OFDM channel estimation with timing offset for

satellite plus terrestrial multipath channels

Yeon-Su Kang, Do-Seob Ahn, Ho-Jin LeeDigital Broadcasting Research Division

Electronics Telecommunications Research Institute (ETRI), Daejeon, Korea{yskang} @etri.re.kr

Abstract- In this paper, we propose a discrete Fourier trans-form (DFT)-based channel estimation and timing synchronizationto cope with satellite plus intermediate module repeater (IMR)channels. Conventional DFT-based channel estimations sufferfrom the timing offset and incorrect channel impulse response,and this results in means square error (MSE) floor of channelestimations. Moreover, timing synchronization accuracy is alsodegraded on IMR channels. We, therefor, propose an improvedDFT-based channel estimation by deciding significant channeltaps based on a threshold and we derive this threshold withrespect to MSE. Using results from proposed channel estimation,we compensate residual timing offset of conventional timingestimation.

I. INTRODUCTION

Orthogonal frequency division multiplexing (OFDM) is themost popular promise for the Beyond 3G (B3G) systems forits advantages in high-bit-rate transmission over dispersivechannels. In the B3G systems, the major role of satellites willbe providing terrestrial fill-in service and efficient multicas-ting/broadcasting services. As the terrestrial fill-in services,satellite systems provide services and applications similar tothose of terrestrial systems outside the terrestrial coverage areaas much as possible. In this regard, in order to enhance thecoverage given by satellite layer in urban and sub-urban, intro-ducing intermediate module repeaters (IMR) is considered asa solution. However, in present IMR environments, multipathpropagation similar to that experienced in the terrestrial chan-nels. Usually, under terrestrial channels, channel estimationand timing synchronization are degraded by multipath effectcomparing with satellite channels having line of sight andsmall delay.

Based on these technological issues, we propose an efficientOFDM channel estimation and synchronization algorithm tocope with both IMR and satellite channels. For channel esti-mation in this paper, we especially consider discrete Fouriertransform (DFT)-based estimation [1]-[4]. This channel es-timation uses time domain properties of channels. Since achannel impulse response (CIR), without losses of generality,is not longer than the guard interval in OFDM systems, thisestimation is modified in [1] by limiting the number of channeltaps in time domain and suppressing noise outside of CIR.However, because the improvement is based on assumptionthat channel impulse response or its delay length is known atthe receiver, these methods can make mean square error (MSE)floor by the energy loss in the excluded channel taps when the

channel impulse response is incorrect [2]. For example, MSEfloor will occur really under the IMR channel (large delay)with assumption on satellite channel (small delay).

Timing synchronization for OFDM system means findingtiming instant for fast Fourier transform (FFT) process amongreceived sampled sequences. Conventional timing synchro-nization algorithms have sufficient performance on satellitechannels which have very small rms delay. On the contrary,the accuracy is very degraded on large delayed channel likeIMR channels and they have residual timing offset.

In this paper, we propose a modified DFT-based channelestimation in order to cope with the MSE floor and compensateresidual timing offset of conventional timing synchronizationby using results form proposed channel estimation. In pro-posed channel estimation, to include all informative channeltaps without prior channel information, we detect significantchannel taps with respect to a threshold. The threshold is de-termined in order to reduce the MSE of the channel estimationand relates to time domain noise power.The next section describes the basic system model and

introduces some earlier estimation algorithms. In Section III,we propose a new channel estimation algorithm. Section IVpresents simulation results and discussions, and Section Voffers some conclusions.

II. SYSTEM DESCRIPTION

A. OFDM systemWe consider an OFDM system that has N subcarriers

and each subcarrier consists of data symbol X[k], where krepresents the subcarreir index. The OFDM transmitter usesan inverse discrete Fourier transform (IDFT) of size N formodulation. Then the transmitted OFDM signal in discrete-time domain can be expressed as

x[n] ={NL,X[k] exp (J27 N) 0< n< N-1k=o

(1)

where n is the time domain sample index of an OFDM signal.In order to avoid inter-symbol interference (ISI) caused bymultipath environments and inter-carrier interference (ICI), acyclic prefix (CP) is appended to the OFDM symbol. Afterpassing through a multipath channel and removing CP, one re-ceived discrete time domain OFDM signal y[n] is representedby

y[n] = x[n] x h[n] + w[n], 0 < n < N-1 (2)

