Measurement Analysis of Spatial and Temporal Correlationin Wideband Radio Channels with Adaptive Antenna Array

P. Karttunen1, K. Kalliola2, T. Laakso1, and P. Vainikainen2

1Helsinki University of TechnologyIRC/Laboratory of Telecommunications Technology

Otakaari 5A, FIN-02015 Espoo, FinlandE-mail: Petri.Karttunen@hut.fi,

Timo.Laakso@hut.fi

2Helsinki University of TechnologyIRC/Radio Laboratory

Otakaari 5A, FIN-02015 Espoo, FinlandE-mail: kka@radio.hut.fi

pva@radio.hut.fi

ABSTRACT

This paper investigates the spatial and temporalcorrelation by measurements of an 8-element adaptiveantenna array. The channel measurement data isgathered at a 2.154 GHz range outdoor radio channel.The measurement analysis is divided into threedifferent categories: Investigation of spatial correlationbetween antenna elements at the base station (BS),spatial correlation of different mobile station (MS)locations and temporal correlation of the differentmultipath components. Also the differences in thecorrelation coefficient functions by using the complex-valued taps instead of the magnitude-valued taps arestudied at the BS. The measurement analysis revealsthat signals strongly correlate in the nearby BS antennaelements. However, at the different MS locationsuncorrelated signals can be received when the physicalseparation is larger than half a wavelength. Themultipath components in the impulse response profilebecome temporally uncorrelated after the excess delayvalues of 50 ns.

1. INTRODUCTION

One way to increase system capacity in futuretelecommunication systems is to employ adaptive antennatechnologies. The adaptive antenna array processingtechniques are sensitive to correlation properties of signals.Correlated signals exist especially in the uplink case (fromMS to BS) where scattering near the MS is a commonphenomenon. These signals have the tendency to impingeon the antenna within a small angular spread and thereforebecome correlated even for larger antenna separations [1].When the correlation between elements is significant, thesignals at different elements fade at the same time.Spatially strongly correlated signals make it difficult forthe antenna processing methods to utilize the spatialstructure of the channel. Thus, correlated fading reducesthe performance of any diversity reception method.

In this paper, we examine the spatial and temporalcorrelation properties of a typical outdoor propagationradio channel based on the measurement data. The paper isorganized as follows: Section 2 presents the mathematicalmodel for the measured radio channel. In Section 3, the

measurement system setup and the propagationenvironment are described. Section 4 analyzes themeasurement results. Finally, in Section 5, the conclusionsare drawn about the analysis results of the correlationproperties of the channel.

2. CHANNEL MODEL

In this section the general multipath channel model andthe correlation models are presented. The typical radiopropagation environment is characterized by numerouspropagation mechanisms like scattering from the nearbyirregularly located buildings [2]. The radio channel modelcan be adequately described by the linear finite impulseresponse (FIR) filter model. The complex-valued impulseresponse of a time invariant wide-band channel can beexpressed as

( )h a eij

ii

Ii( )τ δ τ τφ= −

=

−

∑0

1

(1)

where ai is the path amplitude, φi is the path phase and τi

is the path arrival delay with respect to the first arrivedmultipath component. The total number of resolvedmultipath components is denoted by I. Figure 1 illustratesthe impulse response model. The multipath component isassumed to exist in the impulse response profile at theparticular excess delay range [τi, τi+1] if the total multipathpower is greater than the detectable signal power ofreceiver. The different multipath components receivedduring the bin duration cannot be resolved by the receiverand are merely either added or multiplied vectoriallytogether [3][4].

…

(a 2,φ 2)

(a 1,φ 1)

(a 0,φ0)

(aI -1,φI -1)

τ0

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t

h (t)

Figure 1 Impulse response channel model

The obtained channel tap values are defined formathematical convenience as Apin where p (p=1, …, P) isthe profile index, i (i=1, …, I) is the excess delay in thegiven profile and n (n=1, …, N) is the antenna elementindex. Figure 2 illustrates a possible variation of the tapvalues in the impulse responses at the measurement route.The small changes in the transmitter locations result onlyin small variations in the amplitude values of theindividual multipath components. This small-scale signalfading governs the statistics of the amplitude variations ofindividual multipath components and is a prevailingphenomenon only in a small area ranging to distances ofcouple of wavelengths. A Rayleigh fading process has beentypically used to model rapid small-scale amplitudefluctuations for non-line-of-sight (NLOS) environments orRice distribution when specular or line-of-sight (LOS)component is present [4]. However, the empirical studiessuggest that the behavior of the individual channel taps inthe impulse response profiles can be still better explainedby the log-normal statistics [4].

