OFDM channel

OFDM

channel estimation with timing offset ^for satellite plus terrestrial multipath channels

Yeon-Su Kang, Do-Seob Ahn, Ho-Jin Lee Digital 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 synchronization to cope with satellite plus intermediate module repeater (IMR) channels. Conventional DFT-based channel estimations suffer from the timing offset and incorrect channel impulse response, andthis results in means square error (MSE) floor of channel estimations. Moreover, timing synchronization accuracy is also degraded onIMRchannels. We,therefor, propose an improved DFT-based channel estimation by deciding significant channel taps based on a threshold and we derive this threshold with respect toMSE. Using results from proposed channel estimation, we compensate residual timing offset of conventional timing estimation.

I. INTRODUCTION

Orthogonal frequency division multiplexing (OFDM) is the most popular promise for the Beyond 3G (B3G) systems for its advantages in high-bit-rate transmission over dispersive channels. IntheB3G systems, themajor role of satellites will be providing terrestrial fill-in service and efficient multicas- ting/broadcasting services. As the terrestrial fill-in services, satellite systems provide services and applications similar to those of terrestrial systemsoutside the terrestrialcoverage area as much as possible. In this regard, in order to enhance the coveragegiven by satellite layerinurban andsub-urban, intro- ducing intermediate modulerepeaters (IMR) is considered as a solution. However, in present IMR environments, multipath propagation similartothatexperiencedinthe terrestrial chan- nels. Usually, under terrestrial channels, channel estimation and timing synchronization are degraded by multipath effect comparing with satellite channels having line of sight and small delay.

Basedonthesetechnological issues,wepropose anefficient OFDM channel estimation and synchronization algorithm to cope with both IMR and satellite channels. Forchannel esti- mation in this paper, we especially consider discrete Fourier transform (DFT)-based estimation [1]-[4]. This channel es- timation uses time domain properties of channels. Since a channelimpulseresponse (CIR), without losses ofgenerality, is not longer than the guard interval in OFDM systems, this estimation is modifiedin[1] by limiting the number of channel taps in time domain and suppressing noise outside of CIR.

However, because the improvement is based on assumption that channel impulse response or its delay length is knownat thereceiver, these methodscanmakemeansquare error(MSE) floorby theenergylossinthe excluded channel tapswhen the

channel impulseresponseis incorrect [2]. Forexample, MSE floor will occur really under the IMR channel (large delay) with assumptionon satellite channel (small delay).

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

In this paper, we propose a modified DFT-based channel estimationinordertocopewith theMSEfloor andcompensate residual timing offset of conventional timing synchronization by using results form proposed channel estimation. In pro- posed channel estimation, to include all informative channel taps without prior channel information, we detect significant channel taps withrespect to a threshold. The threshold is de- terminedinordertoreduce theMSEof the channel estimation and relates totime domain noisepower.

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 IV presents simulation results and discussions, and Section V offers some conclusions.

II. SYSTEMDESCRIPTION A. OFDM system

We consider an OFDM system that has N subcarriers and each subcarrier consists of data symbol X[k], where k represents the subcarreir index. The OFDM transmitter uses an inverse discrete Fourier transform (IDFT) of size N for modulation. Then the transmitted OFDM signal in discrete- time domain canbe expressed as

x[n] ={NL,X[k]

^exp

^(J27

^{N) 0< n< N-1}

k=o (1)

wherenis the time domainsample index ofanOFDM signal.

In order to avoid inter-symbol interference (ISI) caused by multipath environments and inter-carrier interference (ICI), a cyclic prefix (CP) is appended to the OFDM symbol. After passing throughamultipathchannel andremoving CP,one re- ceived discrete time domain OFDM signaly[n] isrepresented by

y[n]

⁼

x[n]

^x

h[n]

⁺

w[n],

0<n < N-1 (2) 0-7803-9392-9/06/$20.00 (c)2006IEEE

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

h[n]

⁼L-1^Z

a13[n -1], (3)

1=0

where

ali

represents a different path complex gain, I is the index of the different path delay that is based on sampling time interval, which means there is no channel power loss caused by samplingtime miss-match [3], and L is the lengthof the channel impulseresponse. For simplicity, timedependence nature of the channel impulse response is suppressed in the notation. At the receiver, we assume that the guard interval is longer than the maximum channel delay and the frequency synchronization is perfect. Then, the k-th subcarrieroutput in frequency domain canbe represented by

Y[k] ⁼

X[k]H[k]eJ2w

^N +W[k], 0 < k < N -1 (4) whereW[k] is AWGNsampleinfrequency domain with zero mean and variance 72 ⁼ N72^t [5], 0 indicates normalized timing offset, and H[k] is the channel frequency response given by:

