Robust Time and Frequency Synchronization in

OFDM based 802.1 a WLAN systemsS. K. Manusani, R. S. Kshetrimayum, Member, IEEE, and R. Bhattacharjee, Member, IEEE

Abstract- In this paper, robust and efficient time and fre-quency synchronization technique suitable for IEEE 802.11awireless LAN system is proposed. The proposed method per-forms OFDM symbol boundary detection and frequency offsetestimation using correlation techniques. The conjugate propertyof long preamble is used to reduce the computational complexity.In this proposed method, coarse time and fine frequency offset areestimated jointly and the frequency offset is estimated accuratelybefore fine time estimation.

Index Terms- OFDM, Timing synchronization, Frequencysynchronization, IEEE 802.11a.

I. INTRODUCTIONOrthogonal frequency division multiplexing (OFDM) is an

important modulation technique for high speed and highspectral wireless communications through frequency selectivechannels [1]. In OFDM, wide transmission spectrum is dividedinto narrow bands and data is transmitted in parallel/orthogonalon these overlapped narrow bands unlike the conventionalcommunication systems. Orthogonal frequency division mul-tiplexing (OFDM) has gained interest in recent years becauseOFDM WLAN system can combat impairments due to largemultipath delay spreads very effectively with the help of guardinterval (GI) between the OFDM symbols and OFDM systemsare less sensitive to timing errors due to cyclic extensionof OFDM symbols, which acts as a GI between adjacentOFDM symbols [2], [3]. But one of the biggest problemswith OFDM system is the synchronization. First one of thesesynchronization tasks is to locate and track symbol boundariesbetween consecutively received OFDM symbols and removeguard interval inserted to mitigate Inter-Symbol Interference(ISI). Symbol timing offsets in OFDM receivers not onlyinduce ISI but also cause linear phase rotation of the signalconstellations of the received Fast Fourier Transform (FFT)outputs, which degrades the system performance. Secondly,orthogonality is the main feature to be preserved in OFDMsignals. If this property gets disturbed during the transmissionand reception, undesirable effects such as ISI and Inter-CarrierInterference (ICI) will occur [4]. Due to mismatch of transmit-ter and receiver carrier frequencies, OFDM system is sensitiveto frequency offset. Because, in OFDM, the carriers areinherently closely spaced in frequency compared to the channelbandwidth, the tolerable frequency offset becomes a very smallportion of the channel bandwidth. To estimate frequency offsetand starting position of OFDM packet, we propose here robusttime and frequency synchronization scheme for OFDM WLANsystems of 802.11a standard.

The authors are with the department of Electronics and Communication,Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India (e-mail: shiva@iitg.ernet.in; krs@iitg.ernet.in; ratnajit@iitg.ernet.in).

1-4244-0370-7/06/$20.00 C 2006 IEEE

Several approaches have been proposed on the basis of usingpreambles or using cyclic prefix. For burst mode transmissionsuch as wireless LAN, the method of using preamble symbols[5] is preferred for fast time and frequency synchronization.The IEEE 802.1 la standard specifies a preamble at the start ofevery frame. The preamble consists of 10 short preambles andtwo long training symbols. The conventional timing synchro-nization schemes uses short preambles to estimate coarse timevia auto-correlation and then use long preambles to estimatefine time via cross-correlation [6] or uses short preamblesfor both coarse and fine time estimation via combinationof auto-correlation and cross-correlation methods [7]. In allthese methods, periodicity of preambles is used for estimation.But frequency offset of the local oscillator disturbs the crosscorrelation peaks significantly, which will affect the accuracyand also to estimate time offset, it requires complete shortand long preambles, which will increase complexity. In ourproposed method, before fine time estimation, frequency offsetis accurately estimated and corrected [8], so fine time estima-tion accuracy is not affected by frequency offset and also weutilized conjugate symmetric property of long preamble in theestimation of fine time in addition to it's periodicity property,which uses only one-half of the long preamble in which thetwo 32-sample blocks are complex conjugate symmetric toeach other, instead of the complete long preamble, which willdecrease the complexity and computational time [9].

This paper is organized as follows: Section II covers theOFDM system architecture and Section III describes theproposed method and simulation environment and results arepresented in Section IV. In Section V, a conclusion is drawn.

