Research ArticleRobust Preamble-Based Timing Synchronizationfor OFDM Systems

Yun Liu12 Fei Ji2 Hua Yu2 Dehuan Wan2 Fangjiong Chen2 and Ling Yang1

1School of Information Science and Technology Zhongkai University of Agriculture and Engineering Guangzhou 510225 China2School of Electronics and Information Engineering South China University of Technology Guangzhou 510641 China

Correspondence should be addressed to Hua Yu yuhuascuteducn

Received 19 October 2016 Accepted 14 December 2016 Published 2 January 2017

Academic Editor Xueqin Jiang

Copyright copy 2017 Yun Liu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study presents a novel preamble-based timing offset estimation method for orthogonal frequency division multiplexing(OFDM) systemsThe proposed method is robust immune to the carrier frequency offset (CFO) and independent of the structureof the preambleThe performance of the newmethod is demonstrated in terms of mean square error (MSE) obtained by simulationin multipath fading channelsThe results indicate that the new method significantly improves timing performance in comparisonwith existing methods

1 Introduction

Orthogonal frequency division multiplexing (OFDM) hasbecome an increasingly popular technology in high bit-rate wireless communication systems such as WiFi WiMaxand 3GPP LTE Due to the sensitivity of OFDM systemsto synchronization errors reliable synchronization methodsmust be designed for these systems [1]Many techniques havebeen proposed in the literature for timing and frequencyoffset estimation either jointly or individually in OFDMIn general timing methods in OFDM systems fall intotwo categories blind methods and those that use one ormore preamble at the start of the frame Considering thatthe preamble-based methods are always more efficient incomputation than the blind methods we focus on preamble-aided methods in this paper

In [2] Schmidl and Cox proposed a timing and frequencyestimation method using a preamble containing two identicalhalves Schmidlrsquos method is simple and robust Howeverowing to a quite wide plateau existing in the timing-metricfunction the timing offset estimation in [2] suffers fromlarge mean square error (MSE) To promote the timingaccuracy Minn et al in [3] tried to remove this plateauby convoluting Schmidlrsquos timing metric with a rectangularwidow whose length is equivalent to the cyclic prefix In [4]

Shi and Serpedin extended Minnrsquos method and exploited allself-correlation products to get smaller estimation MSEHowever the estimation accuracy of the methods in [3 4]is still limited due to the side lobes in the timing-metricfunction In [5] Park et al proposed a preamble composedof two symmetrical parts and get a quite sharp timing metricwithout side-lobe by calculating the correlation between thesymmetrical parts All the proposed timing methods in [2ndash5] are based on self-correlation operation immune to theCFO and simple in realization but they generally have muchbigger estimation MSEs compared to the cross-correlationbased methods

Kang et al [6] Hamed and Mahrokh (HM) [7] andYang and Zhang [8] proposed impulse-like timing-metricfunctions using the cross-correlation between the receivedsignal and the known preamble Kangrsquos method is highlyvulnerable to the CFO Furthermore since the number of thecross-correlation terms used in the timing metric is limitedto 119873 the length of the preamble Kangrsquos method performspoorly when 119873 and the signal-noise ratio (SNR) are bothsmall HMrsquos method in [7] improves the timing performanceby using much more correlation terms but it is also sensitiveto the CFO Yangrsquos estimator does not workwhen the absolutevalue of the CFO is larger than the frequency space betweenadjacent subcarriers

HindawiJournal of Computer Networks and CommunicationsVolume 2017 Article ID 9319272 7 pageshttpsdoiorg10115520179319272

2 Journal of Computer Networks and Communications

In [9ndash11] there are timing methods in which self-correlation and cross-correlation are used in combinationRen et al [9] presented a pseudo-noise-sequence weightedpreamble whose specific structure is then exploited in thetiming estimator Renrsquos method improves the accuracy ofthe timing offset estimator significantly In [10 11] HM andLiu proposed preamble-independent timing methods whichperform better than all the previous ones since the number ofthe available correlation terms is far more than that of othermethods It is worthmentioning that themethod proposed in[11] has the same performance but it is less computationallycomplex than that in [10]

To further improve the performance of the timing syn-chronization we investigate the maximum-likelihood (ML)timing algorithm in this paper In the literature severalML timing algorithms have been presented [12ndash14] TheML estimators in [12 13] exploit the redundant informationcontained within the cyclic prefix (CP) thus they are not fitfor OFDM systems without CP such as zero-prefix OFDMThe ML estimator in [14] is based on a preamble composedof more than 2 repeated parts Compared to the existing MLtimingmethods ourmethod is independent of the type of theprefix or the structure of the preamble

The remainder of this paper is organized as followsSection 2 describes the signal model of OFDM system andSection 3 presents our new timing estimation method andits characteristics Section 4 gives the simulation results Thepaper concludes with remarks in Section 5

2 System Description

21 Signal Model In an OFDM system the samples ofcomplex-valued baseband signal at the transmitter output canbe expressed by

119909 (119899) = 1radic119873119873useminus1sum119896=0

1198831198961198901198952120587119896119899119873 0 le 119899 le 119873 minus 1 (1)

where 119899 is the time domain sample index 119873 is the totalnumber of subcarriers with 119873use subcarriers being inactiveand 119883119896 represents the modulated data symbol on the 119896thsubcarrier In practical applications 119909(119899) is computed byinverse fast Fourier transformation (IFFT) In order to avoidintersymbol interference (ISI) and intercarrier interference(ICI) in multipath channels a cyclic prefix of length 119866 isappended in front of 119909(119899) as follows

(119899) = 119909 (119899 + 119873) minus119866 le 119899 le minus1119909 (119899) 0 le 119899 le 119873 minus 1 (2)

The length of the CP is longer than the possible length of thechannel impulse response (CIR)

At the beginning of our study we consider a flat fadingchannel to derive the ML estimator in an intuitive fashionas commonly assumed in [12 14] Later it will be shown bycomputer simulations that the proposed estimator works wellfor frequency-selective channels too Now the received signal

CP

Frame

CPPreamble Data 1 Data 2CP CP Data Mminus 1middot middot middot

Figure 1 Frame structure

is expressed as

119903 [119899] = 119909 [119899 minus 120591] 119890119895(2120587120576119899119873+120579) + 120596 [119899] (3)

where 120591 is the timing offset 120576 is the CFO normalized by thesubcarrier spacing 1119879 (119879 is the OFDM symbol interval) 120579is the phase offset and 120596(119899) is the sample of additive whiteGaussian noise with zero mean and variance 1205902120596

We assume a packet-based OFDM system in which eachframe is composed of a preamble and 119872 minus 1 data OFDMsymbols as shown in Figure 1 The preamble in the timedomain is denoted by a vector as 119878 = [1199040 1199041 119904119873minus1] where119904119896 is the 119896th element of 119878 In addition we assume that theframes are sent consecutively so each frame is preceded bydata samples of the last frame It is worth mentioning thatthe proposed estimator derived in Section 3 also performswell in the case of burst communication where each frame ispreceded by null samples at the transmitter

22 Timing Synchronization In [2] Schmidl and Cox pro-posed a preamble of the form [ 119860 119860 ] where 119860 is a randomcomplex vector of length1198732The preamble can be generatedby modulating a pseudo-noise-sequence on the even sub-carriers and a zero sequence on the odd ones According toSchmidlrsquos estimation method the timing point maximizingthe timing metric of 119872Sch(119899) in (4) shows the start of theframe

119872Sch (119889) = 1003816100381610038161003816119875Sch (119889)10038161003816100381610038162(119864Sch (119889))2 (4)

where

119875Sch (119889) = 1198732minus1sum119899=0

119903lowast (119889 + 119899) 119903 (119889 + 119899 + 1198732 ) (5)

119864Sch (119889) = 1198732minus1sum119899=0

|119903 (119889 + 119899)|2 (6)

119875Sch(119889) is defined to examine the correlation of the transmit-ted preamble 119864Sch(119899) represents the energy of the receivedsignal In (5) (sdot)lowast denotes the complex conjugation operationBased on (4) the timing offset is estimated from

= arg max119889

(119872Sch (119889)) (7)

Due to the cyclic prefix of the preamble Schmidlrsquos timingmetric has a plateau of 119866 samples in length which results inlarge uncertainty of the timing estimation

To exploit the advantage of the constant envelop preamblein the transmission Ren et al in [9] proposed a synchroniza-tionmethod in which time and frequency offset are estimated

Journal of Computer Networks and Communications 3

jointly using one constant envelop preamble of length 119873Renrsquos preamble can be defined as

1199091015840119899 = 119904119899119909119899 119899 = 0 1 119873 minus 1 (8)

where 119909119899 is a constant envelop preamble consisting of tworepetitive sequences similar to Schmidlrsquos 119904119899 is a pseudoran-dom sequence made by +1 and minus1 And Renrsquos timing metricis the same as the one defined by Schmidl in [2] that is (4)but has new correlation function 119875Ren(119889) and normalizationfunction 119864Ren(119889) defined by

119875Ren (119889) = 1198732minus1sum119899=0

119904119899119904119899+1198732119903 lowast (119889 + 119899) 119903 (119889 + 119899 + 1198732 ) (9)

119864Ren (119889) = 12119873minus1sum119899=0

|119903 (119889 + 119899)|2 (10)

Since 119904119899 is a pseudorandom sequence the correlation func-tion 119875Ren(119889) has an impulsive value only at the exact timingpoint 120591

The number of the correlation products used in (9) is only1198732 However for a given checkpoint 119889 there are119873(119873minus1)2correlation productsmade by samples [119903(119889) 119903(119889+1) 119903(119889+119873minus1)] And all the available product terms can be representedby the following set