H[k] =EZa exp (-J2w

)

O

^{< k <} N -1

(5)

1=0

B. Timing synchronization and its problem

One approach of the timing synchronizationuses the sliding correlation as described;

N-1 2

A ⁼arg max , y[n

IH]p

+ [1]

1=0

wherep[l] is a known reference training symbol. Inpractice, synchronization algorithms, including (6), have some timing offset on multipath channels with respect to rms delay of channel.Therefore, although synchronizationis satisfactory on satellite channels, timing offset on IMR channels can cause performance degradation. Mostofi analysis this degradation causedby timing offset [6].Inthispaper,authorsshow that the late symbol timing (i.e., m > 0) cause both a significant ISI created by the samples from thenext symbol and ICIby loss ofothogonality. Incontrary, timing errorfor the early symbol timing (i.e., m < 0) case result in lower interference than late symbol timing(or no interference) due to the presence of CP. As aresult, asimple method toavoid thesedegradation is shifting themeanvalue ofsynchronizaton inside CPregion by addingpreset margin A to estimated pointA, where A must be greaterthan the maximumtiming offset caused by (6). But this method has adrawbackreducing multipath tolerance.

Frequency domn Time domain Frequency domain

,_- ,_

ChannelLS estimation

Fig 1.

[1]

HT.,(°) -

HLS(1)

H (N -1) N-point

IDFT

hL(0) h1 (0)

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

O O

Hi (0)

. Npoint DFT

H (N^-1)

The block diagram of the conventional DFT-based channel estimation

C. DFT-based channel estimation with timing offset

DFT-based channel estimation exploits the typical property ofOFDM systemshavingthe symbol period muchlonger than the duration of the channel impulse response. Because the estimated channel impulse response from least square (LS) hasmost of its power concentrated on a few first samples [1], DFT-based estimationreduces the noise power that exists only outside of the CIR part [2].The basic block diagram of DFT- based estimation is showninFig.l. For simplicity, we assume timing synchronization is perfect. The n-th estimated sample of channel impulse response can be expressed with the LS estimation,then we have

hLs [n] IDFTN{HLs[k]},

O<n<N-1

h[n] +w[n] (7)

where IDFTN } indicates N-point inverse discrete Fourier transform, HLS[n] = Y[k]

IX

^{[k], and}

w[n] ⁼

IDFTN{W[k]IX[k]}.

The channel impulse responseis typicallylimited to the length of channel impulse response L which is less than the guard interval. In (7), the channel impulseresponse canbe describedas:

(6)_{(6) h[n]}h[n] = {

IDFTN{fH[k]} _~0,

L< n< N^{0 < n <L} 1

1

(8)

Byusing (7), (8) canbe divided into two parts; CIR part and noise only existing part, then we have:

hLs[n]

⁼ h[n] +w[n] if 0 < n <

i-vw[n]

otherwiseL-1 (9) Asshownin(8),all informationof channels is contained in the firstLsamples and other samples arejust noise. Hence taking only the first L samples and ignoring noise-only samples, we can achieve abetterperformance. Expressing these processes in equations, we get:

hDFT[n]

⁼ '1h[n] +0w[n] if 0 < n < Lotherwise

1 (10)

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

HDFT[k]=DFTN hDFT[n]},

O<k<N-1 (1 1) Toillustrate theperformance of DFT-based channelestimation, we consider the individualMSEof each subcarriers. In [2], if 2593

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

MSEDFT [k]

_{N SNR}^{L 3}

where SNR= E[X[k]

21] /f

is the average signal to noise ratio

(SNR)

and EF

[ fX[k]

^{2] E}

[lX[k] -2]

^{is a constant}

depending onthe signal constellation. Usually, Lis unknown variable depending on channel environments, and (12) repre- sentssmall channellength has smallMSE. To expressdifferent two satellite channel environments, we definetwo parameters of the channels

. LSAT is the length of the satellite channel impulse response

. LIMR is the length ofa IMRchannel impulse response Especially, satellite channels arecharacterized as small chan- nellength andIMRchannelsarecharacterizedaslarge channel length. Therefore, DFT-based channel estimation ideally has better performance on satellite channels than IMR channels.

However, if we set L as LSAT on IMR channels, MSE will increase significantly by missing the energy in the excluded channel taps [1], andmoreover the length of channels are not known atthe receiver. As aresult, we must set L as LjMR to prevent MSEfloorregardless ofsystemchannel environments.

