Experimental Comparison of Fast-Fading ChannelInterpolation Methods for the LTE Uplink

Martin LerchInstitute of Telecommunications / TU Wien

Gusshausstrasse 25/389, A-1040 Vienna, Austriamlerch@nt.tuwien.ac.at

Abstract—Due to the pilot structure, channel interpolation inthe LTE uplink is a challenging problem in fast fading scenarios.In this paper different channel interpolation methods that includechannel estimates from the previous and from the subsequentsubframe are compared to methods using only one or two channelestimates from the actual subframe. The presented results areobtained by measurements performed on a wireless testbed thatallows for reproducible measurements at velocities of up to 400km/h.

Keywords—LTE; Uplink; Fast Fading; Channel estimation;Measurement

I. INTRODUCTION

The modulation schemes in 3GPP Long Term Evolu-tion (LTE) [1] are based on OFDM. Besides Inter-Carrier-Interference (ICI) caused by Doppler shifts, the quality ofthe channel estimation and interpolation has a strong influenceon the performance of OFDM systems in high mobility sce-narios. In LTE, channel estimation is based on demodulationreference symbols (pilots) which occupy resources accordingto a defined pilot pattern. In the downlink, the pilot patternis a good trade-off between a small temporal and spectralpilot spacing accounting for highly frequency selectiv channelsand fast fading channels and a rather small overhead. Thisis different in the LTE uplink. While the modulation schemein the LTE downlink is OFDM, Single-Carrier-FDMA (SC-FDMA) is applied in the uplink due to a smaller Peak-to-Average-Power-Ratio (PAPR) compared to OFDM. SC-FDMAtransmissions can be modeled as OFDM systems with datasymbols being precoded by an Discrete Fourier Transform(DFT) before the actual OFDM modulation. The pilots for theLTE uplink are Zadoff-Chu sequences occupying the wholesubband (see Fig. 1) having also a low PAPR. While there isno need for channel interpolation over frequency, the temporalspacing between adjacent pilot symbols is about twice aslarge as in the downlink. Furthermore, if frequency hoppingis performed the number of adjacent pilots transmitted in acertain subband is two for inter-subframe frequency hoppingand one for intra-subframe frequency hopping where frequencyhopping is performed on a per-slot basis. Due to this specialstructure of pilot symbols, channel estimation in the LTEuplink is a challenging problem. The authors of [2] proposedan interpolation algorithm based on adaptive order polynomialfitting to mitigate ICI, in [3] the polynomial basis expansionmodel is employed and an autoregressive model is used toimprove the estimation accuracy.

Our novel idea is to include channel estimates from theprevious and from the subsequent subframe into the process of

channel interpolation. The additional delay that is introducedby applying channel estimates from the subsequent subframeis not considered.

This paper is organized as follows. In Section II the systemmodel and the interpolation methods under investigation aredescribed. The measurement and the underlying measurementmethodology is described in Section III followed by a discus-sion of the measurement results in Section IV.

II. SYSTEM MODEL

We consider a continuous single antenna transmission onthe LTE uplink with frequency hopping being disabled. Sound-ing reference symbols (SRS) and the physical uplink controlchannel (PUCCH) are both not considered. Fig. 1 illustrates theresulting time / frequency resource grid for three consecutiveresource blocks that consist only of data symbols and pilotsymbols. At the receiver side we perform a symbol-by-symbolleast squares (LS) channel estimation in the frequency domainand calculate the zero forcing (ZF) equalizer using the differentinterpolation methods under investigation. Although we do notperform frequency hopping we also consider the cases whereonly one or two pilot symbols are available.

• Average: Averaging the channel estimates from pilotpositions p0 and p1. In the static case this methodimproves the channel estimation by 3 dB in terms ofsignal-to-noise ratio (SNR) but averages over temporalvariations in the fast fading case.

• 1 point: Data symbols of slot n are equalized bythe channel estimates from pilot at position pn. This

p-2 p-1 p0 p1 p2 p3

time

freq

uenc

y

subframe n

1. slot 2. slotdata symbolpilot symbol

Fig. 1: Resource grid of the LTE uplink. Due to SC-FDMAmodulation, symbols marked as data symbols are the DFT-precoded data symbols rather than the actual data symbols.

method is applicable in the case of intra-subframefrequency hopping.

• 2 point linear: Linear interpolation and extrapolationbased on the estimates at pilot position p0 and p1.This method is applicable in the case inter-subframefrequency hopping is performed but intra-subframefrequency hopping is not activated.

• 4 point linear: Linear interpolation based on theestimates at pilot position p-1, p0, p1 and p2.

• 4 point spline: Spline interpolation based on the esti-mates at pilot position p-1, p0, p1 and p2.

• 6 point spline: Spline interpolation using the estimatesfrom pilot positions p-2 to p3.

The resulting equalizers are then applied in the frequencydomain on the DFT-precoded data sysmbols transmitted dur-ing subframe n in Fig. 1. The previous subframe and thesubsequent subframe are only considered to obtain additionalchannel estimates.