C119889 = 119873minus1⋃119894=1

119862119889119894 (11)

where

119862119889119894 = 119903 (119889) 119903lowast (119889 + 119894) 119903 (119889 + 1)sdot 119903lowast (119889 + 1 + 119894) 119903 (119889 + 119873 minus 1 minus 119894) 119903lowast (119889 + 119873 minus 1) (12)

is the subset of C119889 In [10] HM proposed a robust timingmethod which can exploit all the available product termsdefined by (11) HMrsquos estimator gets a significant improve-ment in timing accuracy compared to Renrsquos method butperforms still unsatisfactorily when the SNR of the receivedsignal is low

3 Proposed Method

31 ML Synchronization Without loss of generality wedenote the received samples with the length of a frame as

119903 = 119903 [119899] | 119899 = 0 1 120591 119872119873 minus 1 (13)

where 119903(0) and 119903(120591) denote the first sample of the receivedsignal and the start point of the preamble respectively Herewe neglect the effect of the CP in the analysis since theCP little affects the timing synchronization performance butmakes the analysis less intuitive Therefore those receivedsignals are composed of (119872 minus 1)119873 data samples and 119873preamble samples with indices defined by I119901 = 119899 | 120591 le119899 lt 120591 + 119873 and I119889 = 119899 | 0 le 119899 lt 120591 cup 119899 | 120591 + 119873 le119899 lt 119872119873 respectively When119873 is large the data samples can

be regarded as a Gaussian process [12 14] and these samplesfollow independent complex Gaussian distribution with zeromean and variance 12059021 (12059021 = 1205902119909 +1205902120596 where 1205902119909 is the varianceof 119909(119899)) Thus the conditional probability density function(PDF) of 119903(119899) for given 120591 120576 and 120579 can be represented as

119891 (119903 (119899) | 120591 120576 120579)

=

11205871205902120596 119890minus|119903(119899)minus119904119899minus120591119890

119895(2120587120576119899119873+120579)|21205902120596 119899 isin I119901112058712059021 119890minus|119903(119899)|212059021 119899 isin I119889

(14)

It is obvious that elements in 119903 are independent of each otherand their conditional PDF can be obtained as

119891 (119903 | 120591 120576 120579) = prod119899isinI119901cupI119889

119891 (119903 (119899) | 120591 120576 120579) (15)

The optimal joint ML estimation of the delays 120591 120576 and 120579 canbe obtained by maximizing log(119891(119903 | 120591 120576 120579)) that is usingthe following log-likelihood function

Λ (120591 120576 120579) = log (119891 (119903 | 120591 120576 120579)) (16)

After substituting (14) and (15) into (16) by omitting theconstant terms (minus119873 log(1205871205902120596)minus(119872minus1)119873 log(12058712059021 )) andmul-tiplying a constant number 1205902120596 we get a reduced likelihoodfunction described as

Λ1015840 (120591 120576 120579) = minus1205880sum119899isinI119889

|119903 (119899)|2 minus sum119899isinI119901

10038161003816100381610038161003816119903 (119899)minus 119904119899minus120591119890119895(2120587120576119899119873+120579)100381610038161003816100381610038162

(17)

(120591119900 120576119900 120579119900) = argmax(120591120576120579)

minus 1205880sum119899isinI119889

|119903 (119899)|2 minus sum119899isinI119901

10038161003816100381610038161003816119903 (119899)

minus 119904119899minus120591119890119895(2120587120576119899119873+120579)100381610038161003816100381610038162 = arg max(120591120576120579)

2

sdot Re119890minus119895(2120587120576120591119873+120579)119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus1198952120587120576119894119873

minus 1205881119873minus1sum119894=0

|119903 (120591 + 119894)|2 minus 119888

(18)

where 1205880 = 1205902120596(1205902120596 + 1205902119889) Then the ML estimates of (120591 120576 120579)can be represented as (18) at the top of the next page where1205881 = 1205902119889(1205902120596 + 1205902119889) and 119888 is a constant number independentof (120591 120576 120579) described as

119888 = 1205880119872119873minus1sum119894=0

|119903 (119894)|2 + 119873minus1sum119894=0

100381610038161003816100381611990411989410038161003816100381610038162 (19)

It is observed that for any given 120591 and 120576 the right-hand sideof (18) can be maximized to

2 1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816 minus 1205881119873minus1sum

119894=0

|119903 (120591 + 119894)|2 minus 119888 (20)

4 Journal of Computer Networks and Communications

0

200

400

600

800

1000

Tim

ing

met

ric

minus50 0 50 100minus100Sample index

(a)

0

200

400

600

800

1000

Sam

ple i

ndex

minus50 0 50 100minus100Sample index

(b)

Figure 2 Timing metrics of the proposed method (119873 = 1024 and length of the cyclic prefix is 128) (a) without noise and channel distortionand (b) in a 5-tap Rayleigh fading channel

when

120579 = minus2120587120576120591119873 + ang119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus1198952120587120576119894119873 (21)

where ang denotes the argument of a complex number As aresult we can obtain the ML estimation of (120591 120576) at first using(20) as the likelihood function with the constant 119888 omittedAnd the ML estimator is written as

(120591119900 120576119900) = argmax(120591120576)

2 1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816

minus 1205881119873minus1sum119894=0

|119903 (120591 + 119894)|2 (22)

Note that 1205881 in (22) is a constant number dependent onthe SNR of the received signal Furthermore when 119873 islarge sum119873minus1119894=0 |119903(120591 + 119894)|2 in (22) can also be regarded as aconstant number 11987312059021 (where 12059021 is the average power of119903(119909)) As a result by omitting the multiplication of the twoaforementioned constant numbers we get the reduced MLestimator of (120591119900 120576119900) written as

(120591119900 120576119900) = argmax(120591120576)

1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816 (23)

In some applications for example in wired OFDMsystems including baseband digital subscriber line (DSL) theCFO errormay be negligible In this case the joint estimationof (120591119900 120576119900) in (23) reduces to ML timing offset estimationwhich can be easily obtained by searching 120591 maximizing theinner product of [119903(120591) 119903(120591+1) 119903(120591+119873minus1)] and the knownpreamble S When the CFO is uncertain the optimum joint

ML estimation of (120591 120576) given in (23) needs to be obtained bynumerical method requiring high computational complexitybecause of the continuous variable 12057632 Simplified Synchronization It is observed that on theright-hand side of (23) the operations in the absolute valuebars are by nature a discrete-time Fourier transformation(DTFT) of the signal 119903(120591 + 119894)119904lowast119894 with the frequency variable(2120587119873)120576 Considering the truth that discrete Fourier trans-form (DFT) is just the equally spaced samples of the DTFTand for a time domain sequence of length 119873 the 119873 pointsDFT hold the same quantity of information as that of DTFTwe propose a near ML timing estimator written as

= argmax119889

119872 (119889) (24)

where119872(119889)

= max1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (119889 + 119894) 119904lowast119894 119890minus119895(2120587119873)1198961198941003816100381610038161003816100381610038161003816100381610038161003816 0 le 119896 lt 119873 (25)

is the timing metric of the proposed timing offset estimatorSimilar to the timing metric proposed by [9 10] the envelopof the proposed metric is impulse-like because 119872(119889) has itspeak value at the starting point of the preamble while thevalues at all other points are comparatively smaller In Figures2(a) and 2(b) we have depicted the metric of the proposedmethod in two cases of ideal condition (no noise and nochannel distortion) and in a frequency-selective channel of 5paths respectively It is obvious that under both channels theproposed timing metric has a sharp envelope which leads toamuch smaller mean square error of timing offset estimationas shown in later simulation results

Journal of Computer Networks and Communications 5

After the timing offset is acquired by the proposedmethod suboptimal estimation of the CFO can be realizedby methods in existing work such as [15 16] The CFOnormalized by the subcarrier spacing in a system can beexpressed as

120576 = 120576119868 + 120576119891 (26)

where 120576119868 and 120576119891 denote the integer part and the fractionalpart of the frequency offset respectively In [15] firstly thefractional part is achieved by using the characteristics ofa preamble with two identical parts in the time domainand then the integer part is estimated by using the correla-tion between the fractional-part-corrected preamble (chosenfrom the received signal after timing synchronization) andits pure transmitted version When the preamble does nothave repeated identical parts the integer part and fractionalpart can be achieved by the estimator in [16] which isindependent of the preamble structure

33 Computational Complexity Besides the performanceissues computational complexity is equally important in apractical sense We evaluated the complexity of the proposedtiming method by comparing the number of multiplicationsand additions needed by the timing-metric functionwith thatof other timing offset estimators In a OFDM system 119873 isalways set as 2119898 where 119898 is an integer so that the FFTIFFToperations can be used Thus the DFT in (25) can also beperformed by FFT which greatly reduces the computationalcomplexity

Tomake the analysismore intuitive we rewrite the timingmetric in (25) as

119872(119889) = max 10038161003816100381610038161003816(119877119889 ∘ 119878lowast)119882119867119896 10038161003816100381610038161003816 0 le 119896 lt N (27)

where

119877119889 = [119903 (119889) 119903 (119889 + 1) 119903 (119889 + 119873 minus 1)] 119882119896 = [1 119890119895(2120587119873)119896 119890119895(2120587119873)2119896 119890119895(2120587119873)(119873minus1)119896] (28)

The operator ∘ denotes the Hadamard product which isdefined as element-by-elementmultiplications of two vectorsand (sdot)119867 is the conjugate transpose operation

Now we calculate the metric 119872(119889) in (27) for a givencheckpoint indexed by 119889 At first a Hadamard productwhich needs 119873 complex multiplications is used to calculatethe cross-correlation of received signal vector 119877119889 and localpreamble vector 119878 Then the resulting vector transformedto the frequency-domain vector by FFT operations whichrequire 05119873 log2119873 complex multiplications and 119873 log2119873additions At last 119873 complex multiplications and 119873 minus 1complex additions are used to find the maximum elementfrom the resulting frequency-domain vector In total we need119873(05 log2119873+2) complexmultiplications and (log2119873+1)119873minus1additions to calculate 119872(119889) for the checkpoint 119889

