Carrier frequency synchronization for mobiletelevision receivers

Timo RomanNokia Research Center

P.O. Box 407, FIN-00045 NOKIA GROUP, FinlandEmail: timo.roman@nokia.com

Visa Koivunen*

SMARAD CoE, Signal Processing LaboratoryHelsinki University of Technology

P.O. Box 3000, FIN-02015 HUT, FinlandEmail: visa@wooster.hut.fi

Abstract— In this paper, we introduce a novel subspace-based approach for carrier frequency offset (CFO) estimationin OFDM. The proposed estimator exploits both scatteredand continual pilots commonly used in mobile televisionsystems such as DVB-H. Rapid channel estimation and CFOcompensation is necessary in order to deal with high mobil-ity, time-slicing and potential handovers during the receiverswitch-off time. The proposed method achieves frequencysynchronization within a single OFDM block. No extensivetime averaging is needed, which makes the approach veryattractive for time and frequency selective channels where theCFO may be time varying. It is particularly suitable to bursttype of transmission used, for example in DVB-H. Simulationexamples are provided within the framework of mobile DVB-Hsystems.

I. INTRODUCTION

The digital video broadcasting - handheld (DVB-H)standard (see, [1]) allows the mobile reception of DVB -terrestrial (DVB-T) signals. Both DVB-T and DVB-H relyon orthogonal frequency division multiplexing (OFDM).While OFDM yields a powerful technique to mitigatemultipath propagation with simplified receiver design, it ishighly sensitive to carrier frequency offsets (CFO) causedby oscillator inaccuracies and Doppler shift due to mobility.CFOs give rise to inter-carrier interference (ICI) and shouldtherefore be estimated and compensated with high fidelity.

Time-slicing is a key feature of DVB-H that allowsthe support of small and portable battery-operated mobiledevices. The idea is to send data for a given broadcastservice in bursts. In this way, the receiver is required to stayactive only a small fraction of the time which saves batterypower significantly. In order to fully exploit the benefitsof time-slicing, the synchronization of DVB-H receiversshould be accomplished much faster compared to standardDVD-T receiver. Furthermore, DVB-H receivers should alsodeal with rapid time fluctuations of the mobile radio channeland therefore be able to update channel and synchronizationparameters frequently.

In this paper, we introduce a novel subspace-based fastcarrier frequency synchronization scheme applicable to

*This work was done while the author was Nokia Visiting Fellow atNokia Research Center during his sabbatical leave.

OFDM. The method uses in-band pilots, including bothscattered and continual pilots. Only a single OFDM symbolis needed to perform carrier frequency synchronization intime and frequency selective channels, unlike the majorityof existing techniques [2]–[5] which typically require ex-tensive time averaging. Hence, the proposed estimator isparticularly suited to burst type of transmissions such as inDVB-H.

Novelty of the paper relies on the fact that low-ranksignal model may be derived without any virtual subcarriers(VSC), which are commonly assumed to be available inexisting subspace CFO estimators for OFDM [6]. The keyidea is to exploit channel correlation at pilot subcarriersin conjunction with pilot information. If included in thesystem design, VSCs may be exploited for CFO estimationadditionally to pilot symbols. Also, the proposed methoddoes not impose any restriction on the symbol modulationscheme such as, e.g., the constant modulus property [5], [7].Simulation results demonstrate that the proposed algorithmoutperforms existing estimators based on virtual subcarrierssolely [6].

The rest of the paper is organized as follows. The systemmodel is briefly described next. Then, Section 3 introducesthe proposed CFO estimator. Simulation results specific tocase of DVB-H systems are presented in Section 4. Section5 concludes the paper.

II. SYSTEM MODEL

A. OFDM signal model with carrier frequency offset

Let us assume an OFDM transmission with Na modulatedsubcarriers out of a total of N , and consider a single blockof data for simplicity. Assuming perfect symbol timing, thereceived OFDM signal in time domain after cyclic prefixremoval, including the frequency offset, is expressed as

yε = βCεFDha + w, (1)

where yε is a N×1 vector, β =√

N/Na ensures that thetotal transmitted power is constant regardless of Na, F isthe unitary N×N inverse discrete Fourier transform (IDFT)matrix, and a is the N×1 symbol vector. The diagonal

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matrix Cε introduces the frequency offset and is definedas

Cε = ej2πεLCP/N · diag{

1, . . . , ej2πε(N−1)/N}

, (2)

where LCP is the length of the cyclic prefix (LCP<N )and diag{} denotes the diagonal matrix constructed fromthe argument vector. The quantity ε is referred to asnormalized frequency offset wrt. intercarrier spacing. Theeffective frequency deviation is Bsc×ε [Hz], where Bsc

[Hz] is the inter-carrier spacing. The diagonal matrix Dh

in (1) contains the channel frequency response (CFR)h=[h1, . . . , hN ]T at each subcarrier frequency on its maindiagonal. A block fading frequency selective channel modelis considered. The CFO is assumed to vary block-wise aswell. The complex noise term w is assumed to be zero-meancircular complex Gaussian with covariance matrix σ2I.