III. MEASUREMENT

We were interested in a comparison in terms of physicallayer throughput of the different channel interpolation methodsdescribed in Section II at different velocities and differentvalues of SNR. In order to omit the impact of feedback that isusually necessary for link adaption in LTE, a brute-force ap-proach [4] was used. Here all possible modulation and codingschemes (MCS) are transmitted without considering the actualchannel quality. Although we are interested in a comparison ofdifferent receiver techniques where the same received signalsare employed by different receiver implementations, the brute-force approach as well as the comparison at different valuesof SNR demands on transmissions of different transmit signalsand transmitting at different transmit powers over the sametime-varying channel. The major measurement parameters aresummarized in Table I.

A. Measurement setup

Measurements were performed by the Vienna MIMOtestbed [4] located at TU Wien in downtown Vienna, Austria.This testbed consists of three transmitters located on differentrooftop locations using off-the-shelf sector antennas and areceiver located indoors. Fig. 3 shows the setup where at thereceiver side we use a rotary unit [5], [6] developed at TU Wiento generate fast fading conditions in a reproducible and fullycontrollable way, which is necessary for repeated transmissionsover the same time-varying channels. Therefore the receiveantenna rotates around a central pivot at the desired velocity.A light barrier which is connected to the trigger system [7] ofthe testbed allows for precise timing of transmissions startingat any desired angle of the receive antenna. The spatial length∆z of the time varying channel is given by the length of oneLTE subframe of T=1 ms and the maximum velocity of v=400km/h and calculates to ∆z=T·v≈11 cm. This corresponds to anangle of about 6◦ for the arm the receive antenna is mounted onhaving a length of 1 m. In order to generate different channelrealizations the whole rotary unit can be moved along two axiswithin an area of about 3λ×2.2λ.

TABLE I: MEASUREMENT PARAMETERS

Center frequency 2.506 GHz (λ ≈ 12 cm)

Velocities 50, 100, 200 and 400 km/hDifferent channelrealizations 49 (within an area of about 3λ×2.2λ)

Transmission mode10 MHz LTE uplink, single antenna transmission,normal cyclic prefix, all resources scheduled for asingle user, no SRS, no PUCCH

Modulation and coding 15 different MCSs according to the 15 differentChannel Quality Indicators defined in the standard

Receiver single antenna, LS channel estimation, ZF equalization

∆ztrigger point z

subframe n− 1 subframe n subframe n+ 1

r=1 v=400 km/h

n− 1 n

n− 1

n+ 1

n n+ 1

r=1

r=2

v=200 km/h

Fig. 2: Transmitting over the same spatial channels allows fora fair comparison at different velocities.

B. Measurement methodology

Both, the generation of transmit signals and the processingof the received signals is based on the Vienna LTE uplink linklevel simulator [8], [9]. In order to measure the physical layerthroughput using the brute-force approach one subframe forany of the 15 different MCSs are pregenerated. Every subframeis repeated three times for transmissions at the maximumvelocity of v=400 km/h whereas the central subframe n isthe subframe to be decoded and the neighboring subframesn− 1 and n+ 1 are included to obtain the additional channelestimates. At half of the maximum velocity (200 km/h) twosubframes of interest (n) are transmitted over the desired chan-nel (∆z) and so forth. Fig. 2 illustrates this idea of transmittingover the same spatial channel at different velocities whereasthe number of subframes considered in the evaluation is givenby R (v) = 400

v .

C. Evaluation

As figure of merit for the comparison of different chan-nel interpolation methods the physical layer throughput isconsidered. Furthermore the SNR as well as the Signal-to-Interference Ratio (SIR) and the Signal-to-Interference-plus-Noise Ratio (SINR) as measures for the amount of ICI accuredare evaluated.

1) Physical layer throughput: By using the brute-forceapproach perfect knowledge of the best performing MCS isemulated for every channel realization and every value of trans-mit power by transmitting all different MCSs over the samechannel. The independent evaluation of all received signalsthen yields a value of throughput Dm for every combinationof measurement parameters whereas k denotes the channelrealization, r being the temporal repitition, v the velocity, PTX

receiver

transmit antenna

(a)

∆x=3λ∆y=2.2λ

∆z

receive antenna

light barrier

(b)

Fig. 3: Measuremt setup in downtown Vienna, Austria: (a) The transmitter is located on a rooftop at TU Wien using an off-the-shelf sector antenna. (b) The receiver is located indoors using a rotary unit to generate fast fading channels. The box illustratesthe area measurements were performed in.

the transmit power and I the channel interpolation method. Thethroughput Dm is maximized over the different MCSs by

Dm (k, r, v, I, PTX) = maxMCS

Dm (k, r, v, I, PTX,MCS) (1)

before the average throughput

D (v, I, PTX) =1

K

1

R (v)

K∑k=1

R(v)∑r=1

Dm (k, r, v, I, PTX) (2)

is obtained by averaging over all K different channel realiza-tions and R (v) temporal repititions.