In Table 1 we have demonstrated the complexity of theproposed method in comparison with the previous onesNote that although the proposed method is more complex

Table 1 Computational complexity of different estimators

Method Complex multiplication Complexaddition

Schmidl[2] 2 2

Ren [9] 1 119873 minus 1Kang [6] 2 119873 minus 1HM [10] 119897119904 + 119871 + 1 where 0 lt 119897119904 lt 119873119871 le (1198732 minus 119873)2 119871Proposed 119873(05 log2119873 + 2) 119873(log2119873+1)minus1

than methods of Schmidl Ren and Kang it achieves a sig-nificantly better performance than those methods as shownin the next section As to HMrsquos method the computationalcomplexity is adjustable by setting reasonable index vectors119865 = [1198651 1198652 119865119894 119865119897119904] and 119866 = [1198661 1198662 119866119894 119866119897119904]in which 119865119894 or 119866119894 is a subvector The number of elementsin 119865 or 119866 is noted as 119871 which can be extended up to (119873 minus1)(1198732) if necessary Naturally higher 119871means higher timingperformance However from the simulation results given inSection 4 we will see that the performance of the proposedmethod is better than that of HMrsquos estimator even when allthe available products are used in the latter method

4 Simulation Results

The performance of the proposed method has been investi-gated in comparison with other methods using Monte Carlosimulations The parameters used in the OFDM system are64 subcarriers 64-point IFFTFFT 18 guard interval (119866 =8) and 100 000 simulation runs in each examination Thenormalized CFO is set to 120576 = 31 Considering that theOFDM systems always work under multipath channel weadopt two different multipath channels for the simulationThe first channel is based on Stanford university interim(SUI) channel modeling [17] with the sampling rate of 5MHzThe second one is a multipath Rayleigh fading channel of 5paths We evaluate the performance of the proposed timingmethods bymean square error (MSE) sinceMSE reflects boththe bias and the variance of the estimation

In Figure 3 we have depicted the MSE of the proposedmethods in comparison with the MSEs of five previousmethods under the SUI-1 channel We can see that theproposedmethod has a significantly better performance thanthe previous methods It is worth mentioning that all thepossible product terms have been used in HMrsquos method inthe simulation Thus the proposed estimator performs betterthan HMrsquos method even though the latter involves muchhigher computational complexity Furthermore we can seethat Kangrsquos and Yangrsquos methods suffer great performancedegradation from the CFO in the simulation

Figure 4 demonstrates the MSEs of different estimatorsin another multipath Rayleigh fading channel with 5 pathspath delays ℓ = 0 1 4 and the channel delay profile119890(ℓ5) Here we have 119873 = 64 and 119866 = 12 For HMrsquos method[10] to get the best performance it could achieve we use

6 Journal of Computer Networks and Communications

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

5 10 15 20 25 300SNR (dB)

10minus1

100

101

102

103

104

MSE

Figure 3 TimingMSE versus SNR for six methods in SUI-1 channel(119873 = 64 and 119866 = 8)

10minus1

100

101

102

103

104

MSE

5 10 15 20 25 300SNR (dB)

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

Figure 4 Timing MSE versus SNR for six methods in a 5-tapRayleigh fading channel (119873 = 64 and 119866 = 12)

all the available correlation products in the simulation It isevident that the proposed method has a remarkably betterperformance than others

5 Conclusions

In this paper at first we derived the ML joint estimatorof timing offset and CFO for OFDM systems Then a sim-

plified timing synchronization method has been proposedbased on the ML estimator The proposed timing method isindependent of the structure of the preamble and immuneto the normalized CFO (by subcarrier space) in the rangeof [minus1198732 1198732] As shown in the simulation result theproposed estimator performs better than the existing meth-ods For any given preamble the joint timing and frequencysynchronization for OFDM systems can be achieved by usingour proposed timing method and the CFO estimator in [16]

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National Natu-ral Science Foundation of China (61431005 61501531 and61671211) and the Natural Science Foundation of Guang-dong Province China (2015A030313602 2014A030311034and 2016A030308006)

References

[1] T Pollet M Van Bladel and M Moeneclaey ldquoBER sensitivityof OFDM systems to carrier frequency offset and wiener phasenoiserdquo IEEE Transactions on Communications vol 43 no 234pp 191ndash193 1995

[2] T M Schmidl and D C Cox ldquoRobust frequency and timingsynchronization for OFDMrdquo IEEE Transactions on Communi-cations vol 45 no 12 pp 1613ndash1621 1997

[3] H Minn M Zeng and V K Bhargava ldquoOn timing offsetestimation for OFDM systemsrdquo IEEE Communications Lettersvol 4 no 7 pp 242ndash244 2000

[4] K Shi and E Serpedin ldquoCoarse frame and carrier synchroniza-tion of OFDM systems a new metric and comparisonrdquo IEEETransactions onWireless Communications vol 3 no 4 pp 1271ndash1284 2004

[5] B Park H Cheon C Kang and D Hong ldquoA novel timingestimation method for OFDM systemsrdquo IEEE CommunicationsLetters vol 7 no 5 pp 239ndash241 2003

[6] Y Kang S Kim D Ahn and H Lee ldquoTiming estimation forOFDM systems by using a correlation sequence of preamblerdquoIEEE Transactions on Consumer Electronics vol 54 no 4 pp1600ndash1608 2008

[7] H Abdzadeh-Ziabari M G Shayesteh and M Manaffar ldquoAnimproved timing estimation method for OFDM systemsrdquo IEEETransactions on Consumer Electronics vol 56 no 4 pp 2098ndash2105 2010

[8] F Yang and X Zhang ldquoRobust time-domain fine symbolsynchronization for OFDM-based packet transmission usingCAZAC preamblerdquo in Proceedings of the IEEE Military Com-munications Conference (MILCOM rsquo13) pp 436ndash440 IEEE SanDiego Calif USA November 2013

[9] G Ren Y Chang H Zhang and H Zhang ldquoSynchronizationmethod based on a new constant envelop preamble for OFDMsystemsrdquo IEEE Transactions on Broadcasting vol 51 no 1 pp139ndash143 2005

Journal of Computer Networks and Communications 7

[10] H Abdzadeh-Ziabari and M G Shayesteh ldquoRobust timingand frequency synchronization for OFDM systemsrdquo IEEETransactions on Vehicular Technology vol 60 no 8 pp 3646ndash3656 2011

[11] Y Liu H Yu F Ji F Chen and W Pan ldquoRobust timing estima-tionmethod forOFDMsystemswith reduced complexityrdquo IEEECommunications Letters vol 18 no 11 pp 1959ndash1962 2014

[12] J-J Van De Beek M Sandell and P O Borjesson ldquoMLestimation of time and frequency offset in OFDM systemsrdquoIEEE Transactions on Signal Processing vol 45 no 7 pp 1800ndash1805 1997

[13] W-L Chin ldquoML estimation of timing and frequency offsetsusing distinctive correlation characteristics of OFDM signalsover dispersive fading channelsrdquo IEEE Transactions on Vehic-ular Technology vol 60 no 2 pp 444ndash456 2011

[14] J-W Choi J Lee Q Zhao and H-L Lou ldquoJoint ML estimationof frame timing and carrier frequency offset for OFDM systemsemploying time-domain repeated preamblerdquo IEEE Transactionson Wireless Communications vol 9 no 1 pp 311ndash317 2010

[15] A B Awoseyila C Kasparis and B G Evans ldquoRobust time-domain timing and frequency synchronization for OFDMsystemsrdquo IEEE Transactions on Consumer Electronics vol 55no 2 pp 391ndash399 2009

[16] G Ren Y Chang H Zhang and H Zhang ldquoAn efficient fre-quency offset estimation method with a large range for wirelessOFDM systemsrdquo IEEE Transactions on Vehicular Technologyvol 56 no 4 pp 1892ndash1895 2007

[17] V Erceg K Hari M Smith et al ldquoChannel models for fixedwireless applicationsrdquo Tech Rep IEEE Broadband WirelessAccess Working Group 2001

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Computer Networks and Communications 3

jointly using one constant envelop preamble of length 119873Renrsquos preamble can be defined as

1199091015840119899 = 119904119899119909119899 119899 = 0 1 119873 minus 1 (8)

where 119909119899 is a constant envelop preamble consisting of tworepetitive sequences similar to Schmidlrsquos 119904119899 is a pseudoran-dom sequence made by +1 and minus1 And Renrsquos timing metricis the same as the one defined by Schmidl in [2] that is (4)but has new correlation function 119875Ren(119889) and normalizationfunction 119864Ren(119889) defined by

119875Ren (119889) = 1198732minus1sum119899=0

119904119899119904119899+1198732119903 lowast (119889 + 119899) 119903 (119889 + 119899 + 1198732 ) (9)

119864Ren (119889) = 12119873minus1sum119899=0

|119903 (119889 + 119899)|2 (10)

Since 119904119899 is a pseudorandom sequence the correlation func-tion 119875Ren(119889) has an impulsive value only at the exact timingpoint 120591

The number of the correlation products used in (9) is only1198732 However for a given checkpoint 119889 there are119873(119873minus1)2correlation productsmade by samples [119903(119889) 119903(119889+1) 119903(119889+119873minus1)] And all the available product terms can be representedby the following set

C119889 = 119873minus1⋃119894=1

119862119889119894 (11)

where

119862119889119894 = 119903 (119889) 119903lowast (119889 + 119894) 119903 (119889 + 1)sdot 119903lowast (119889 + 1 + 119894) 119903 (119889 + 119873 minus 1 minus 119894) 119903lowast (119889 + 119873 minus 1) (12)

is the subset of C119889 In [10] HM proposed a robust timingmethod which can exploit all the available product termsdefined by (11) HMrsquos estimator gets a significant improve-ment in timing accuracy compared to Renrsquos method butperforms still unsatisfactorily when the SNR of the receivedsignal is low