0-7803-9392-9/06/$20.00 (c) 2006 IEEE

2592

where x denotes cyclic convolution operation, w [n] is inde-pendent and identically distributed additive white Gaussiannoise (AWGN) sample in time domain with zero mean andvariance uwt2 = E [ w[n] 2] and h[n] is the discrete timechannel impulse response given by

L-1

h[n] = Z a13[n -1], (3)1=0

where ali represents a different path complex gain, I is theindex of the different path delay that is based on samplingtime interval, which means there is no channel power losscaused by sampling time miss-match [3], and L is the length ofthe channel impulse response. For simplicity, time dependencenature of the channel impulse response is suppressed in thenotation. At the receiver, we assume that the guard intervalis longer than the maximum channel delay and the frequencysynchronization is perfect. Then, the k-th subcarrier output infrequency domain can be represented by

Y[k] = X[k]H[k]eJ2w N + W[k], 0 < k < N -1 (4)

where W[k] is AWGN sample in frequency domain with zeromean and variance 72 = N72 t [5], 0 indicates normalizedtiming offset, and H[k] is the channel frequency responsegiven by:

H[k] =EZa exp (-J2w ) O < k < N -1 (5)1=0

B. Timing synchronization and its problem

One approach of the timing synchronization uses the slidingcorrelation as described;

N-1 2A = argmax , y [n +IH]p [1]

1=0

where p[l] is a known reference training symbol. In practice,synchronization algorithms, including (6), have some timingoffset on multipath channels with respect to rms delay ofchannel. Therefore, although synchronization is satisfactory onsatellite channels, timing offset on IMR channels can causeperformance degradation. Mostofi analysis this degradationcaused by timing offset [6]. In this paper, authors show that thelate symbol timing (i.e., m > 0) cause both a significant ISIcreated by the samples from the next symbol and ICI by lossof othogonality. In contrary, timing error for the early symboltiming (i.e., m < 0) case result in lower interference thanlate symbol timing (or no interference) due to the presence ofCP. As a result, a simple method to avoid these degradation isshifting the mean value of synchronizaton inside CP region byadding preset margin A to estimated point A, where A mustbe greater than the maximum timing offset caused by (6). Butthis method has a drawback reducing multipath tolerance.

Frequency dom n Time domain Frequency domain,_- ,_

LSChannelestimation

Fig 1.[1]

HT., (°) -

HLS (1)

H (N -1)

N-pointIDFT

hL (0) h1 (0)

h (L-1) h1 (L -1)

O

O

Hi (0)

. NpointDFT

H (N - 1)

The block diagram of the conventional DFT-based channel estimation

C. DFT-based channel estimation with timing offsetDFT-based channel estimation exploits the typical property

of OFDM systems having the symbol period much longer thanthe duration of the channel impulse response. Because theestimated channel impulse response from least square (LS)has most of its power concentrated on a few first samples [1],DFT-based estimation reduces the noise power that exists onlyoutside of the CIR part [2]. The basic block diagram of DFT-based estimation is shown in Fig.l. For simplicity, we assumetiming synchronization is perfect. The n-th estimated sampleof channel impulse response can be expressed with the LSestimation, then we have

hLs [n] IDFTN{HLs[k]}, O<n<N-1h[n] + w[n] (7)

where IDFTN } indicates N-point inverse discreteFourier transform, HLS [n] = Y [k]IX [k], andw[n] = IDFTN{W[k]IX[k]}. The channel impulseresponse is typically limited to the length of channel impulseresponse L which is less than the guard interval. In (7), thechannel impulse response can be described as:

(6) h[n] = { IDFTN{fH[k]} 0 < n < L(6) h[n] ~0, L<n<N

11 (8)

By using (7), (8) can be divided into two parts; CIR part andnoise only existing part, then we have:

hLs[n] = h[n] +w[n] if 0 < n < L-1i-vw[n] otherwise (9)

As shown in (8), all information of channels is contained in thefirst L samples and other samples are just noise. Hence takingonly the first L samples and ignoring noise-only samples, wecan achieve a better performance. Expressing these processesin equations, we get:

hDFT[n] = h[n] +w[n] if 0 < n < L'1 0 otherwise

1(10)