B. Pilot symbols and guard bands in DVB-H

In DVB-H systems, each OFDM block is comprised ofdata and pilot symbols located on disjoint sets of subcarri-ers. Pilot information is sent both continuously on specifiedsubcarriers (continual pilots) and in a periodical fashion(scattered pilots). Additionally, transmission parameter sig-nalling (TPS) subcarriers convey system level information[1]. Also, some subcarriers at the edges of the transmissionspectrum may be left unmodulated. They are referred to asvirtual subcarriers and act as guard bands.

Given the symbol vector a = [a1, . . . , aN ]T , we define

ad = [{an, n ∈ ND}]T ∈ RNd×1 (3)

ap = [{an, n ∈ NP}]T ∈ RNp×1 (4)

av = [{an, n ∈ NV}]T = 0Nv×1 (5)

the data, pilot and VSC symbol vectors, respectively. Thedisjoint subsets of indices ND, NP, NV ∈ {0, . . . , N − 1}index data, pilot and virtual subcarriers, respectively.

C. CFO compensation

Given an estimate µ of the true value ε, CFO compensa-tion may be performed in time domain at the receiver priorto the discrete Fourier transform (DFT). The resulting N×1vector yµ,ε in frequency domain may be expressed as

yµ,ε = FHC∗µyε (6)

= β MDha + FHC∗µw, (7)

where we defined Mµ,ε=FHC∗µCεF. The matrix Cµ has

the same structure as in (2), H is the Hermitian transposeoperator and ∗ denotes the complex conjugate. In caseof perfect frequency synchronization, µ=ε and Mε,ε=IN ,where IN is the N×N identity matrix. Then, equation (7)becomes

yε,ε = βDha + FHC∗εw, (8)

and the orthogonality of the transmission is thus restored.

III. SUBSPACE-BASED FREQUENCY SYNCHRONIZATION

In the following, we introduce a CFO estimator whichaims at restoring the signal subspace structure at both pilotand virtual subcarrier locations.

A. Pilot signal subspace

The received signal at pilot subcarriers may derivedsimilarly to (6) as

yp,µ,ε =[FH

]{NP,1:N} C∗

µyε, (9)

where[FH

]{NP,1:N} is the DFT matrix truncated to the

lines within the subset NP and columns ranging from 1 to N .Assuming perfect frequency synchronization and a noise-free situation, (9) may be expressed similarly to (8) as

yp,ε,ε = β diag{ap}hp, (10)

where the vector hp = [{hn, n ∈ NP}]T contains the CFRcoefficients at pilot subcarrier positions.

Now, hp is related via DFT to a channel impulse response(CIR) h of length Lh in time domain as

hp =√

N[FH

]{NP,1:Lh} h, (11)

Note that for successful OFDM transmission, the length ofthe cyclic prefix is chosen as LCP≥Lh−1 in order to avoidboth inter-block and inter-carrier interference.

Finally, (10) and (11) may be combined together as

yp,ε,ε = Gph, Gp = β√

N diag{ap}[FH

]{NP,1:Lh} .

(12)We may easily notice from (12) that the signal space at pilotsubcarriers is spanned by the columns of the Np×Lh matrixGp. Assuming Np > Lh pilots symbols, a low-rank modelarises from correlation in the channel frequency response.

Carrier frequency mismatch (µ�=ε) leads to Mµ,ε �=IN in(7), which causes ICI and further invalidates the relationshipin (12). Based on this observation, we further derive a novelCFO estimator relying on the pilot signal subspace.

B. Virtual subcarrier subspace

Assuming the presence of virtual subcarriers (i.e., NV �=∅),the projection of the received signal to the subspace of VSCsmay be obtained similarly to (6) as

yv,µ,ε =[FH

]{NV,1:N} C∗

µyε. (13)

Under perfect CFO compensation and in a noise-free case,(13) reduces to yv,ε,ε=0Nv×1. The latter does not hold trueanymore in case of carrier frequency mismatch (µ�=ε). Thisproperty may be exploited for carrier frequency synchro-nization in OFDM [6].