3 Proposed Method

31 ML Synchronization Without loss of generality wedenote the received samples with the length of a frame as

119903 = 119903 [119899] | 119899 = 0 1 120591 119872119873 minus 1 (13)

where 119903(0) and 119903(120591) denote the first sample of the receivedsignal and the start point of the preamble respectively Herewe neglect the effect of the CP in the analysis since theCP little affects the timing synchronization performance butmakes the analysis less intuitive Therefore those receivedsignals are composed of (119872 minus 1)119873 data samples and 119873preamble samples with indices defined by I119901 = 119899 | 120591 le119899 lt 120591 + 119873 and I119889 = 119899 | 0 le 119899 lt 120591 cup 119899 | 120591 + 119873 le119899 lt 119872119873 respectively When119873 is large the data samples can

be regarded as a Gaussian process [12 14] and these samplesfollow independent complex Gaussian distribution with zeromean and variance 12059021 (12059021 = 1205902119909 +1205902120596 where 1205902119909 is the varianceof 119909(119899)) Thus the conditional probability density function(PDF) of 119903(119899) for given 120591 120576 and 120579 can be represented as

119891 (119903 (119899) | 120591 120576 120579)

=

11205871205902120596 119890minus|119903(119899)minus119904119899minus120591119890

119895(2120587120576119899119873+120579)|21205902120596 119899 isin I119901112058712059021 119890minus|119903(119899)|212059021 119899 isin I119889

(14)

It is obvious that elements in 119903 are independent of each otherand their conditional PDF can be obtained as

119891 (119903 | 120591 120576 120579) = prod119899isinI119901cupI119889

119891 (119903 (119899) | 120591 120576 120579) (15)

The optimal joint ML estimation of the delays 120591 120576 and 120579 canbe obtained by maximizing log(119891(119903 | 120591 120576 120579)) that is usingthe following log-likelihood function

Λ (120591 120576 120579) = log (119891 (119903 | 120591 120576 120579)) (16)

After substituting (14) and (15) into (16) by omitting theconstant terms (minus119873 log(1205871205902120596)minus(119872minus1)119873 log(12058712059021 )) andmul-tiplying a constant number 1205902120596 we get a reduced likelihoodfunction described as

Λ1015840 (120591 120576 120579) = minus1205880sum119899isinI119889

|119903 (119899)|2 minus sum119899isinI119901

10038161003816100381610038161003816119903 (119899)minus 119904119899minus120591119890119895(2120587120576119899119873+120579)100381610038161003816100381610038162

(17)

(120591119900 120576119900 120579119900) = argmax(120591120576120579)

minus 1205880sum119899isinI119889

|119903 (119899)|2 minus sum119899isinI119901

10038161003816100381610038161003816119903 (119899)

minus 119904119899minus120591119890119895(2120587120576119899119873+120579)100381610038161003816100381610038162 = arg max(120591120576120579)

2

sdot Re119890minus119895(2120587120576120591119873+120579)119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus1198952120587120576119894119873

minus 1205881119873minus1sum119894=0

|119903 (120591 + 119894)|2 minus 119888

(18)

where 1205880 = 1205902120596(1205902120596 + 1205902119889) Then the ML estimates of (120591 120576 120579)can be represented as (18) at the top of the next page where1205881 = 1205902119889(1205902120596 + 1205902119889) and 119888 is a constant number independentof (120591 120576 120579) described as

119888 = 1205880119872119873minus1sum119894=0

|119903 (119894)|2 + 119873minus1sum119894=0

100381610038161003816100381611990411989410038161003816100381610038162 (19)

It is observed that for any given 120591 and 120576 the right-hand sideof (18) can be maximized to

2 1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816 minus 1205881119873minus1sum

119894=0

|119903 (120591 + 119894)|2 minus 119888 (20)

4 Journal of Computer Networks and Communications

0

200

400

600

800

1000

Tim

ing

met

ric

minus50 0 50 100minus100Sample index

(a)

0

200

400

600

800

1000

Sam

ple i

ndex

minus50 0 50 100minus100Sample index

(b)

Figure 2 Timing metrics of the proposed method (119873 = 1024 and length of the cyclic prefix is 128) (a) without noise and channel distortionand (b) in a 5-tap Rayleigh fading channel

when

120579 = minus2120587120576120591119873 + ang119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus1198952120587120576119894119873 (21)

where ang denotes the argument of a complex number As aresult we can obtain the ML estimation of (120591 120576) at first using(20) as the likelihood function with the constant 119888 omittedAnd the ML estimator is written as

(120591119900 120576119900) = argmax(120591120576)

2 1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816

minus 1205881119873minus1sum119894=0

|119903 (120591 + 119894)|2 (22)

Note that 1205881 in (22) is a constant number dependent onthe SNR of the received signal Furthermore when 119873 islarge sum119873minus1119894=0 |119903(120591 + 119894)|2 in (22) can also be regarded as aconstant number 11987312059021 (where 12059021 is the average power of119903(119909)) As a result by omitting the multiplication of the twoaforementioned constant numbers we get the reduced MLestimator of (120591119900 120576119900) written as

(120591119900 120576119900) = argmax(120591120576)

1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816 (23)

In some applications for example in wired OFDMsystems including baseband digital subscriber line (DSL) theCFO errormay be negligible In this case the joint estimationof (120591119900 120576119900) in (23) reduces to ML timing offset estimationwhich can be easily obtained by searching 120591 maximizing theinner product of [119903(120591) 119903(120591+1) 119903(120591+119873minus1)] and the knownpreamble S When the CFO is uncertain the optimum joint

ML estimation of (120591 120576) given in (23) needs to be obtained bynumerical method requiring high computational complexitybecause of the continuous variable 12057632 Simplified Synchronization It is observed that on theright-hand side of (23) the operations in the absolute valuebars are by nature a discrete-time Fourier transformation(DTFT) of the signal 119903(120591 + 119894)119904lowast119894 with the frequency variable(2120587119873)120576 Considering the truth that discrete Fourier trans-form (DFT) is just the equally spaced samples of the DTFTand for a time domain sequence of length 119873 the 119873 pointsDFT hold the same quantity of information as that of DTFTwe propose a near ML timing estimator written as

= argmax119889

119872 (119889) (24)

where119872(119889)

= max1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (119889 + 119894) 119904lowast119894 119890minus119895(2120587119873)1198961198941003816100381610038161003816100381610038161003816100381610038161003816 0 le 119896 lt 119873 (25)

is the timing metric of the proposed timing offset estimatorSimilar to the timing metric proposed by [9 10] the envelopof the proposed metric is impulse-like because 119872(119889) has itspeak value at the starting point of the preamble while thevalues at all other points are comparatively smaller In Figures2(a) and 2(b) we have depicted the metric of the proposedmethod in two cases of ideal condition (no noise and nochannel distortion) and in a frequency-selective channel of 5paths respectively It is obvious that under both channels theproposed timing metric has a sharp envelope which leads toamuch smaller mean square error of timing offset estimationas shown in later simulation results

Journal of Computer Networks and Communications 5

After the timing offset is acquired by the proposedmethod suboptimal estimation of the CFO can be realizedby methods in existing work such as [15 16] The CFOnormalized by the subcarrier spacing in a system can beexpressed as

120576 = 120576119868 + 120576119891 (26)

where 120576119868 and 120576119891 denote the integer part and the fractionalpart of the frequency offset respectively In [15] firstly thefractional part is achieved by using the characteristics ofa preamble with two identical parts in the time domainand then the integer part is estimated by using the correla-tion between the fractional-part-corrected preamble (chosenfrom the received signal after timing synchronization) andits pure transmitted version When the preamble does nothave repeated identical parts the integer part and fractionalpart can be achieved by the estimator in [16] which isindependent of the preamble structure

33 Computational Complexity Besides the performanceissues computational complexity is equally important in apractical sense We evaluated the complexity of the proposedtiming method by comparing the number of multiplicationsand additions needed by the timing-metric functionwith thatof other timing offset estimators In a OFDM system 119873 isalways set as 2119898 where 119898 is an integer so that the FFTIFFToperations can be used Thus the DFT in (25) can also beperformed by FFT which greatly reduces the computationalcomplexity

Tomake the analysismore intuitive we rewrite the timingmetric in (25) as

119872(119889) = max 10038161003816100381610038161003816(119877119889 ∘ 119878lowast)119882119867119896 10038161003816100381610038161003816 0 le 119896 lt N (27)

where

119877119889 = [119903 (119889) 119903 (119889 + 1) 119903 (119889 + 119873 minus 1)] 119882119896 = [1 119890119895(2120587119873)119896 119890119895(2120587119873)2119896 119890119895(2120587119873)(119873minus1)119896] (28)

The operator ∘ denotes the Hadamard product which isdefined as element-by-elementmultiplications of two vectorsand (sdot)119867 is the conjugate transpose operation

Now we calculate the metric 119872(119889) in (27) for a givencheckpoint indexed by 119889 At first a Hadamard productwhich needs 119873 complex multiplications is used to calculatethe cross-correlation of received signal vector 119877119889 and localpreamble vector 119878 Then the resulting vector transformedto the frequency-domain vector by FFT operations whichrequire 05119873 log2119873 complex multiplications and 119873 log2119873additions At last 119873 complex multiplications and 119873 minus 1complex additions are used to find the maximum elementfrom the resulting frequency-domain vector In total we need119873(05 log2119873+2) complexmultiplications and (log2119873+1)119873minus1additions to calculate 119872(119889) for the checkpoint 119889

In Table 1 we have demonstrated the complexity of theproposed method in comparison with the previous onesNote that although the proposed method is more complex