II. OFDM SYSTEM ARCHITECTUREIn IEEE 802.1 la, OFDM is used for data transmission.

OFDM symbol can be constructed as follows. First, the datato be transmitted is mapped to complex symbols in frequencydomain. Secondly, these complex symbols are modulated onto the N subcarriers by using Inverse Fast Fourier Transform(IFFT) to get a time domain complex OFDM symbol, whichis represented as

N-1

x() VN =0X k) n = 0,1,... N -1 (1)

where X(k) denotes the data symbol in subcarrier k, x(n) isthe nih sample of OFDM symbol. The last Ng samples ofIFFT outputs are copied and added to form the cyclic prefixat the beginning of each OFDM symbol. In IEEE 802.1 la, Nis equal to 64, and Ng equal to 16. 52 subcarriers out of these64 are used for data and remaining are equal to zero and four

subcarriers out of these 52 are used as pilot tones. Finally thetime domain samples are D/A converted, mixed with carrier,filtered and transmitted. At receiver, the opposite operationsare performed.IEEE 802.11a is a packet based communication system.

Each packet is preceded by a known data sequence, thepreamble as defined by the IEEE 802.11a specification [10].The preamble consists of ten short preambles, each having 0.8,us duration and followed by two long preambles, each having3.2 Us duration. These two long preambles are preceded by acyclic prefix of 1.6 ,us duration.

L-1A(r -=) Ne DZ(k

k=O

Phase of A(n) is expressed as

n) 2 (4)

Nc ~tan- 1(A* (12))2WND (5)

Note that, phase of resultant auto-correlation samples is mainlydue to normalized frequency offset (e) [8]. But, arctangentoperation is limited to [-7, 7], so there is a limitation in thefrequency offset estimation which is given by

III. THE PROPOSED ALGORITHM

Proposed time and frequency synchronization algorithm canbe broken into two stages- one is joint coarse time andfrequency offset estimation using short preamble and secondis fine time estimation using long preamble.

A. Joint Coarse Time and Frequency Offset Estimation

At receiver, auto-correlation of the received signal with itsdelayed version is first computed.

L-1A(n) Zr(k+n)r* (k+n+ ND) (2)

k=O

where ND is the amount of delay introduced to the signaland the value of L should be between 16 to 144 as well asa multiple of 16. Clearly, as in Fig. 1, the synchronizationalgorithm gives a large correlation value when the shortpreamble in the received signal data is captured and this largevalue lasts for a period of time due to periodicity of shortpreamble. We choose jump point as the starting point of theshort preamble, which gives the coarse time estimation value.The received signal effected by frequency offset can be

represented as,

r(n) x(n) j2 N + v(n) (3)

where x(n) is the original OFDM transmitted symbol, N isFFT window size and e is the normalized frequency offset.Auto-correlation of this received sequence can be representedas

27WEND-FN< <i

Or,

6<

(6)

(7)N2ND

If ND is 16 samples, we achieve estimation range of e = ±2(coarse frequency offset estimation, parameter Q) and if ND is64 samples, we achieve an estimation range of e = ±0.5 (finefrequency offset estimation, parameter a ). So, in our proposedmethod, two auto-correlators having 16 and 64 samples longare used. The auto-correlator of length 16 is used for bothcoarse time estimation and coarse frequency offset estimation(parameter Q ). The auto-correlator of length 64 is used toprovide a fine frequency offset estimation (parameter a). Thenfinal estimated value of normalized frequency offset is the non-linear combination of both parameters a and Q. The non-linearcombination is given by

L= Q3+ a (8)where L ] means truncating to integer towards zero.

Proposed algorithm considers the frequency offsets to be inthe range e = ±1.5, i.e. twice the maximum value expectedby the standard.