However, in this case, the MSE of conventional DFT-based estimation is fixedas Lim,R eventhoughwe cangetmuch betterperformance on satellite channels.

In addition to this property, timing offset also affect the performance of DFT-based channel estimation.Inbrief, timing offset circularly shift CIR in (7) [6]. Incase ofusing method insubsectionB, timing offset always occur atleft hand side of exacttiming pointinreceived data sequence. this offset shifts CIR in(7)toright hand sideasshowninFig2. As aresult, in order to prevent MSE floor caused by missing channel taps, L in (12) must be set as LjMR +A. Consequently, the MSE of DFT-based channel estimation is degraded as follow:

MSEDFT [k] ^LjMR

_N^+A_SNR

¹³

⁽¹³⁾

On the contrary, if we can adaptively choose L both satellite channels and IMR channels, we could expect the better per- formance onboth channels environments. Hence, we propose animproved estimation algorithminthenextsection basedon this idea.

III. PROPOSED CHANNEL ESTIMATION

In this section, we propose an efficient joint channel es- timation and timing synchronization algorithm for satellite OFDM systems. In the proposed algorithm, we introduce a new significant channel tap estimation (SCTE) to detect significant and effective channel taps. we also refine the timing synchronization by using the result of SCTE block.

The detail procedure of proposed algorithm are described by the following steps withFig.2:

1) Estimate the initialtiming instants Tusing (6).

2) To prevent ISI and ICI, subtract preset margin A (as mentioned in subsection b) from initial timing instant;

T-A.

3) Do FFT with timing instant T- A and estimate the channel impulse response from LS estimation through 4) In

(7)

order to determine effective channel taps, we detect

significant channel taps as below decision rule:

hscTE[nl =

{hLS

[n] if hLs[n] > A

0 otherwise (14)

whereA is the threshold deciding the significant channel taps. Since LIMR + A is the largest channel length with timing offset, we consider significant channel tap decisionsjust in the region 0 < n < LjMR+A -1.

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

A,.

6) The final estimated timing instant is T- A + a 7) Compensate (14) for residualtiming offset a

hprop [n]

^{{ O}

_L,MR+±

^{(7< n}_<^<_n

^LJMR+u1

_{< N +o- I} ⁽¹⁵⁾

The final channel frequency response ofproposed 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 channeltaps and estimate residualtiming offset and compensation. Especially, the performance in step 4) depend onthe threshold. Inorder todecide the threshold, wecompare MSEoftwo alternativecaseswhichoccurin step 4); zero-substitution case and no-substitution case. First, we consider no-substitution case. When this case occurin step 4) channel estimation issame toconventional DFT-based channel estimation, and sincewe setthe L as LIMR (for convenience, we assumeperfect synchronization )toprevent MSEfloor, the individual MSE of k-th subcarrier is

MSEDFT[k] =N SNR

A

cI 0

,

ⁱ

S

(17)

Initialtiminginstantby usingcorrelation method

N

Exacttiming

t

point Receivedsample

sequence:y[n]

hLs[n]without noise N LIMR a

Fig2. Channel impulseresponsewithtimingoffset.

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

MSE

~

^{2 LImR -1 /3 <n<N 118}

MSEzero[k]=7h[y]

d

^N

*SNR'

^{<n<N- 1(18)}

From (17) and (18), it is obvious that MSE is reduced by zero-substitution, ifMSEzero-MSEDFT < 0; thatis,

MSEzero- MSEDFT < 0 :

1 13

N*

SNR < 0

(19)

where _N1 SSNRcanbeexpressed with time domain noisepower

1 13 ^F

21J2

NSNR=

^E

[EX[kl j(wt

⁽²⁰⁾

Because the estimated channel

hLS

[n] includes the noise power aswell aschannel information, weadd the noisepower to both side of(19) then, we get,

hDFT[] < 2 F

[EX[k] |2] GWt

⁼ A/ (21) where

or?

^(7h

2[^]+E [X[k] |2] ^o%t

^and

^A'

^is

optimal

threshold for the average observations of channel samples.

However, in (14), we should set the threshold A for an instantaneous observation

IhLS

[y] 2 not for the mean value

hDF [].

Since the available

sample

is

just

^one

sampled

value, the only unbiased point estimator is equaltothe observedone sampled data itself[7]. Therefore, the optimal threshold A for instantaneous sample

hLS

[y] 2 is same to A'.

A=2E

E[X[k]l 2]52

⁽²²⁾

Bythese processing, we can adaptively determine the thresh- oldagainst the variable SNRand channel environments.