Table 1 Computational complexity of different estimators

Method Complex multiplication Complexaddition

Schmidl[2] 2 2

Ren [9] 1 119873 minus 1Kang [6] 2 119873 minus 1HM [10] 119897119904 + 119871 + 1 where 0 lt 119897119904 lt 119873119871 le (1198732 minus 119873)2 119871Proposed 119873(05 log2119873 + 2) 119873(log2119873+1)minus1

than methods of Schmidl Ren and Kang it achieves a sig-nificantly better performance than those methods as shownin the next section As to HMrsquos method the computationalcomplexity is adjustable by setting reasonable index vectors119865 = [1198651 1198652 119865119894 119865119897119904] and 119866 = [1198661 1198662 119866119894 119866119897119904]in which 119865119894 or 119866119894 is a subvector The number of elementsin 119865 or 119866 is noted as 119871 which can be extended up to (119873 minus1)(1198732) if necessary Naturally higher 119871means higher timingperformance However from the simulation results given inSection 4 we will see that the performance of the proposedmethod is better than that of HMrsquos estimator even when allthe available products are used in the latter method

4 Simulation Results

The performance of the proposed method has been investi-gated in comparison with other methods using Monte Carlosimulations The parameters used in the OFDM system are64 subcarriers 64-point IFFTFFT 18 guard interval (119866 =8) and 100 000 simulation runs in each examination Thenormalized CFO is set to 120576 = 31 Considering that theOFDM systems always work under multipath channel weadopt two different multipath channels for the simulationThe first channel is based on Stanford university interim(SUI) channel modeling [17] with the sampling rate of 5MHzThe second one is a multipath Rayleigh fading channel of 5paths We evaluate the performance of the proposed timingmethods bymean square error (MSE) sinceMSE reflects boththe bias and the variance of the estimation

In Figure 3 we have depicted the MSE of the proposedmethods in comparison with the MSEs of five previousmethods under the SUI-1 channel We can see that theproposedmethod has a significantly better performance thanthe previous methods It is worth mentioning that all thepossible product terms have been used in HMrsquos method inthe simulation Thus the proposed estimator performs betterthan HMrsquos method even though the latter involves muchhigher computational complexity Furthermore we can seethat Kangrsquos and Yangrsquos methods suffer great performancedegradation from the CFO in the simulation

Figure 4 demonstrates the MSEs of different estimatorsin another multipath Rayleigh fading channel with 5 pathspath delays ℓ = 0 1 4 and the channel delay profile119890(ℓ5) Here we have 119873 = 64 and 119866 = 12 For HMrsquos method[10] to get the best performance it could achieve we use

6 Journal of Computer Networks and Communications

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

5 10 15 20 25 300SNR (dB)

10minus1

100

101

102

103

104

MSE

Figure 3 TimingMSE versus SNR for six methods in SUI-1 channel(119873 = 64 and 119866 = 8)

10minus1

100

101

102

103

104

MSE

5 10 15 20 25 300SNR (dB)

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

Figure 4 Timing MSE versus SNR for six methods in a 5-tapRayleigh fading channel (119873 = 64 and 119866 = 12)

all the available correlation products in the simulation It isevident that the proposed method has a remarkably betterperformance than others

5 Conclusions

In this paper at first we derived the ML joint estimatorof timing offset and CFO for OFDM systems Then a sim-

plified timing synchronization method has been proposedbased on the ML estimator The proposed timing method isindependent of the structure of the preamble and immuneto the normalized CFO (by subcarrier space) in the rangeof [minus1198732 1198732] As shown in the simulation result theproposed estimator performs better than the existing meth-ods For any given preamble the joint timing and frequencysynchronization for OFDM systems can be achieved by usingour proposed timing method and the CFO estimator in [16]

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National Natu-ral Science Foundation of China (61431005 61501531 and61671211) and the Natural Science Foundation of Guang-dong Province China (2015A030313602 2014A030311034and 2016A030308006)

References

[1] T Pollet M Van Bladel and M Moeneclaey ldquoBER sensitivityof OFDM systems to carrier frequency offset and wiener phasenoiserdquo IEEE Transactions on Communications vol 43 no 234pp 191ndash193 1995

[2] T M Schmidl and D C Cox ldquoRobust frequency and timingsynchronization for OFDMrdquo IEEE Transactions on Communi-cations vol 45 no 12 pp 1613ndash1621 1997

[3] H Minn M Zeng and V K Bhargava ldquoOn timing offsetestimation for OFDM systemsrdquo IEEE Communications Lettersvol 4 no 7 pp 242ndash244 2000

[4] K Shi and E Serpedin ldquoCoarse frame and carrier synchroniza-tion of OFDM systems a new metric and comparisonrdquo IEEETransactions onWireless Communications vol 3 no 4 pp 1271ndash1284 2004

[5] B Park H Cheon C Kang and D Hong ldquoA novel timingestimation method for OFDM systemsrdquo IEEE CommunicationsLetters vol 7 no 5 pp 239ndash241 2003

[6] Y Kang S Kim D Ahn and H Lee ldquoTiming estimation forOFDM systems by using a correlation sequence of preamblerdquoIEEE Transactions on Consumer Electronics vol 54 no 4 pp1600ndash1608 2008

[7] H Abdzadeh-Ziabari M G Shayesteh and M Manaffar ldquoAnimproved timing estimation method for OFDM systemsrdquo IEEETransactions on Consumer Electronics vol 56 no 4 pp 2098ndash2105 2010

[8] F Yang and X Zhang ldquoRobust time-domain fine symbolsynchronization for OFDM-based packet transmission usingCAZAC preamblerdquo in Proceedings of the IEEE Military Com-munications Conference (MILCOM rsquo13) pp 436ndash440 IEEE SanDiego Calif USA November 2013

[9] G Ren Y Chang H Zhang and H Zhang ldquoSynchronizationmethod based on a new constant envelop preamble for OFDMsystemsrdquo IEEE Transactions on Broadcasting vol 51 no 1 pp139ndash143 2005

Journal of Computer Networks and Communications 7

[10] H Abdzadeh-Ziabari and M G Shayesteh ldquoRobust timingand frequency synchronization for OFDM systemsrdquo IEEETransactions on Vehicular Technology vol 60 no 8 pp 3646ndash3656 2011

[11] Y Liu H Yu F Ji F Chen and W Pan ldquoRobust timing estima-tionmethod forOFDMsystemswith reduced complexityrdquo IEEECommunications Letters vol 18 no 11 pp 1959ndash1962 2014

[12] J-J Van De Beek M Sandell and P O Borjesson ldquoMLestimation of time and frequency offset in OFDM systemsrdquoIEEE Transactions on Signal Processing vol 45 no 7 pp 1800ndash1805 1997

[13] W-L Chin ldquoML estimation of timing and frequency offsetsusing distinctive correlation characteristics of OFDM signalsover dispersive fading channelsrdquo IEEE Transactions on Vehic-ular Technology vol 60 no 2 pp 444ndash456 2011

[14] J-W Choi J Lee Q Zhao and H-L Lou ldquoJoint ML estimationof frame timing and carrier frequency offset for OFDM systemsemploying time-domain repeated preamblerdquo IEEE Transactionson Wireless Communications vol 9 no 1 pp 311ndash317 2010

[15] A B Awoseyila C Kasparis and B G Evans ldquoRobust time-domain timing and frequency synchronization for OFDMsystemsrdquo IEEE Transactions on Consumer Electronics vol 55no 2 pp 391ndash399 2009

[16] G Ren Y Chang H Zhang and H Zhang ldquoAn efficient fre-quency offset estimation method with a large range for wirelessOFDM systemsrdquo IEEE Transactions on Vehicular Technologyvol 56 no 4 pp 1892ndash1895 2007

[17] V Erceg K Hari M Smith et al ldquoChannel models for fixedwireless applicationsrdquo Tech Rep IEEE Broadband WirelessAccess Working Group 2001

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Journal of Computer Networks and Communications

0

200

400

600

800

1000

Tim

ing

met

ric

minus50 0 50 100minus100Sample index

(a)

0

200

400

600

800

1000

Sam

ple i

ndex

minus50 0 50 100minus100Sample index

(b)

Figure 2 Timing metrics of the proposed method (119873 = 1024 and length of the cyclic prefix is 128) (a) without noise and channel distortionand (b) in a 5-tap Rayleigh fading channel

when

120579 = minus2120587120576120591119873 + ang119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus1198952120587120576119894119873 (21)

where ang denotes the argument of a complex number As aresult we can obtain the ML estimation of (120591 120576) at first using(20) as the likelihood function with the constant 119888 omittedAnd the ML estimator is written as

(120591119900 120576119900) = argmax(120591120576)

2 1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816

minus 1205881119873minus1sum119894=0

|119903 (120591 + 119894)|2 (22)

Note that 1205881 in (22) is a constant number dependent onthe SNR of the received signal Furthermore when 119873 islarge sum119873minus1119894=0 |119903(120591 + 119894)|2 in (22) can also be regarded as aconstant number 11987312059021 (where 12059021 is the average power of119903(119909)) As a result by omitting the multiplication of the twoaforementioned constant numbers we get the reduced MLestimator of (120591119900 120576119900) written as

(120591119900 120576119900) = argmax(120591120576)

1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (120591 + 119894) 119904lowast119894 119890minus11989521205871205761198941198731003816100381610038161003816100381610038161003816100381610038161003816 (23)

In some applications for example in wired OFDMsystems including baseband digital subscriber line (DSL) theCFO errormay be negligible In this case the joint estimationof (120591119900 120576119900) in (23) reduces to ML timing offset estimationwhich can be easily obtained by searching 120591 maximizing theinner product of [119903(120591) 119903(120591+1) 119903(120591+119873minus1)] and the knownpreamble S When the CFO is uncertain the optimum joint