C. Novel subspace-based CFO estimator

In this section, we introduce the proposed CFO estimator.As described earlier, frequency mismatch leads to ICI. The

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latter alters the components of both pilot and data symbolswhich do not lie in orthogonal subspaces anymore. Thissuggests that by restoring the subspace structure perfectsynchronization may be achieved. Similarly to [7], this maybe performed by maximizing the projection of the receivedsignal to the signal subspace, or equivalently, by minimizingthe projection to the orthogonal subspace.

We choose the following composite criterion as a costfunction to be minimized:

C(µ) =∥∥Π⊥

P yp,µ,ε

∥∥2+ ‖yv,µ,ε‖2

, (14)

where yp,µ,ε and yv,µ,ε are defined in (9) and (13), respec-tively. Note that the criterion C is a function of the CFOcompensation factor µ. The first part of the cost function,Cp(µ)=

∥∥Π⊥P yp,µ,ε

∥∥2, is the squared Euclidean norm of the

projection of the received CFO-compensated signal at pilotsubcarriers, yp,µ,ε, to the orthogonal column subspace ofGp. The matrix Π⊥

P performs the projection operation andis expressed as

Π⊥P = INp

− Gp

(GH

p Gp

)−1GH

p . (15)

Since Gp given by (12) depends only on the kwowledgeof the pilot symbol vector ap, it may be computed offline.A low-rank approximation may also be used when buildingΠ⊥

P (e.g., via truncated singular value decomposition). Thiswould both reduce computational complexity and increaserobustness of the algorithm (ill-conditioning of Gp mayoccur for large values of N ). The criterion Cp differsfrom the one in [8] since only a limited number of pilotsubcarriers are exploited here for CFO estimation instead ofan entire block of pilots. The second part of the criterion,Cv(µ)= ‖yv,µ,ε‖2, is the squared norm of the projection tothe subspace of VSCs. It is equivalent to the cost functionin [6].

An estimate ε of the CFO is found by minimizing thecomposite criterion over µ as

ε = arg minµ

C (µ) . (16)

Numerical solution to (16) may be found e.g. using agradient descent method. Computational cost is not pro-hibitive due to a one-dimensional search space. Smoothcost function leads also to faster convergence to globalminimum (see, Figure 1). Note that it is not necessaryto have both VSCs and pilot symbols simultaneously inorder to estimate the CFO. The method is not limited toestimation of fractional CFOs either [7]. We further comparein simulations the performance of the proposed subspace-based composite approach (denoted ’Proposed VSC+pilot’in simulation graphs) to the VSC-based method in [6].

IV. SIMULATION RESULTS

In this section, simulation results are reported. TheOFDM system parameters are chosen accordingly to the

−2 −1.5 −1 −0.5 0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

µ

C(µ

)

µ=0.81267

VSCProposed VSC+pilot

Fig. 1. Cost functions (normalized) for VSC and proposed subspace CFOestimators (ε=0.81335, SNR=20 dB, N=2048, Na=1706, Nv=342).

DVH-H 2k mode. The number of subcarriers is equal toN=2048, out of which Na=1706 are active. A total ofNv=342 null subcarriers are placed at the edges of thetransmission spectrum. The system bandwidth is set to 8MHz with 3.9 kHz intercarrier spacing. The length of thecyclic prefix is LCP=64. 16QAM modulation is used. EachOFDM block contains 45 continual pilot subcarriers and 130scattered pilots symbols, leading to 10.3% pilot overhead.

The DVB-H was primarily designed for use on theUHF band (470-860 MHz) globally reserved for televisionbroadcast. We choose to perform our simulations on channelCH40 (626 MHz) with a bandwidth of 8 MHz. As the 2kmode of DVB-H provides a Doppler tolerance for very high-speed reception, a broad range of terminal velocities (from3 to 240 km/h) is considered. The upper limit is close tothe maximum speed of operation specified in the standardfor this frequency band. The maximum Doppler frequencyis 139 Hz in this case.

The wireless channel is generated according to the COST207 model in a typical urban (TU) scenario, with a total ofLh=41 non-zero taps [9]. In our simulations, we consider8 channel samples in time for each OFDM symbol. Finally,the normalized frequency offset is assumed to be uniformlydistributed between [0, 1], and to vary block-wise.

A. Performance versus SNR

The Mean Square Error (MSE) is chosen as an errorcriterion for CFO estimation: MSE=E |ε−ε|2. Plot of theMSE versus the signal-to-noise ratio (SNR=Eb/N0) is de-picted in Figure 2. Results are ensemble averaged over 2000different channel and CFO realizations. At 10−4 MSE, weobtained 16.5 dB gain over the method exploiting VSCsonly [6]. Highly accurate estimates of time-varying CFOare achieved with a single OFDM block in time-frequencyselective channels. Because the required sample support

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is so small, the CFO may be tracked with high fidelity.Numerous frequency synchronization techniques have beenproposed in the literature related to OFDM, but most ofthem need extensive time-averaging in order to get rid ofthe influence of both noise and data symbols.

