models for a MIMOchannel with a choice of either thecorrelation-based or geometry-based

channel model. The two-stage OTAmethod has the advantage of reduced

complexity and cost as well as fastersystem calibration and test timewhen compared to the multiple testprobe method. The disadvantages to

the two-stage OTA method are therequired access to the antenna portsand the lack of potential receiver-to-receiver cross-coupling and antennainteractions. Even with these short-comings, excellent correlation existsbetween the two-stage OTA methodand the multiple probe OTA methodusing commercially available MIMOdevices.

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References

[1] Agilent Application Note, "MIMO Wireless LAN PHY Layer [RF] Operation & Measurement," April 2008, 5989-3443EN

[2] Agilent Application Note, "MIMO Receiver Test Accurately Testing MIMO Receivers Under Real-World Conditions,"

January 2010, 5990-4045EN

[3] Agilent Application Note, "MIMO Channel Modeling and Emulation Test Challenges," January 2010, 5989-8973EN

[4] 3GPP TR 25.996 v6.1.0 (2003-09) 3rd Generation Partnership Project; Technical Specification Group Radio Access Network;

Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 6)

[5] 3GPP TS 34.114 V8.3.0 (2009-12) Technical Specification 3rd Generation Partnership Project; Technical Specification Group Radio

Access Network; User Equipment (UE)/Mobile Station (MS) Over-The-Air (OTA) antenna performance; Conformance testing (Release 8)

[6] 3GPP TR 37.976 V1.1.0 (2010-05) "Measurement of radiated performance for MIMO and multi-antenna reception for HSPA and

LTE terminals" (Release 10)

[7] Kermoal, J.P.; Schumacher, L.; Pedersen, K.I.; Mogensen, P.E.; Frederiksen, F., A stochastic MIMO radio channel model with

experimental validation, IEEE Journal on Selected Areas in Communications, Volume 20, Issue 6, 2002, Page(s): 1211 1226

[8] 3GPP TR 25.996 V6.1.0 (2003-09) Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 6)

[9] Xiao, H., Alister G., "Full channel correlation matric of a time-variant wideband spatial channel model, The 17th Annual IEEE

International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06), 2006

[10] 3GPP TSG-RAN WG4, Tdoc R4-091949, Agilent Technologies, Applying measured MIMO antenna patterns to MIMO channel models

for OTA analysis, San Francisco, CA, May 2009

[11] Ozcelik, H.; et al, "Deficiencies of 'Kronecker' MIMO radio channel model," Electronics Letters, Volume: 39, Issue: 16, 2003

[12] COST 2100 TD(09) 924, Agilent Technologies, "Two-stage MIMO OTA method," Vienna, Austria, Sept. 28-30, 2009

[13] COST 2100 TD(10) 10049, Agilent Technologies: "Test MIMO Antenna Effects on a MIMO Handset Using Two-stage OTA Method,"

Athens, Greece, Feb. 3-5, 2010

[14] 3GPP TSG-RAN4 R4-091362, Spirent Communications:Practical MIMO OTA Testing, Seoul, Korea, March 2009

[15] 3GPP R4-094678, Elektrobit:, Optimum number of antennas in MIMO OTA system, Jeju, Korea, November 9 13, 2009

[16] Garcia-Garcia, L., et.al., "MIMO capacity of antenna arrays evaluated using radio channel measurements, reverberation chamber and

radiation patterns," IET Microwave Antennas Propagation, December 2007, Volume 1, Issue 6, p.11601169

[17] 3GPP TSG-RAN WG4, Tdoc R4-093095, Agilent Technologies, "Experimental validation of two-stage MIMO OTA method versus

SCM approximation method, ShenZhen, China, August 2428, August 2009

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