ML estimation of (120591 120576) given in (23) needs to be obtained bynumerical method requiring high computational complexitybecause of the continuous variable 12057632 Simplified Synchronization It is observed that on theright-hand side of (23) the operations in the absolute valuebars are by nature a discrete-time Fourier transformation(DTFT) of the signal 119903(120591 + 119894)119904lowast119894 with the frequency variable(2120587119873)120576 Considering the truth that discrete Fourier trans-form (DFT) is just the equally spaced samples of the DTFTand for a time domain sequence of length 119873 the 119873 pointsDFT hold the same quantity of information as that of DTFTwe propose a near ML timing estimator written as

= argmax119889

119872 (119889) (24)

where119872(119889)

= max1003816100381610038161003816100381610038161003816100381610038161003816119873minus1sum119894=0

119903 (119889 + 119894) 119904lowast119894 119890minus119895(2120587119873)1198961198941003816100381610038161003816100381610038161003816100381610038161003816 0 le 119896 lt 119873 (25)

is the timing metric of the proposed timing offset estimatorSimilar to the timing metric proposed by [9 10] the envelopof the proposed metric is impulse-like because 119872(119889) has itspeak value at the starting point of the preamble while thevalues at all other points are comparatively smaller In Figures2(a) and 2(b) we have depicted the metric of the proposedmethod in two cases of ideal condition (no noise and nochannel distortion) and in a frequency-selective channel of 5paths respectively It is obvious that under both channels theproposed timing metric has a sharp envelope which leads toamuch smaller mean square error of timing offset estimationas shown in later simulation results

Journal of Computer Networks and Communications 5

After the timing offset is acquired by the proposedmethod suboptimal estimation of the CFO can be realizedby methods in existing work such as [15 16] The CFOnormalized by the subcarrier spacing in a system can beexpressed as

120576 = 120576119868 + 120576119891 (26)

where 120576119868 and 120576119891 denote the integer part and the fractionalpart of the frequency offset respectively In [15] firstly thefractional part is achieved by using the characteristics ofa preamble with two identical parts in the time domainand then the integer part is estimated by using the correla-tion between the fractional-part-corrected preamble (chosenfrom the received signal after timing synchronization) andits pure transmitted version When the preamble does nothave repeated identical parts the integer part and fractionalpart can be achieved by the estimator in [16] which isindependent of the preamble structure

33 Computational Complexity Besides the performanceissues computational complexity is equally important in apractical sense We evaluated the complexity of the proposedtiming method by comparing the number of multiplicationsand additions needed by the timing-metric functionwith thatof other timing offset estimators In a OFDM system 119873 isalways set as 2119898 where 119898 is an integer so that the FFTIFFToperations can be used Thus the DFT in (25) can also beperformed by FFT which greatly reduces the computationalcomplexity

Tomake the analysismore intuitive we rewrite the timingmetric in (25) as

119872(119889) = max 10038161003816100381610038161003816(119877119889 ∘ 119878lowast)119882119867119896 10038161003816100381610038161003816 0 le 119896 lt N (27)

where

119877119889 = [119903 (119889) 119903 (119889 + 1) 119903 (119889 + 119873 minus 1)] 119882119896 = [1 119890119895(2120587119873)119896 119890119895(2120587119873)2119896 119890119895(2120587119873)(119873minus1)119896] (28)

The operator ∘ denotes the Hadamard product which isdefined as element-by-elementmultiplications of two vectorsand (sdot)119867 is the conjugate transpose operation

Now we calculate the metric 119872(119889) in (27) for a givencheckpoint indexed by 119889 At first a Hadamard productwhich needs 119873 complex multiplications is used to calculatethe cross-correlation of received signal vector 119877119889 and localpreamble vector 119878 Then the resulting vector transformedto the frequency-domain vector by FFT operations whichrequire 05119873 log2119873 complex multiplications and 119873 log2119873additions At last 119873 complex multiplications and 119873 minus 1complex additions are used to find the maximum elementfrom the resulting frequency-domain vector In total we need119873(05 log2119873+2) complexmultiplications and (log2119873+1)119873minus1additions to calculate 119872(119889) for the checkpoint 119889

In Table 1 we have demonstrated the complexity of theproposed method in comparison with the previous onesNote that although the proposed method is more complex

Table 1 Computational complexity of different estimators

Method Complex multiplication Complexaddition

Schmidl[2] 2 2

Ren [9] 1 119873 minus 1Kang [6] 2 119873 minus 1HM [10] 119897119904 + 119871 + 1 where 0 lt 119897119904 lt 119873119871 le (1198732 minus 119873)2 119871Proposed 119873(05 log2119873 + 2) 119873(log2119873+1)minus1

than methods of Schmidl Ren and Kang it achieves a sig-nificantly better performance than those methods as shownin the next section As to HMrsquos method the computationalcomplexity is adjustable by setting reasonable index vectors119865 = [1198651 1198652 119865119894 119865119897119904] and 119866 = [1198661 1198662 119866119894 119866119897119904]in which 119865119894 or 119866119894 is a subvector The number of elementsin 119865 or 119866 is noted as 119871 which can be extended up to (119873 minus1)(1198732) if necessary Naturally higher 119871means higher timingperformance However from the simulation results given inSection 4 we will see that the performance of the proposedmethod is better than that of HMrsquos estimator even when allthe available products are used in the latter method

4 Simulation Results

The performance of the proposed method has been investi-gated in comparison with other methods using Monte Carlosimulations The parameters used in the OFDM system are64 subcarriers 64-point IFFTFFT 18 guard interval (119866 =8) and 100 000 simulation runs in each examination Thenormalized CFO is set to 120576 = 31 Considering that theOFDM systems always work under multipath channel weadopt two different multipath channels for the simulationThe first channel is based on Stanford university interim(SUI) channel modeling [17] with the sampling rate of 5MHzThe second one is a multipath Rayleigh fading channel of 5paths We evaluate the performance of the proposed timingmethods bymean square error (MSE) sinceMSE reflects boththe bias and the variance of the estimation

In Figure 3 we have depicted the MSE of the proposedmethods in comparison with the MSEs of five previousmethods under the SUI-1 channel We can see that theproposedmethod has a significantly better performance thanthe previous methods It is worth mentioning that all thepossible product terms have been used in HMrsquos method inthe simulation Thus the proposed estimator performs betterthan HMrsquos method even though the latter involves muchhigher computational complexity Furthermore we can seethat Kangrsquos and Yangrsquos methods suffer great performancedegradation from the CFO in the simulation

Figure 4 demonstrates the MSEs of different estimatorsin another multipath Rayleigh fading channel with 5 pathspath delays ℓ = 0 1 4 and the channel delay profile119890(ℓ5) Here we have 119873 = 64 and 119866 = 12 For HMrsquos method[10] to get the best performance it could achieve we use

6 Journal of Computer Networks and Communications

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

5 10 15 20 25 300SNR (dB)

10minus1

100

101

102

103

104

MSE

Figure 3 TimingMSE versus SNR for six methods in SUI-1 channel(119873 = 64 and 119866 = 8)

10minus1

100

101

102

103

104

MSE

5 10 15 20 25 300SNR (dB)

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

Figure 4 Timing MSE versus SNR for six methods in a 5-tapRayleigh fading channel (119873 = 64 and 119866 = 12)

all the available correlation products in the simulation It isevident that the proposed method has a remarkably betterperformance than others

5 Conclusions

In this paper at first we derived the ML joint estimatorof timing offset and CFO for OFDM systems Then a sim-

plified timing synchronization method has been proposedbased on the ML estimator The proposed timing method isindependent of the structure of the preamble and immuneto the normalized CFO (by subcarrier space) in the rangeof [minus1198732 1198732] As shown in the simulation result theproposed estimator performs better than the existing meth-ods For any given preamble the joint timing and frequencysynchronization for OFDM systems can be achieved by usingour proposed timing method and the CFO estimator in [16]

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National Natu-ral Science Foundation of China (61431005 61501531 and61671211) and the Natural Science Foundation of Guang-dong Province China (2015A030313602 2014A030311034and 2016A030308006)

References

[1] T Pollet M Van Bladel and M Moeneclaey ldquoBER sensitivityof OFDM systems to carrier frequency offset and wiener phasenoiserdquo IEEE Transactions on Communications vol 43 no 234pp 191ndash193 1995

[2] T M Schmidl and D C Cox ldquoRobust frequency and timingsynchronization for OFDMrdquo IEEE Transactions on Communi-cations vol 45 no 12 pp 1613ndash1621 1997

[3] H Minn M Zeng and V K Bhargava ldquoOn timing offsetestimation for OFDM systemsrdquo IEEE Communications Lettersvol 4 no 7 pp 242ndash244 2000

[4] K Shi and E Serpedin ldquoCoarse frame and carrier synchroniza-tion of OFDM systems a new metric and comparisonrdquo IEEETransactions onWireless Communications vol 3 no 4 pp 1271ndash1284 2004

[5] B Park H Cheon C Kang and D Hong ldquoA novel timingestimation method for OFDM systemsrdquo IEEE CommunicationsLetters vol 7 no 5 pp 239ndash241 2003

[6] Y Kang S Kim D Ahn and H Lee ldquoTiming estimation forOFDM systems by using a correlation sequence of preamblerdquoIEEE Transactions on Consumer Electronics vol 54 no 4 pp1600ndash1608 2008

[7] H Abdzadeh-Ziabari M G Shayesteh and M Manaffar ldquoAnimproved timing estimation method for OFDM systemsrdquo IEEETransactions on Consumer Electronics vol 56 no 4 pp 2098ndash2105 2010

[8] F Yang and X Zhang ldquoRobust time-domain fine symbolsynchronization for OFDM-based packet transmission usingCAZAC preamblerdquo in Proceedings of the IEEE Military Com-munications Conference (MILCOM rsquo13) pp 436ndash440 IEEE SanDiego Calif USA November 2013

[9] G Ren Y Chang H Zhang and H Zhang ldquoSynchronizationmethod based on a new constant envelop preamble for OFDMsystemsrdquo IEEE Transactions on Broadcasting vol 51 no 1 pp139ndash143 2005