IV. SIMULATIONRESULTS

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 used inthispaper. TheMSE and biterror rate(BER)performances areexamined. AnOFDM system with symbols modulated by QPSK is usedonmultipath channel. The systembandwidth is 10MHz, which is divided into 1024 tones withatotal symbol period of 128Ms, of which 25.6Ms constitutes the CP, and the carrier frequency is 2GHz. An OFDM symbol thus consists of 1024 samples, 256 of which are included in the CP. Unit delay of channel is assumedtobe thesame as OFDM sample period. Thus, there is no power losses caused by non-sample spaced [3]. We assume channels are static over an OFDM frame, where the preamble is 1 OFDM symbollong and data arecomposed of30 OFDM symbols. Through thesimulation, we set the timing offset margin A as 100 samples in this simulation andsetLIMR as 111 from tableI. The threshold

A,

to detect the first channel tapsis4time of time domain noise power. IMR channel model at table I is based on multipath channel profile shownin [8]. Aa aresult, from (13) the MSE

TABLEI CHANNELPARAMETERS

SAT-channel IMR-channel

relative delay Avg. Power relativedelay Avg. Power

(sample ) (dB) (sample ) (dB)

0 0.0 0 -6.5

4 15 16 -3.7

19 -4.7

100 0

103 -1

107 9

111 -10

of channel estimation is fixedas

100+110

₁₀₂₄

S3

_SNReven onsatellite channel. However, with proposed estimation, MSE decrease by deciding significant channel taps. As shown in Fig. 3, theperformance wassignificantly improved about 10dB when proposed algorithm was adopted.

Fig.4displays theBERperformance of proposed algorithm on satellite channel with Rician factor 10. On satellite chan- nels, since timing synchronization with (6) has very small timing offset, conventional DFT-based channel estimation achieves better performance than least square (LS) channel estimation.Especially, proposed channel estimation has almost sameperformance with perfect channel estimation.

On IMR channels, since conventional channel estimation suffer from timing synchronization and has large timing offset, BER floor induced by significant ISI. Contrary to this, with proposed algorithm, BER floor does not occur and performance is same with that of perfect channel estimation and synchronization on IMR channels. Fig. 5 confirms these results.

V. CONCLUSIONS

Wepropose a newpractical channel estimation and timing synchronization to cope with the performance degradation on IMR channels. Proposed channel estimation and timing synchronization improves the performance both on satellite channels andIMRchannels. Moreoverit doesnotmakeMSE flooronanyof the channels by adaptively deciding significant channel taps based on threshold. We calculate the threshold used to determine significant channel taps in proposed esti- mation. Proposed synchronization,moreover, compensatesthe residual timing offset and increases the accuracy of synchro- nization. Propose method also effective on terrestrial mobile system.

APPENDIX

InAppendix, we derive the MSE of zero-substitution case in (18). The individual MSE of k-th subcarrier is derivedas, for 0 <n < N-1,

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

[n]j}

^2]

E DFTN

{E

^Z6[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[10a12]

LIMR-1 LIMR-1/

+z E[w[n]w*[m]]^exp(-

n=O,no-y m=O,mO-Y

100 LS-CE

Conventional DFT-CE Proposed DFT-CE 1-10

10o2

LuCO

j2w k(nm))

= h±[]+(LIMR 1) E[w[n]w*[n] ⁽²⁴

where 7

[2]

E ^{[a 2]} represents ^the average power ^of

-th channeltap. By using the definition of theDFT and(24), the MSE of zero-substitution case is derivedas follow:

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

x EE [l] exp ( j2 N))

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

- 1 2

(7] ^LMR -N fEI

N2

+X[ki

^1]

2 _LIMR -1

N SNR

10 10 15

SNR 20 25 30

Fig 3. Comparing MSE performancewithperfecttiming synchronization.

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

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

Proposedmethod

10o PerfectCE,Perfectsynch.

rr T -.. \XXTXXX-

LLJ - t--< '.

-.

in2~ ~ ~~ ~ ~ ~ ~ ~ ~~~~~~~~~~E

(25) Hence, we can obtain the desired MSE equation.

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0 2 4 6 8 10

SNR

12 14 16 18

Fig 4. BERperformance^onsatellite channels with rician factor 10.

100 000^{LS-CE,Perfectsynch.}

FT-CE, Synch ith Eq. (6) Proposedmethod

--- 0Perfect CE, Perfect synch.

rr -2 \

L1] 102----000 0 0 0 00 0 0 X X X _ -, ^----

5 10 15 20 25 30

SNR

Fig5. BERperformance^onIMRchannels.

L-1

E c,6[n-

v]

V=O,VO7