…Profile 2

…

…

λ/4

Channel 1

Profile 1

Profile P

Figure 2 Illustration of tap variations in the channelimpulse responses along the measurement route

Both the spatial and temporal correlation properties ofmultipath components have been explored by manyauthors, for example by Rappaport et al. in [5] and Dossiet al. in [6]. The correlation research work here has beenrefined by taking into account the complex valued taps andis especially extended to include the adaptive antennaarrays. Spatial correlation function measures the amplitudecorrelation between different antenna elements and iscaused by the signal scattering around the transmitter asseen from the base station. The spatial correlation definesthe level of correlation at two different antenna elements nand n’ at the same excess delay index τi. The spatialcorrelation ρs between two linearly dependent randomvariables Apin and Apin’ which are either complex-valued ormagnitude-valued can be computed from the formula ofPearson’s correlation coefficient [7] as

[ ][ ] [ ]

ρs

E

E E=

− −

− −

( )( )

( ) ( )

’ ’

’ ’

A A A A

A A A A

pin pin pin pin

pin pin pin pin2 2

(2)

Temporal correlation function measures the amplitudecorrelation between different excess delays τi and τi’ in thesame channel impulse response profile extracted from aparticular antenna element. The temporal correlation iscaused by propagation path differences of multipathcomponents. The temporal correlation ρt between twolinearly dependent random variables Apin and Api’n can becomputed from a formula similar to Eq. (2) as

[ ][ ] [ ]

ρt

E

E E=

− −

− −

( )( )

( ) ( )

’ ’

’ ’

A A A A

A A A A

pin pin pi n pi n

pin pin pi n pi n2 2

(3)

For the obtained correlation functions the exponentiallydecaying curves was fitted at the MS end

f t Ae CBt( ) = −− (4)

where A, B and C are constants to be determined accordingto the minimum mean square error (MMSE) criterion [9].The assumption of uniform scattering around the MSresults in Bessel functions [2] which can be modeled by theexponential functions for small lag values. For generatingexponentially correlated signals auto-regressive movingaverage (ARMA) models of different orders can beutilized.

3. MEASUREMENT SYSTEM

The used measurement system is based on a complexwideband radio channel sounder and a fast RF switch torecord the channel impulse responses (IR) from multipleantenna elements [8]. The bandwidth of the receiver of thesounder is 100 MHz at carrier frequency of 2154 MHz.The chip frequency of the modulating pseudo noise (PN)code in the transmitter can be selected between 2.5 and 60MHz. The received demodulated signal is divided into Iand Q branches and sampled with two 120 Ms/s A/D -converters. The signal samples from every antenna elementare then stored for off-line processing to obtain thecomplex IR of the channel. The length of a continuousmeasurement run is limited by the size of the memorybuffer of the sampling card (currently 2×4 Mbytes for I andQ) and depends on the length of the used PN-code in thetransmitter. The maximum number of recorded impulseresponses is determined by the memory buffer of 8 Mbytes,which is used to store the signal samples beforetransferring to a hard disk.

BS antenna was connected to the receiver of the sounderthrough the element switching unit and located at a fixedposition while the transmitter was positioned on a cartmoving at a constant velocity. IRs were recorded from eachelement of the array while the cart was moving. The BSantenna array was a vertically polarized 8-element array ofmicrostrip patch elements with λ/2 spacing. Thebeamwidth of the element limits the maximum viewable

sector of the array to approximately 120°. Anomnidirectional discone antenna was used at the MS. Thetransmitter power level was 41.8 dBm. The measurementparameters are shown in Table 1.