From (10), DFT-based channel estimation is denoted as:

HDFT[k]=DFTN hDFT[n]}, O<k<N-1 (1 1)

To illustrate the performance of DFT-based channel estimation,we consider the individual MSE of each subcarriers. In [2], if

2593

we assume channel has sample-spaced impluse response, theindividual MSE of DFT-based channel estimation is given as

MSEDFT [k]L 3N SNR

where SNR= E[ X[k] 21]/f is the average signal to noiseratio (SNR) and EF [ fX[k] 2] E [lX[k] -2] is a constantdepending on the signal constellation. Usually, L is unknownvariable depending on channel environments, and (12) repre-sents small channel length has small MSE. To express differenttwo satellite channel environments, we define two parametersof the channels

. LSAT is the length of the satellite channel impulseresponse

. LIMR is the length of a IMR channel impulse responseEspecially, satellite channels are characterized as small chan-nel length and IMR channels are characterized as large channellength. Therefore, DFT-based channel estimation ideally hasbetter performance on satellite channels than IMR channels.However, if we set L as LSAT on IMR channels, MSE willincrease significantly by missing the energy in the excludedchannel taps [1], and moreover the length of channels are notknown at the receiver. As a result, we must set L as LjMR toprevent MSE floor regardless of system channel environments.However, in this case, the MSE of conventional DFT-basedestimation is fixed as Lim,R even though we can get muchbetter performance on satellite channels.

In addition to this property, timing offset also affect theperformance of DFT-based channel estimation. In brief, timingoffset circularly shift CIR in (7) [6]. In case of using methodin subsection B, timing offset always occur at left hand side ofexact timing point in received data sequence. this offset shiftsCIR in (7) to right hand side as shown in Fig 2. As a result, inorder to prevent MSE floor caused by missing channel taps,L in (12) must be set as LjMR + A. Consequently, the MSEof DFT-based channel estimation is degraded as follow:

MSEDFT [k] LjMR +A 13N SNR

(13)

On the contrary, if we can adaptively choose L both satellitechannels and IMR channels, we could expect the better per-formance on both channels environments. Hence, we proposean improved estimation algorithm in the next section based onthis idea.

III. PROPOSED CHANNEL ESTIMATION

In this section, we propose an efficient joint channel es-timation and timing synchronization algorithm for satelliteOFDM systems. In the proposed algorithm, we introducea new significant channel tap estimation (SCTE) to detectsignificant and effective channel taps. we also refine thetiming synchronization by using the result of SCTE block.The detail procedure of proposed algorithm are described bythe following steps with Fig.2:

1) Estimate the initial timing instants T using (6).2594

2) To prevent ISI and ICI, subtract preset margin A (asmentioned in subsection b) from initial timing instant;T -A.

3) Do FFT with timing instant T- A and estimate thechannel impulse response from LS estimation through(7)

4) In order to determine effective channel taps, we detectsignificant channel taps as below decision rule:

hscTE[nl = {hLS [n] if hLs [n] > A

0 otherwise(14)

where A is the threshold deciding the significant channeltaps. Since LIMR + A is the largest channel lengthwith timing offset, we consider significant channel tapdecisions just in the region 0 < n < LjMR + A -1.

5) To estimate residual timing offset 7, find the first nonzero sample from the result of (14) with threshold A,.

6) The final estimated timing instant is T- A + a7) Compensate (14) for residual timing offset a

hprop [n] { O(7 < n < LJMR+u1

L,MR+±< n < N +o- I(15)

The final channel frequency response of proposed esti-mation is

Hprop[k] = DFTN {hprop[}n], 7 < n < N+- 1.(16)

The core of the proposed algorithm is in step 4), 6) and 7)detecting significant channel taps and estimate residual timingoffset and compensation. Especially, the performance in step4) depend on the threshold. In order to decide the threshold,we compare MSE of two alternative cases which occur in step4); zero-substitution case and no-substitution case. First, weconsider no-substitution case. When this case occur in step 4)channel estimation is same to conventional DFT-based channelestimation, and since we set the L as LIMR (for convenience,we assume perfect synchronization ) to prevent MSE floor, theindividual MSE of k-th subcarrier is

MSEDFT [k] =N SNR

A

cI 0, i S

(17)

Initial timing instant byusing correlation method

N

tExact timing point

Received samplesequence: y[n]

hLs [n] without noise

N LIMR a

Fig 2. Channel impulse response with timing offset.