2) SIR, SINR and SNR: The power of each subcarrier isestimated in the frequency domain whereas we obtain thesignal-plus-interference-plus-noise power PSIN at data subcar-rier positions, the interference-plus-noise power PIN at the DCsubcarrier where no data is transmitted and the noise power PN

by measuring at the same subcarrier positions during a noisegap when no signal is transmitted. These thereby obtainedpower estimates are averaged similar to (2) seperately over allchannel realizations and temporal repititions. PSIN and PIN arefurthermore averaged over all different MCSs. The SIR thencalculates to

SIR (v, PTX) =P SIN (v, PTX) − P IN (v, PTX)

P IN (v, PTX) − PN (v, PTX), (3)

the SINR to

SINR (v, PTX) =P SIN (v, PTX) − P IN (v, PTX)

P IN (v, PTX)(4)

and the SNR calculates to

SNR (v, PTX) =P SIN (v, PTX) − P IN (v, PTX)

PN (v, PTX). (5)

IV. RESULTS

The conditions in terms of SIR, SINR and SNR underwhich the measurement was performed are shown in Fig. 4.Due to the methodology described in Section III-B the SNR

50 100 150 200 250 300 350 400

20

25

30

35

40

45

velocity v (km/h)

SIR

,SIN

R,S

NR

(dB

)

10 MHz LTE uplink, fc=2.5 GHz

measured

Jakes’ modeluniform

SNR≈21 dB

SINRSNR

SIR

SNR≈38 dB

Fig. 4: Measured SIR, SINR and SNR. The measured SIR ishigher than the analytical derived SIR for the Jakes’ and theuniform model. The SNR is constant over velocity allowingfor a fair comparison at different velocities.

is constant over the whole range of velocities considered.Comparing the SIR to analytical results [10] derived for twopopular models shows a higher SIR in our scenario. Bothmodels, Jakes’ spectrum and the uniform model are basedon uniformly distributed scattering objects which is not thecase in our scenario. The SINR is upper bounded by noise atlow velocities and upper bounded by the ICI power at highvelocities. While we observe a large decrease of SINR forincreasing velocity at high SNR, the SINR curve flattens forlow SNR. The impact of SINR on the throughput becomesnearly independent of the velocity and the performance israther determined by noise and the quality of the channelinterpolation method than by ICI.

Fig. 5 compares the considered channel interpolation meth-ods in terms of physical layer throughput for two different

50 100 150 200 250 300 350 4000

10

20

30

40

velocity v (km/h)

thro

ughp

utD

(Mbi

t/s)

10 MHz LTE uplink, fc=2.5 GHz, SNR≈38 dB

avg.

1 pt.

2 pt.

4 pt. linear

4 pt. spline

6 pt. spline

95% confidence interval

estimated scenario mean

(a)

50 100 150 200 250 300 350 4000

10

20

30

40

velocity v (km/h)

thro

ughp

utD

(Mbi

t/s)

10 MHz LTE uplink, fc=2.5 GHz, SNR≈21 dB

avg.

1 pt.

2 pt.

4 pt. linear

4 pt. spline6 pt. spline

95% confidence interval

estimated scenario mean

(b)

Fig. 5: Measurement results comparing different channel interpolation methods in terms of throughput for two different valuesof transmit power resulting in an average SNR of (a) ≈38 dB and (b) ≈21 dB.

values of SNR. As expected, the worst performance is observedwhen channel estimates from two pilots are averaged. Theperformance increases with the number of pilots in the channelinterpolation. The highest gains at high SNR are observedbetween 1 point, where no interpolation is performed and 2point interpolation and moreover when channel extrapolationin the 2 point case is replaced by interpolation when doing 4point linear interpolation. Additional gains are observed whenusing spline interpolation, especially at high SNR and highvelocities. At lower SNR, spline interpolation outperforms 4point linear interpolation only at moderate to high velocities.The averaging method is still the worst method as it averagesthe channel variations.

V. CONCLUSION

Channel interpolation under fast fading conditions is achallenging task and its quality has a strong influence onthe performance of a mobile communication system such asLTE. The quality of channel interpolation depends on the pilotpattern and the temporal spacing of the pilot symbols, which isfor the LTE uplink about twice the spacing as for the downlink.We compared the performance of different channel interpo-lation methods for the LTE uplink using different number ofpilots. We observed large gains when frequency hopping is notperformed and therefore additional channel estimates from theprevious and from the subsequent subframe can be includedin the process of channel interpolation. The presented resultswere obtained experimentally using a testbed that allows forreproducible and controlled measurements at velocities of upto 400 km/h.

ACKNOWLEDGMENT

The authors would like to thank the LTE research group andin particular Prof. Christoph Mecklenbrauker for continuoussupport. This work has been funded by the Christian DopplerLaboratory for Wireless Technologies for Sustainable Mobility,KATHREIN Werke KG and A1 Telekom Austria AG.

The financial support by the Austrian Federal Ministry ofEconomy, Family and Youth and the National Foundation forResearch, Technology and Development is gratefully acknowl-edged.

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