Journal of Computer Networks and Communications 7

[10] H Abdzadeh-Ziabari and M G Shayesteh ldquoRobust timingand frequency synchronization for OFDM systemsrdquo IEEETransactions on Vehicular Technology vol 60 no 8 pp 3646ndash3656 2011

[11] Y Liu H Yu F Ji F Chen and W Pan ldquoRobust timing estima-tionmethod forOFDMsystemswith reduced complexityrdquo IEEECommunications Letters vol 18 no 11 pp 1959ndash1962 2014

[12] J-J Van De Beek M Sandell and P O Borjesson ldquoMLestimation of time and frequency offset in OFDM systemsrdquoIEEE Transactions on Signal Processing vol 45 no 7 pp 1800ndash1805 1997

[13] W-L Chin ldquoML estimation of timing and frequency offsetsusing distinctive correlation characteristics of OFDM signalsover dispersive fading channelsrdquo IEEE Transactions on Vehic-ular Technology vol 60 no 2 pp 444ndash456 2011

[14] J-W Choi J Lee Q Zhao and H-L Lou ldquoJoint ML estimationof frame timing and carrier frequency offset for OFDM systemsemploying time-domain repeated preamblerdquo IEEE Transactionson Wireless Communications vol 9 no 1 pp 311ndash317 2010

[15] A B Awoseyila C Kasparis and B G Evans ldquoRobust time-domain timing and frequency synchronization for OFDMsystemsrdquo IEEE Transactions on Consumer Electronics vol 55no 2 pp 391ndash399 2009

[16] G Ren Y Chang H Zhang and H Zhang ldquoAn efficient fre-quency offset estimation method with a large range for wirelessOFDM systemsrdquo IEEE Transactions on Vehicular Technologyvol 56 no 4 pp 1892ndash1895 2007

[17] V Erceg K Hari M Smith et al ldquoChannel models for fixedwireless applicationsrdquo Tech Rep IEEE Broadband WirelessAccess Working Group 2001

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Computer Networks and Communications 5

After the timing offset is acquired by the proposedmethod suboptimal estimation of the CFO can be realizedby methods in existing work such as [15 16] The CFOnormalized by the subcarrier spacing in a system can beexpressed as

120576 = 120576119868 + 120576119891 (26)

where 120576119868 and 120576119891 denote the integer part and the fractionalpart of the frequency offset respectively In [15] firstly thefractional part is achieved by using the characteristics ofa preamble with two identical parts in the time domainand then the integer part is estimated by using the correla-tion between the fractional-part-corrected preamble (chosenfrom the received signal after timing synchronization) andits pure transmitted version When the preamble does nothave repeated identical parts the integer part and fractionalpart can be achieved by the estimator in [16] which isindependent of the preamble structure

33 Computational Complexity Besides the performanceissues computational complexity is equally important in apractical sense We evaluated the complexity of the proposedtiming method by comparing the number of multiplicationsand additions needed by the timing-metric functionwith thatof other timing offset estimators In a OFDM system 119873 isalways set as 2119898 where 119898 is an integer so that the FFTIFFToperations can be used Thus the DFT in (25) can also beperformed by FFT which greatly reduces the computationalcomplexity

Tomake the analysismore intuitive we rewrite the timingmetric in (25) as

119872(119889) = max 10038161003816100381610038161003816(119877119889 ∘ 119878lowast)119882119867119896 10038161003816100381610038161003816 0 le 119896 lt N (27)

where

119877119889 = [119903 (119889) 119903 (119889 + 1) 119903 (119889 + 119873 minus 1)] 119882119896 = [1 119890119895(2120587119873)119896 119890119895(2120587119873)2119896 119890119895(2120587119873)(119873minus1)119896] (28)

The operator ∘ denotes the Hadamard product which isdefined as element-by-elementmultiplications of two vectorsand (sdot)119867 is the conjugate transpose operation

Now we calculate the metric 119872(119889) in (27) for a givencheckpoint indexed by 119889 At first a Hadamard productwhich needs 119873 complex multiplications is used to calculatethe cross-correlation of received signal vector 119877119889 and localpreamble vector 119878 Then the resulting vector transformedto the frequency-domain vector by FFT operations whichrequire 05119873 log2119873 complex multiplications and 119873 log2119873additions At last 119873 complex multiplications and 119873 minus 1complex additions are used to find the maximum elementfrom the resulting frequency-domain vector In total we need119873(05 log2119873+2) complexmultiplications and (log2119873+1)119873minus1additions to calculate 119872(119889) for the checkpoint 119889

In Table 1 we have demonstrated the complexity of theproposed method in comparison with the previous onesNote that although the proposed method is more complex

Table 1 Computational complexity of different estimators

Method Complex multiplication Complexaddition

Schmidl[2] 2 2

Ren [9] 1 119873 minus 1Kang [6] 2 119873 minus 1HM [10] 119897119904 + 119871 + 1 where 0 lt 119897119904 lt 119873119871 le (1198732 minus 119873)2 119871Proposed 119873(05 log2119873 + 2) 119873(log2119873+1)minus1

than methods of Schmidl Ren and Kang it achieves a sig-nificantly better performance than those methods as shownin the next section As to HMrsquos method the computationalcomplexity is adjustable by setting reasonable index vectors119865 = [1198651 1198652 119865119894 119865119897119904] and 119866 = [1198661 1198662 119866119894 119866119897119904]in which 119865119894 or 119866119894 is a subvector The number of elementsin 119865 or 119866 is noted as 119871 which can be extended up to (119873 minus1)(1198732) if necessary Naturally higher 119871means higher timingperformance However from the simulation results given inSection 4 we will see that the performance of the proposedmethod is better than that of HMrsquos estimator even when allthe available products are used in the latter method

4 Simulation Results

The performance of the proposed method has been investi-gated in comparison with other methods using Monte Carlosimulations The parameters used in the OFDM system are64 subcarriers 64-point IFFTFFT 18 guard interval (119866 =8) and 100 000 simulation runs in each examination Thenormalized CFO is set to 120576 = 31 Considering that theOFDM systems always work under multipath channel weadopt two different multipath channels for the simulationThe first channel is based on Stanford university interim(SUI) channel modeling [17] with the sampling rate of 5MHzThe second one is a multipath Rayleigh fading channel of 5paths We evaluate the performance of the proposed timingmethods bymean square error (MSE) sinceMSE reflects boththe bias and the variance of the estimation

In Figure 3 we have depicted the MSE of the proposedmethods in comparison with the MSEs of five previousmethods under the SUI-1 channel We can see that theproposedmethod has a significantly better performance thanthe previous methods It is worth mentioning that all thepossible product terms have been used in HMrsquos method inthe simulation Thus the proposed estimator performs betterthan HMrsquos method even though the latter involves muchhigher computational complexity Furthermore we can seethat Kangrsquos and Yangrsquos methods suffer great performancedegradation from the CFO in the simulation

Figure 4 demonstrates the MSEs of different estimatorsin another multipath Rayleigh fading channel with 5 pathspath delays ℓ = 0 1 4 and the channel delay profile119890(ℓ5) Here we have 119873 = 64 and 119866 = 12 For HMrsquos method[10] to get the best performance it could achieve we use

6 Journal of Computer Networks and Communications

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

5 10 15 20 25 300SNR (dB)

10minus1

100

101

102

103

104

MSE

Figure 3 TimingMSE versus SNR for six methods in SUI-1 channel(119873 = 64 and 119866 = 8)

10minus1

100

101

102

103

104

MSE

5 10 15 20 25 300SNR (dB)

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

Figure 4 Timing MSE versus SNR for six methods in a 5-tapRayleigh fading channel (119873 = 64 and 119866 = 12)

all the available correlation products in the simulation It isevident that the proposed method has a remarkably betterperformance than others

5 Conclusions

In this paper at first we derived the ML joint estimatorof timing offset and CFO for OFDM systems Then a sim-

plified timing synchronization method has been proposedbased on the ML estimator The proposed timing method isindependent of the structure of the preamble and immuneto the normalized CFO (by subcarrier space) in the rangeof [minus1198732 1198732] As shown in the simulation result theproposed estimator performs better than the existing meth-ods For any given preamble the joint timing and frequencysynchronization for OFDM systems can be achieved by usingour proposed timing method and the CFO estimator in [16]

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National Natu-ral Science Foundation of China (61431005 61501531 and61671211) and the Natural Science Foundation of Guang-dong Province China (2015A030313602 2014A030311034and 2016A030308006)

References

[1] T Pollet M Van Bladel and M Moeneclaey ldquoBER sensitivityof OFDM systems to carrier frequency offset and wiener phasenoiserdquo IEEE Transactions on Communications vol 43 no 234pp 191ndash193 1995

[2] T M Schmidl and D C Cox ldquoRobust frequency and timingsynchronization for OFDMrdquo IEEE Transactions on Communi-cations vol 45 no 12 pp 1613ndash1621 1997

[3] H Minn M Zeng and V K Bhargava ldquoOn timing offsetestimation for OFDM systemsrdquo IEEE Communications Lettersvol 4 no 7 pp 242ndash244 2000

[4] K Shi and E Serpedin ldquoCoarse frame and carrier synchroniza-tion of OFDM systems a new metric and comparisonrdquo IEEETransactions onWireless Communications vol 3 no 4 pp 1271ndash1284 2004

[5] B Park H Cheon C Kang and D Hong ldquoA novel timingestimation method for OFDM systemsrdquo IEEE CommunicationsLetters vol 7 no 5 pp 239ndash241 2003

[6] Y Kang S Kim D Ahn and H Lee ldquoTiming estimation forOFDM systems by using a correlation sequence of preamblerdquoIEEE Transactions on Consumer Electronics vol 54 no 4 pp1600ndash1608 2008

[7] H Abdzadeh-Ziabari M G Shayesteh and M Manaffar ldquoAnimproved timing estimation method for OFDM systemsrdquo IEEETransactions on Consumer Electronics vol 56 no 4 pp 2098ndash2105 2010