An increased terminal velocity has a detrimental effect onCFO estimation: time-variations of the channel within theduration of the OFDM symbol introduce ICI. However, forthe proposed estimator, the carrier frequency synchroniza-tion error remains well below 1% (wrt. intercarrier spacing)at 10 dB SNR and a speed of 240 km/h. Hence, it providesa very robust and feasible approach for practical mobileDVB-H systems.

0 5 10 15 20 25 30

10−6

10−5

10−4

10−3

10−2

SNR [dB]

MS

E

Proposed VSC+pilot

VSC−based method

240 km/h120 km/h60 km/h3 km/h

Fig. 2. MSE of VSC-based and proposed CFO estimators versus SNR(Eb/N0) for the DVB-H 2k mode; 16-QAM modulation; COST 207 TUchannel of length Lh=41; uniformly distributed CFO in [0, 1] and varyingblock-wise; v=[3, 60, 120, 240] km/h; ensemble average (2000 blocks).

B. Sensitivity to unknown channel order

Previous results were obtained assuming the knowledgeof channel length at the receiver (i.e., Lh=41 taps). Delayspread needs to be estimated in practice. Figure 3 shows thesensitivity of the proposed algorithm to unknown channelorder. The proposed estimator suffers from under-estimateddelay spread, while still performs well with larger assumedchannel order. Therefore, uncertainty in the channel orderis not a major issue provided that the estimated channellength, Lh, is chosen large enough, i.e, Lh<Lh≤LCP. Notethat purely VSC-based estimators are not affected by anunknown channel length, as the subspace structure is deter-mined by the location of virtual carriers, assumed to be ofprior knowledge. However, the performance is worse.

V. CONCLUSIONS

In this paper, we introduce a novel subspace-based es-timator for carrier frequency offset estimation in OFDM.The proposed algorithm is particularly suitable for mobiletelevision receivers based on the DVB-H standard, where

1 20 40 60 80 100 120 12810

−6

10−5

10−4

10−3

10−2

10−1

True channel length: 41 taps

Assumed channel length

MS

E

VSC−based methodProposed VSC+pilot

Fig. 3. MSE of VSC-based and proposed CFO estimators versus assumedchannel length; the actual channel length is Lh=41; SNR=20 dB; v=3km/h; ensemble average (2000 blocks).

time-slicing in conjunction with mobility may require fre-quent updates of synchronization parameters. Moreover, ahand-over may take place while the receiver is in inactivestate which leads to rapid change in channel coefficientsand CFO. The key idea of the method is to exploit thechannel correlation at pilot subcarrier locations. Low-ranksignal model is obtained without virtual subcarriers, butthose may still be exploited if present, in addition tocontinual and scattered pilot symbols. No extensive timeaveraging is needed as the proposed estimator performsfrequency synchronization with only one OFDM block.The proposed method outperforms other considered CFOestimators exploiting virtual carriers solely.

REFERENCES

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[3] Schmidl, T.M., Cox, D.C., “Robust frequency and timing synchro-nization for OFDM”, IEEE TCOMM, Vol. 45, Issue: 12, pp. 1613-1621, 1997.

[4] Xiaoli M., Tepedelenlioglu, C., Giannakis, G.B., Barbarossa, S.,“Non-data-aided carrier offset estimators for OFDM with null sub-carriers: identifiability, algorithms, and performance”, IEEE JSAC,Vol. 19, Issue: 12, pp. 2504-2515, 2001.

[5] Ghogho, M., Swami, A., “Carrier frequency synchronization forOFDM systems”, in Signal processing for mobile communicationshandbook, Ch. 8, CRC Press, 2005.

[6] Tureli U., Liu, H., Zoltowski, M.D., “OFDM blind carrier offsetestimation: ESPRIT”, IEEE TCOMM, Vol. 48, Issue: 9, pp. 1459-1461, 2000.

[7] Roman, T., Koivunen, V., “Subspace method for blind CFO estima-tion for OFDM systems with constant modulus constellations”, IEEEVTC, Vol. 2, pp. 1253-1257, 2005.

[8] Tang, T., Heath, R.W., “Joint frequency offset estimation and inter-ference cancellation for MIMO-OFDM systems”, IEEE VTC, Vol. 3,pp. 1553-1557, 2004.

[9] European Project final report, “COST 207: Digital land mobile radiocommunications”, EUR 12160, 1998.

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