B. Fine Time EstimationBy examining the long preamble structure, we have found

that it exhibits a conjugate symmetry property in additionto it's repetition (periodic) feature. The complete 128-samplelong preamble can be denoted as [yA(k) yB(k) yA(k) yB(k)],in which we have,

yB(k) = YA(32 -k),

and design equations are

k = 0,1, ... 31

N12a(n) = y(n + k)y(n-

k=O

N12b(n) = y(n + k)2

k=O

S(n) _ la(n)2

(b(n))2

50 100 150 200 250 300Received Sample Index

Fig. 1. Auto-Correlation curve for coarse time estimation using shortpreamble for ideal case (No noise, no multipath and no frequency offset).

k)

(9)

(10)

(1 1)

(12)

Starting position of long preamble is detected when S(n)exceeds certain threshold. If this threshold is selected relativeto the received signal strength, then we can estimate fine

1.2

a 0.8

E 0.6

0.4

0.2

time more accurately. Fig. 2 shows the simulation result ofthe proposed method. Note that the above timing estimationalgorithm uses only one-half of the long preamble in whichthe two 32-sample blocks are complex conjugate symmetricto each other, instead of the complete long preamble.Thusby using conjugate symmetric property of long preamble,we are able to estimate fine time with less complexity andcomputational load is reduced by approximately one-quarterof that required by the conventional methods.

0.9

0.8

0.7a

0.6

05

0.4

0.3

0.2

0.1

260 270 280 290 300 310Received Sample Index

Fig. 2. Auto-Correlation curve for Fine time estimation using long preamblefor ideal case (no noise, no multipath and no frequency offset).

IV. SIMULATION RESULTS AND DISCUSSIONWe simulated transmitter and receiver according to the para-

meters established by the 802.1 la standard in the presence ofAWGN noise, multipath channel and local oscillator frequencyoffset.

TABLE IDELAY PROFILE OF ETSI A

European Telecommunications Standards Institute (ETSI)

made several channel models for WLANs. ETSI A channelamong the channel models corresponds to a typical office

environment and delay spread is 50 ns. This tapped-delay-linemodel is used in the simulation.

Fig. 3 shows the auto-correlation magnitude plot of shortpreamble for 10 dB of SNR, 200 kHz carrier frequency offsetand delay spread is 50 ns.

0.16 -

0.14 - -

0.12FI

0.1

aE0.08

0.06

0.04

0.02

0 50 100 150 200 250Received Sample Index

Fig. 3. Auto-Correlation curve for coarse time estimation using shortpreamble for SNR of 10 dB, multipath delay spread of 50 ns and frequencyoffset of 200 kHz.

Selection of various parameters of equation (2) is basedon iterative simulations. For better averaging L is chosen as

80 in equation. With the selection of appropriate threshold,coarse time value is estimated. Note that, as frequency offsetis increased the magnitudes of auto-correlation peaks are

drastically reduced.By using non-linear combination of coarse and fine fre-

quency offset estimated parameters, we are able to estimatefinal value of frequency offset.

Fig. 4 shows the auto-correlation magnitude plot of longpreamble for 10 dB SNR and delay spread is 50 ns. The jumppoint is chosen as fine time estimation value.

0.6

0.5

0.3

0.2

0.1

o240 250 260 270 280 290 300 310Received Sample Index

Fig. 4. Auto-Correlation curve for fine time estimation using long preamblefor SNR of 10 dB, delay spread of 50 ns.

V. CONCLUSION

In this paper, we proposed robust time and frequencysynchronization algorithms for 802.1 la WLAN system. Abovesimulations shows that our proposed time and frequencysynchronization algorithms are able to estimate time andfrequency offset accurately and in addition to this, conjugatesymmetry property of long preamble is exploited to reduce

Tap number Delay (ns) Relative Power [dB]1 0 0.02 10 -10.03 20 -10.34 30 -10.65 40 -6.46 50 -7.27 60 -8.18 70 -9.09 80 -7.910 90 -9.411 110 -10.812 140 -12.313 170 -11.714 200 -14.315 240 -15.816 290 -19.617 340 -22.718 390 -27.6

computational complexity. These algorithms are simulated forAWGN, multipath channel and frequency offset models.

VI. REFERENCES[1] R. W. Chang, "Synthesis of band-limited orthogonal signals for multi-

channel data transmission," Bell Syst. Tech. J., vol. 46, pp. 1775-1796,Dec. 1996.

[2] S. B. Weinstein and P. M. Ebert, "Data transmission by frequency-division multiplexing using discrete Fourier transform," IEEE Trans.Commun. Technol., vol. COM-19, pp. 628-634, Oct. 1971.