[8] F Yang and X Zhang ldquoRobust time-domain fine symbolsynchronization for OFDM-based packet transmission usingCAZAC preamblerdquo in Proceedings of the IEEE Military Com-munications Conference (MILCOM rsquo13) pp 436ndash440 IEEE SanDiego Calif USA November 2013

[9] G Ren Y Chang H Zhang and H Zhang ldquoSynchronizationmethod based on a new constant envelop preamble for OFDMsystemsrdquo IEEE Transactions on Broadcasting vol 51 no 1 pp139ndash143 2005

Journal of Computer Networks and Communications 7

[10] H Abdzadeh-Ziabari and M G Shayesteh ldquoRobust timingand frequency synchronization for OFDM systemsrdquo IEEETransactions on Vehicular Technology vol 60 no 8 pp 3646ndash3656 2011

[11] Y Liu H Yu F Ji F Chen and W Pan ldquoRobust timing estima-tionmethod forOFDMsystemswith reduced complexityrdquo IEEECommunications Letters vol 18 no 11 pp 1959ndash1962 2014

[12] J-J Van De Beek M Sandell and P O Borjesson ldquoMLestimation of time and frequency offset in OFDM systemsrdquoIEEE Transactions on Signal Processing vol 45 no 7 pp 1800ndash1805 1997

[13] W-L Chin ldquoML estimation of timing and frequency offsetsusing distinctive correlation characteristics of OFDM signalsover dispersive fading channelsrdquo IEEE Transactions on Vehic-ular Technology vol 60 no 2 pp 444ndash456 2011

[14] J-W Choi J Lee Q Zhao and H-L Lou ldquoJoint ML estimationof frame timing and carrier frequency offset for OFDM systemsemploying time-domain repeated preamblerdquo IEEE Transactionson Wireless Communications vol 9 no 1 pp 311ndash317 2010

[15] A B Awoseyila C Kasparis and B G Evans ldquoRobust time-domain timing and frequency synchronization for OFDMsystemsrdquo IEEE Transactions on Consumer Electronics vol 55no 2 pp 391ndash399 2009

[16] G Ren Y Chang H Zhang and H Zhang ldquoAn efficient fre-quency offset estimation method with a large range for wirelessOFDM systemsrdquo IEEE Transactions on Vehicular Technologyvol 56 no 4 pp 1892ndash1895 2007

[17] V Erceg K Hari M Smith et al ldquoChannel models for fixedwireless applicationsrdquo Tech Rep IEEE Broadband WirelessAccess Working Group 2001

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Computer Networks and Communications

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

5 10 15 20 25 300SNR (dB)

10minus1

100

101

102

103

104

MSE

Figure 3 TimingMSE versus SNR for six methods in SUI-1 channel(119873 = 64 and 119866 = 8)

10minus1

100

101

102

103

104

MSE

5 10 15 20 25 300SNR (dB)

Ren [9]Kang [6]Yang [8]

Schmidl [2]HM and Liu [10-11]Proposed

Figure 4 Timing MSE versus SNR for six methods in a 5-tapRayleigh fading channel (119873 = 64 and 119866 = 12)

all the available correlation products in the simulation It isevident that the proposed method has a remarkably betterperformance than others

5 Conclusions

In this paper at first we derived the ML joint estimatorof timing offset and CFO for OFDM systems Then a sim-

plified timing synchronization method has been proposedbased on the ML estimator The proposed timing method isindependent of the structure of the preamble and immuneto the normalized CFO (by subcarrier space) in the rangeof [minus1198732 1198732] As shown in the simulation result theproposed estimator performs better than the existing meth-ods For any given preamble the joint timing and frequencysynchronization for OFDM systems can be achieved by usingour proposed timing method and the CFO estimator in [16]

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National Natu-ral Science Foundation of China (61431005 61501531 and61671211) and the Natural Science Foundation of Guang-dong Province China (2015A030313602 2014A030311034and 2016A030308006)

References

[1] T Pollet M Van Bladel and M Moeneclaey ldquoBER sensitivityof OFDM systems to carrier frequency offset and wiener phasenoiserdquo IEEE Transactions on Communications vol 43 no 234pp 191ndash193 1995

[2] T M Schmidl and D C Cox ldquoRobust frequency and timingsynchronization for OFDMrdquo IEEE Transactions on Communi-cations vol 45 no 12 pp 1613ndash1621 1997

[3] H Minn M Zeng and V K Bhargava ldquoOn timing offsetestimation for OFDM systemsrdquo IEEE Communications Lettersvol 4 no 7 pp 242ndash244 2000

[4] K Shi and E Serpedin ldquoCoarse frame and carrier synchroniza-tion of OFDM systems a new metric and comparisonrdquo IEEETransactions onWireless Communications vol 3 no 4 pp 1271ndash1284 2004

[5] B Park H Cheon C Kang and D Hong ldquoA novel timingestimation method for OFDM systemsrdquo IEEE CommunicationsLetters vol 7 no 5 pp 239ndash241 2003

[6] Y Kang S Kim D Ahn and H Lee ldquoTiming estimation forOFDM systems by using a correlation sequence of preamblerdquoIEEE Transactions on Consumer Electronics vol 54 no 4 pp1600ndash1608 2008

[7] H Abdzadeh-Ziabari M G Shayesteh and M Manaffar ldquoAnimproved timing estimation method for OFDM systemsrdquo IEEETransactions on Consumer Electronics vol 56 no 4 pp 2098ndash2105 2010

[8] F Yang and X Zhang ldquoRobust time-domain fine symbolsynchronization for OFDM-based packet transmission usingCAZAC preamblerdquo in Proceedings of the IEEE Military Com-munications Conference (MILCOM rsquo13) pp 436ndash440 IEEE SanDiego Calif USA November 2013

[9] G Ren Y Chang H Zhang and H Zhang ldquoSynchronizationmethod based on a new constant envelop preamble for OFDMsystemsrdquo IEEE Transactions on Broadcasting vol 51 no 1 pp139ndash143 2005

Journal of Computer Networks and Communications 7

[10] H Abdzadeh-Ziabari and M G Shayesteh ldquoRobust timingand frequency synchronization for OFDM systemsrdquo IEEETransactions on Vehicular Technology vol 60 no 8 pp 3646ndash3656 2011

[11] Y Liu H Yu F Ji F Chen and W Pan ldquoRobust timing estima-tionmethod forOFDMsystemswith reduced complexityrdquo IEEECommunications Letters vol 18 no 11 pp 1959ndash1962 2014

[12] J-J Van De Beek M Sandell and P O Borjesson ldquoMLestimation of time and frequency offset in OFDM systemsrdquoIEEE Transactions on Signal Processing vol 45 no 7 pp 1800ndash1805 1997

[13] W-L Chin ldquoML estimation of timing and frequency offsetsusing distinctive correlation characteristics of OFDM signalsover dispersive fading channelsrdquo IEEE Transactions on Vehic-ular Technology vol 60 no 2 pp 444ndash456 2011

[14] J-W Choi J Lee Q Zhao and H-L Lou ldquoJoint ML estimationof frame timing and carrier frequency offset for OFDM systemsemploying time-domain repeated preamblerdquo IEEE Transactionson Wireless Communications vol 9 no 1 pp 311ndash317 2010

[15] A B Awoseyila C Kasparis and B G Evans ldquoRobust time-domain timing and frequency synchronization for OFDMsystemsrdquo IEEE Transactions on Consumer Electronics vol 55no 2 pp 391ndash399 2009

[16] G Ren Y Chang H Zhang and H Zhang ldquoAn efficient fre-quency offset estimation method with a large range for wirelessOFDM systemsrdquo IEEE Transactions on Vehicular Technologyvol 56 no 4 pp 1892ndash1895 2007

[17] V Erceg K Hari M Smith et al ldquoChannel models for fixedwireless applicationsrdquo Tech Rep IEEE Broadband WirelessAccess Working Group 2001

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Computer Networks and Communications 7

[10] H Abdzadeh-Ziabari and M G Shayesteh ldquoRobust timingand frequency synchronization for OFDM systemsrdquo IEEETransactions on Vehicular Technology vol 60 no 8 pp 3646ndash3656 2011

[11] Y Liu H Yu F Ji F Chen and W Pan ldquoRobust timing estima-tionmethod forOFDMsystemswith reduced complexityrdquo IEEECommunications Letters vol 18 no 11 pp 1959ndash1962 2014

[12] J-J Van De Beek M Sandell and P O Borjesson ldquoMLestimation of time and frequency offset in OFDM systemsrdquoIEEE Transactions on Signal Processing vol 45 no 7 pp 1800ndash1805 1997

[13] W-L Chin ldquoML estimation of timing and frequency offsetsusing distinctive correlation characteristics of OFDM signalsover dispersive fading channelsrdquo IEEE Transactions on Vehic-ular Technology vol 60 no 2 pp 444ndash456 2011

[14] J-W Choi J Lee Q Zhao and H-L Lou ldquoJoint ML estimationof frame timing and carrier frequency offset for OFDM systemsemploying time-domain repeated preamblerdquo IEEE Transactionson Wireless Communications vol 9 no 1 pp 311ndash317 2010

[15] A B Awoseyila C Kasparis and B G Evans ldquoRobust time-domain timing and frequency synchronization for OFDMsystemsrdquo IEEE Transactions on Consumer Electronics vol 55no 2 pp 391ndash399 2009

[16] G Ren Y Chang H Zhang and H Zhang ldquoAn efficient fre-quency offset estimation method with a large range for wirelessOFDM systemsrdquo IEEE Transactions on Vehicular Technologyvol 56 no 4 pp 1892ndash1895 2007

[17] V Erceg K Hari M Smith et al ldquoChannel models for fixedwireless applicationsrdquo Tech Rep IEEE Broadband WirelessAccess Working Group 2001

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of