The second case is that we substitute 'y-th arbitrary channeltap as zero. As derived in Appendix, the individual MSE ofthe zero-substituted channel hzero[n] is:

MSE ~ 2 LImR -1 /3 <n<N 118MSEzero [k] =7h[y]d N *SNR' <n<N- 1(18)

From (17) and (18), it is obvious that MSE is reduced byzero-substitution, if MSEzero- MSEDFT < 0; that is,

MSEzero- MSEDFT < 0 :

1 13N* SNR < 0 (19)

where 1 S can be expressed with time domain noise powerN SNR1 13 F 21J2NSNR= E[EX[kl j(wt (20)

Because the estimated channel hLS [n] includes the noisepower as well as channel information, we add the noise powerto both side of (19) then, we get,

hDFT [] < 2 F[EX[k] |2] GWt = A/ (21)

where or? (7h2[^]+E [X[k] |2] o%t and A' is optimalthreshold for the average observations of channel samples.However, in (14), we should set the threshold A for aninstantaneous observation IhLS[y] 2 not for the mean valuehDF []. Since the available sample is just one sampled value,

the only unbiased point estimator is equal to the observed onesampled data itself [7]. Therefore, the optimal threshold A forinstantaneous sample hLS [y] 2 is same to A'.

A=2EE[X[k]l 2]52 (22)

By these processing, we can adaptively determine the thresh-old against the variable SNR and channel environments.

IV. SIMULATION RESULTS

In this section, we investigate the performance of the pro-posed algorithm on both satellite channel and IMR channels.Table I show the channel parameters of these two cases usedin this paper. The MSE and bit error rate (BER) performancesare examined. An OFDM system with symbols modulated byQPSK is used on multipath channel. The system bandwidth is10MHz, which is divided into 1024 tones with a total symbolperiod of 128Ms, of which 25.6Ms constitutes the CP, and thecarrier frequency is 2GHz. An OFDM symbol thus consistsof 1024 samples, 256 of which are included in the CP. Unitdelay of channel is assumed to be the same as OFDM sampleperiod. Thus, there is no power losses caused by non-samplespaced [3]. We assume channels are static over an OFDMframe, where the preamble is 1 OFDM symbol long and dataare composed of 30 OFDM symbols. Through the simulation,we set the timing offset margin A as 100 samples in thissimulation and set LIMR as 111 from table I. The threshold A,to detect the first channel taps is 4 time of time domain noisepower. IMR channel model at table I is based on multipathchannel profile shown in [8]. Aa a result, from (13) the MSE

TABLE ICHANNEL PARAMETERS

SAT-channel IMR-channelrelative delay Avg. Power relative delay Avg. Power(sample ) (dB) (sample ) (dB)

0 0.0 0 -6.54 15 16 -3.7

19 -4.7100 0103 -1107 9111 -10

of channel estimation is fixed as 100+110 S3 even on satellite1024 SNRchannel. However, with proposed estimation, MSE decreaseby deciding significant channel taps. As shown in Fig. 3,the performance was significantly improved about 10dB whenproposed algorithm was adopted.

Fig. 4 displays the BER performance of proposed algorithmon satellite channel with Rician factor 10. On satellite chan-nels, since timing synchronization with (6) has very smalltiming offset, conventional DFT-based channel estimationachieves better performance than least square (LS) channelestimation. Especially, proposed channel estimation has almostsame performance with perfect channel estimation.On IMR channels, since conventional channel estimation

suffer from timing synchronization and has large timingoffset, BER floor induced by significant ISI. Contrary tothis, with proposed algorithm, BER floor does not occur andperformance is same with that of perfect channel estimationand synchronization on IMR channels. Fig. 5 confirms theseresults.

V. CONCLUSIONS

We propose a new practical channel estimation and timingsynchronization to cope with the performance degradationon IMR channels. Proposed channel estimation and timingsynchronization improves the performance both on satellitechannels and IMR channels. Moreover it does not make MSEfloor on any of the channels by adaptively deciding significantchannel taps based on threshold. We calculate the thresholdused to determine significant channel taps in proposed esti-mation. Proposed synchronization, moreover, compensates theresidual timing offset and increases the accuracy of synchro-nization. Propose method also effective on terrestrial mobilesystem.