[3] J. A. C. Bingham, "Multicarrier modulation for data transmission: Anidea whose time has come," IEEE Commun. Mag., vol. 28, pp. 17-25,Mar. 1990.

[4] T. Pollet, M. V. Bladel, and M. Moeneclaey, "BER sensitivity ofOFDM system to carrier frequency offset and Wiener phase noise,"IEEE Trans. Commun., vol. 43, pp. 191-193, Feb. 1993.

[5] T. M. Schmidl and D. C. Cox, "Blind synchronization for OFDM,"Electron. Lett., vol. 33, pp. 113-114, Feb. 1997.

[6] J. Heiskala and J. Terry, OFDM Wireless LANs: A Theoretical andPractical Guide. SAMS. 2002.

[7] S. Nandula and K. Giridhar, "Robust timing synchronization forOFDM based wireless LAN system," TENCON 2003, Conference onConvergent Technologies for Asia-Pacific Region, vol. 4, pp. 1558-1561, Oct. 2003.

[8] Y Chiu, D. Markovic and N. Zhang, OFDM Receiver Design, FinalReport 12/12/2000. Available: http://bwrc.eecs.berkeley.edu.

[9] M. Wu and W. P. Zhu, "A preamble-aided symbol and frequencysynchronization scheme for OFDM systems," ISCAS 2005 IEEEInternational Symposium, vol. 3, pp. 2627-2630, May 2005.

[10] IEEE, "IEEE802.lla-1999 part 11: Wireless LAN Medium AccessControl (MAC) and physical layer (PHY) specifications," IEEE 1999.

Ratnajit Bhattacharjee received B. E. in Elec-tronics and Telecommunication Engineering (firstclass honors) from Gauhati University (REC (NIT)Silchar), M. Tech. (E and ECE, Microwave Engi-neering specialization) from IIT Kharagpur and Ph.D. (Engineering) from Jadavpur University Kolkata.Presently he is working as a faculty in the Dept. ofECE IIT Guwahati. Prior to joining IIT Guwahati,he was faculty in REC (NIT) Silchar. His researchinterest includes Wireless communication, Wirelessnetworks, Microstrip antennas, Microwave Engineer-

ing and Electromagnetics. He has published around fifty research papers injournals, international and national conferences. He is a member of IEEE andlife member of Indian Society of Technical Education.

VII. BIOGRAPHIES

Shiva Kumar Manusani received the B. Tech (firstclass honors) degree in Electronics and Communi-cation Engineering from Osmania university, India,in 2004 and presently he is a M. Tech scholar inthe department of Electronics and Communication atthe Indian Institute of Technology, Guwahati, Assam.His research interests are Wireless LAN, MIMO-OFDM.

Rakhesh Singh Kshetrimayum (S'01-M'05) re-ceived the B. Tech. (first class honors) degree inElectrical Engineering from the Indian Institute ofTechnology, Bombay, India, in 2000 and the Ph.D.degree in Electrical and Electronic Engineering fromthe Nanyang Technological University, Singapore,in 2005. From 2001 to 2002, he was a SoftwareEngineer at the Mphasis Architecting Value, Pune,India. From 2004 to 2005, he was a Research As-sociate at the Electrical Communication EngineeringDepartment, Indian Institute of Science, Bangalore,

India. In 2005, he was a Post-Doctoral Visiting Scholar at the ElectricalEngineering Department, Pennsylvania State University, Pennsylvania, USA.Presently, he is a faculty at the Electronics and Communication Engineeringdepartment of the Indian Institute of Technology, Guwahati. His research inter-ests include Fast and Efficient algorithms for computational electromagnatics,Periodic structures, Lateral programming, Performance enhanced microwavedevices and Space-time signal processing for mobile wireless networks. DrKshetrimayum is a member of the IEICE, Japan, IEE, UK and life memberof SEMCE (I), IETE, India. He was awarded the KTH-Royal Institute ofTechnology-Stockholm Electrum Foundation Scholarship (2003-2004), theNanyang Technological University - Singapore PhD Research Scholarship(2001-2004), the Travel Grant to attend the International Symposium onMicrowave and Optical Technologies ISMOT 2005 at Fukouka, Japan. Heis listed in Who's Who in the World 2006 23rd Edition and premier editionof Who's Who in the Asia 2007 1st Edition.