Table 1 Parameters of measurement systemParameter Value

Carrier frequency 2154 MHzChip frequency of PN code 30 MHzSample rate 120 MHzCode length 63Delay resolution 33 nsDelay window 2.1 µsElement switching rate 238.1 kHzNumber of array elements 8Samples / element / wavelength 4Samples / element / m 28.7MS speed 0.4 m/sBS antenna height 11.5 mMS antenna height 1.8 mNumber of measured array IRs 990Length of MS Route 34.5 m

The measurements were carried out in the campus area ofHelsinki university of technology (HUT) in Espoo,Finland. The BS antenna array was located on the roof ofthe 3-storey building of the Department of Electrical andCommunications Engineering (see Figure 3). At the timeof the measurement there were no moving objects in theenvironment other than the MS. The average distance fromthe transmitter to the receiver was 60 m.

5 0 m

T x R o u te0 ° D i re c t io n S

R x

Figure 3 Illustration of measurement site

4. MEASUREMENT RESULTS

In this section both the spatial and temporal correlationproperties are analyzed based on the measurement results.The measurement data is from the uniform linear array(ULA) antenna system where the first element has beenused as the reference element. The threshold value of 25dB from the maximum amplitude was set for each impulseresponse profile in order to remove correlated noise causedby the measurement system setup. The components left inthe impulse response profile are the LOS component andthe reflected components from the nearby wall. In thetemporal correlation case the processing of the results has

been started from the first arrived multipath component,i.e., from the LOS component.

4.1 Spatial correlation at the BS end

Figure 4 shows the spatial correlation results between theantenna elements at the BS end. Eq. (2) was utilized forcalculating the spatial correlation function. The absolutepower value of each tap in the impulse responses wasconsidered. The correlation is computed here by taking theimpulse response values in each excess delay from thereference element and comparing them to the nearbyelements in the array from each measurement point alongthe measurement route. Figure 4a) shows the spatialcorrelation function as a function of route distance and thephysical antenna separation of (n-1)λ/2 wavelengths withrespect to the reference element. The result plot shows thatthe correlation changes only very little as a function of theroute distance. Figure 4b) shows the results whencorrelation coefficient functions have been averaged alongthe route. The resulting plots show that the spatialcorrelation function has strong correlation at shortdistances between antenna elements. High correlation iscaused by the presence of LOS component in the impulse

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Figure 4 Spatial correlation coefficient functions based onthe magnitude values of the channel taps at the BS. a)Spatial correlation coefficient function as a function ofantenna element index n and route distance b) Averagespatial correlation coefficient function as a function ofantenna element index n.

response profiles. The amplitude values of taps are morecorrelated than the complex-valued taps because the phasechanges are more sensitive to the small changes in thetransmitter locations. This effect is confirmed by the plotsof Figure 5 where the same analysis was performed butwith the complex-valued taps.

4.2 Spatial correlation at the MS end

Figure 6 shows the results for the spatial correlation at theMS end. The spatial correlation is calculated here as thecorrelation of magnitude-valued channel taps for profilesobtained at different locations with the same excess delaystaken from the reference element. The obtained spatialcorrelation functions have been averaged along themeasurement route. Figure 6a) shows the spatialcorrelation as a function of excess delay τi and the physicaltransmitter separation distance. The resulting plot showthat the correlation values are naturally close to zero whenthere is no component in the particular excess delay. It canbe also seen the existence of LOS and reflectedcomponents from the spatial correlation function as ahigher correlation level. Figure 6b) shows the average

correlation function. The spatial correlation function hasreduced to a very small correlation level after the physicaldistance of 0.5λ. The exponentially decaying correlationfunction has the parameters A=0.9706, B=2.3529 and C=-0.0196.

4.3 Temporal correlation

Figure 7 shows the results for the temporal correlation.The temporal correlation was computed from Eq. (3)where only the measurement data from the referenceelement was taken into account. The results for otherantenna elements were similar and were not subsequentlyconsidered. The computation of the correlation function isaccomplished by taking 7 measurement valuesencompassing one small-scale local area. The obtainedcorrelation functions were averaged along each local areain the measurement route. Figure 7a) shows the temporalcorrelation function where the excess delay difference isdefined as τi-τi’ , i>i’ and the excess delay as τi’ , i’ ≥0. Theexcess delay τ0 corresponds to first arrived multipathcomponent. From the result plot it can be observed thepresence of LOS and reflected components as higher

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Figure 5 Spatial correlation coefficient functions based onthe complex channel taps at the BS. a) Spatial correlationcoefficient function as a function of antenna element indexn and route distance. b) Average spatial correlationcoefficient function as a function of antenna element indexn.