APPENDIX

In Appendix, we derive the MSE of zero-substitution casein (18). The individual MSE of k-th subcarrier is derived as,for 0 < n < N -1,

MSEzero[k] =E [ DFT\ {h[n]-hzero [n]j} 2]

E DFTN {EZ6[n -u]u=o

(23)

2595

LIMR-1 2

, [n]n=O,no&-yI

where DFTN{-} represents the discrete Fourier transform.We rewrite (23) as follow:

MSEzero [k] = E [ DFTN {o- 6 [n Y] } 12]

+E[ E w[n] exp( j27N)Ln=O,no&-y

E [10a 12]LIMR-1 LIMR-1/

+z E [w [n]w*[m] ] exp(-n=O,no-y m=O,mO-Y

100LS-CEConventional DFT-CEProposed DFT-CE

1 -10

10o2LuCO

j2w k(n m))

= h±[]+ (LIMR 1) E [w[n]w*[n] (24

where 7[2] E [a 2] represents the average power of

-th channel tap. By using the definition of the DFT and (24),the MSE of zero-substitution case is derived as follow:

MSEzero[k] = o-h[Y] + (LIMR - 1)

x E E [l] exp ( j2 N))

x (NE E LX[k2] jexp ( j2 N)))

- 1 2

(7]LMR

-N fEIN2 +X[ki1]

2 _LIMR -1N SNR

1010 15

SNR20 25 30

Fig 3. Comparing MSE performance with perfect timing synchronization.

100XplXXX XXXXt: alu LS-CE, Perfect synch.

----t - .'"'. DFT-CE, Synch. with Eq. (6)Proposed method

10o Perfect CE, Perfect synch.

rr T --.. \XXTXXX

LLJ - t - -< '.

-.in2~ ~ ~~ ~ ~ ~ ~ ~ ~~~~~~~~~~E

(25)

Hence, we can obtain the desired MSE equation.

REFERENCES

[1] J.-J van de Beek, 0. Edfors, M. Sandell, S. K. Wilson, and P. 0.

Borjesson, "On channel estimation in OFDM systems," IEEE Veh. Tech.Conf., vol. 2, pp. 815-819, July 1995.

[2] 0. Edfors, M. Sandell, J.-J van de Beek, S. K. Wilson, and P. 0. Bor-jesson, "Analysis of DFT-based channel estimators for OFDM," WirelessPersonal commun., vol. 12, no. 1, pp. 55-70, Jan. 2000.

[3] B. Yang, Z. Cao, and K. B. Letaief, "Analysis of Low-ComplexityWindowed DFT-based MMSE Channel Estimation for OFDM systems,"IEEE Trans. Commun., vol. 49, pp. 1977-1987, Nov. 2001.

[4] B. Yang, K. B. Letaief, R. S. Cheng and Z.Cao, "Channel estimation forOFDM transmission in multipath fading channels based on parametricchannel modeling," IEEE Trans. Commun., vol. 49, pp. 467-479, March2001.

[5] C. S. Yeh and Y. Lin, "Channel estimation using pilot tones in OFDMsystems," IEEE Trans. Broadcasting, vol. 45, no. 4, pp. 400-409, Dec.1999.

[6] Y. Mostofi and D. C. Cox, "Timing synchronization in high mobilityOFDM systems," IEEE Int. Conf. on Commun., vol. 4, pp.2402-2406,June 2004

[7] S. M. KAY, Fundamentals of statistical signal processing: Estimationtheory, Prentice-Hall, 1993.

[8] SATIN IST 2000-25030. "Simulation Results and Evaluation," Deliver-able n. 7, March 2003.

0 2 4 6 8 10SNR

12 14 16 18

Fig 4. BER performance on satellite channels with rician factor 10.

100000LS-CE, Perfect synch.

FT-CE, Synch ith Eq. (6)Proposed method

------------ 0Perfect CE, Perfect synch.

rr -2 \L1] 10 -000 0 0 0 00 0 0 X X X _ -,2-------- ----

5 10 15 20 25 30SNR

Fig 5. BER performance on IMR channels.

2596

L-1

E c,6[n- v]V=O,VO7