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Measured correlation functionFitted exponential curve

Figure 6 Spatial correlation coefficient functions based onthe magnitude values of the channel taps at the MS end. A)Spatial correlation coefficient function as a function ofdistance and excess delay τi. b) Average spatial correlationcoefficient function as a function of distance

temporal correlation as a function of excess delaydifference. The existence of the multipath componentsresults in higher correlation values. Signal components inLOS case do not correlate after any excess delay values of50 ns. Figure 7b) shows the temporal correlation functionaveraged along the excess delays τi. The X-axis gridspacing has been chosen to be the delay resolution of 33.3ns. The reflected components do not have effect on thetemporal correlation after the excess delay values of 25 ns.The exponentially fitted curve has the parametersA=0.9314, B=1.1765, C=-0.0588.

5. CONCLUSIONS

In this paper, the spatial and temporal correlationproperties of the adaptive antenna array were studied. Theresults for the spatial correlation at the BS end confirmthat strongly correlated signals exist in closely locatedantenna elements unless the antenna elements are widelyseparated. The correlation computation based on themagnitude-valued channel taps results in more correlatedsignals than the usage of the complex-valued channel taps.Spatial uncorrelateness at the MS end is already achievedafter half a wavelength distance. Temporally uncorrelatedsignals are achieved after the excess delay values of 50 nswhen the first LOS component has arrived at the excessdelay value τ0=0 ns. The signal components arriving afterthe LOS component become uncorrelated much faster,already after the excess delay values of 25 ns. These resultsfor the spatial and the temporal correlation are in closeagreement with those presented by Rappaport in [5].

ACKNOWLEDGEMENTS

This research study is part of project of the Institute ofRadio Communication (IRC) funded by the TechnologyDevelopment Center (TEKES), NOKIA Research Center,Finnish Telecom and the Helsinki Telephone Company.The authors wish to thank colleagues Pauli Aikio andJarmo Kivinen from Radio Laboratory for providinghelpful hints for analyzing the channel measurement data.

REFERENCES

[1] J. Salz and J. H. Winters, “Effect of fading correlation onadaptive arrays in digital mobile radio”, IEEE Trans. OnVehicular Technology, Vol. 43, No. 4, Nov. 1994, pp.1049-1057.

[2] K. Pahlavan and A. H. Levesque, Wireless InformationNetworks, John Wiley & Sons, 1995, pp. 572.

[3] H. Hashemi, “Simulation of the urban radio propagationchannel”, IEEE Trans. on Vehicular Technology, Vol. VT-28, No. 3, Aug, 1979, pp. 213-225.

[4] H. Hashemi, “The Indoor radio propagation channel”,Proceedings of the IEEE, Vol. 81, No. 7, July, 1993, pp.943-968.

[5] T. S. Rappaport, S. Y. Seidel and K. Takamizawa,“Statistical channel impulse response models for factoryand open plan building radio communication system

Design”, IEEE Trans. On Communications, Vol. 39, No. 5,May, 1991, pp. 794-806.

[6] L. Dossi, G. Tartara and F. Tallone, “Statistical analysis ofmeasured impulse response functions of 2.0 GHz indoorradio channels”, IEEE Journal on Selected Areas inCommunications, Vol. 14, No. 3, April, 1996, pp. 405-410.

[7] J. S. Bendat and A. G. Piersol, Random Data: Analysis andMeasurement Procedures, 2nd Edition, John Wiley & Sons,New York, 1986, pp. 566.

[8] K. Kalliola and P. Vainikainen, “Characterization systemfor radio channel of adaptive array antennas”, Proceedingsof 8th IEEE International Symposium on Personal, Indoorand Mobile Radio Communications, Helsinki, Finland,September 1-4, 1997, pp. 95-99.

[9] S. Haykin, Adaptive Filter Theory, 3rd edition, Prentice-Hall, 1996, pp. 989.

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Figure 7 Temporal correlation coefficient functionsbased on the magnitude values of the channel taps. a)Temporal correlation coefficient function as a function ofexcess delay difference and excess delay. b) Averagetemporal correlation coefficient function along the excessdelays.