Inter national J our nal of Electrical and Computer Engineering (IJECE) V ol. 7, No. 2, April 2017, pp. 905 912 ISSN: 2088-8708 905       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w       i                       l       c       m     Impr o v ed T iming Estimation Using Iterati v e Normalization T echnique f or OFDM Systems Suy oto 1 , Iskandar 2 , Sugihartono 3 , and Adit K ur niawan 4 1,2,3,4 School of Electrical Engineering and Informatics, Institut T eknologi Bandung (ITB), Indonesia 1 Research Center of Informatics, Lembag a Ilmu Pengetahuan Indonesia (LIPI), Indonesia Article Inf o Article history: Recei v ed Oct 25, 2016 Re vised Feb 9, 2017 Accepted Feb 24, 2017 K eyw ord: OFDM multipath channel timing estimation high delay spread ABSTRA CT Con v entional timing estimation schemes based on autocorrelation e xperience performance de gradation in the multipath channel en vironment with high delay spread. T o o v ercome this problem, we proposed an impro v ement of the timing estimat ion for the OFDM system based on statistical change of symmetrical correlator . The ne w method uses iterati v e normalization technique to the correlator output before the detection based on statistical change of sym- metric correlator is applied. Thus, it increases the detection probability and achie v es better performance than pre vi ously published methods in t he multipath en vironment. Computer simulation sho ws that our method is v ery rob ust in the f ading multipath channel. Copyright c 2017 Institute of Advanced Engineering and Science . All rights r eserved. Corresponding A uthor: Suyoto Research Center of Informatics, Lembag a Ilmu Pengetahuan Indonesia K omplek LIPI Gedung 20. lt.3 Jl. Cisitu No.21/154D Bandung 40135 +62222504711 yoto@informatika.lipi.go.id 1. INTR ODUCTION Orthogonal Frequenc y Di vision Mul tiple xing (OFDM) systems of fer high bandwidth ef ficienc y and rob ust ag ainst multipath delay . Hence, OFDM systems ha v e been widely adopted for a high dat a rate, wireless communi- cation systems, such as WLAN [1], D VB-T2 [2], and WMAN 802.16m [3]. Both of D VB-T2 and WMAN 802.16m are supporting applications that run in a high speed mobility en vironment. Recently OFDM technique is also used for cogniti v e radio systems, which t h e use of frequenc y spectrum in the OFDM systems can be done as ef ficiently as possible [4]-[5]. Ho we v er , OFDM systems need strict timing synchronization between transmitter and recei v er , as an error in timing estimation gi v e rise to InterSymbol Interference (ISI) and can decrease the o v erall performance of OFDM systems [6]-[7]. F or symbol timing estim ation, Schmidl [8] used a preamble consists of tw o identical parts for symbol timing estimation. But, the timing metric of Schmidl’ s method has a plateau, which causes a lar ge v ariance in the timing of fset est imation. T o decrease the plateau, Mi nn [9] proposed a ne w training symbol with four identical parts. It results a sharper timing metric than Schmidl’ s method, ho we v er , it still has ambiguity due to some side-lobes at a side of the peak correlation re gion, thus estimation v ariance is still lar ge. In order to reduce the v ariance, P ark [10] proposed a sharper timing metric using symmetric correlation property of the preamble. Y et, the timing metric of P ark’ s method has tw o lar ge side-lobes . T o eliminate the side-lobes of P ark’ s timing m etric, Y i [11] proposed a ne w preamble structure that has symmetric correlation property . The perform ance of all the abo v e-mentioned approaches decrease in multipath channel en vironments. T o o v ercome this problem, Cho [12] proposed a met h od that e xploits statistical change of symmetric corre- lator . It reduces the multipath channel ef fect, hence the v ariance of the timing of fset estimation is small. Ho we v er , Cho’ s method generates error detection if the correlation magnitude on the first arri ving path is much smaller than the strongest path. T o o v ercome this problem, we proposed an iterati v e normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. Considering the v ery small correla- tion magnitude on the first arri ving path, we attempt to increase the correlation magnitude on the first a rri ving path to J ournal Homepage: http://iaesjournal.com/online/inde x.php/IJECE       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w       i                       l       c       m     DOI:  10.11591/ijece.v7i2.pp905-912 Evaluation Warning : The document was created with Spire.PDF for Python.
906 ISSN: 2088-8708 Figure 1. The Block diagram of OFDM transmission systems (synch.: synchronization). produce an estimation method with better performance. Our e xperimental results sho w that the ne w timing estimator achie v es better performance than pre viously published methods. 2. OFDM SIGN AL MODEL Fig. 1 sho ws an OFDM transmission system that consists of a sequence of OFDM symbols, where each of the OFDM symbol which has a duration of T s seconds is generated by a number of N s points In v erse F ast F ourier T ransform (IFFT) from a block of sub-symbols f C k g . Cyclic Prefix (CP) with a length of N g is added at the start of the OFDM sym bol that is longer than the duration of the Channel Impulse Response (CIR). Thus, the OFDM signal transmitted through the frequenc y selecti v e f ading channel with a delay spread length of L ch is e xpressed as follo ws: y ( d ) = L ch 1 X m =0 h ( m ) x ( d m ) + w ( d ) ; (1) where d is time inde x, h ( m ) is the channel impulse response, w ( d ) is white Gaussian noise with zero mean, and x ( d ) is the output signal from IFFT describes as follo ws: x ( d ) = N 1 X k =0 C k e j 2 k d= N s : (2) The delay of the recei ving signal r ( d ) at the recei v er can be modelled as follo ws: r ( d ) = y ( d d ) e j 2 d N s f ; (3) where d is an unkno wn inte ger -v alued of arri v al time of an OFDM symbol and f is the Carrier Frequenc y Of fset (CFO) normalized to the subcarrier spacing. 3. PR OPOSED METHOD 3.1. Symmetric Corr elator In time domain, the form of P ark’ s preamble is defined as follo ws [10]: P P ar k = [ A N s = 4 B N s = 4 A N s = 4 B N s = 4 ] ; (4) IJECE V ol. 7, No. 2, April 2017: 905 912 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 907 where A N s = 4 represents samples with length N s = 4 generated by IFFT of a Pseudo Noise (PN) sequence, and A N s = 4 represents the conjug ate of A N s = 4 . B N s = 4 is symmetric of A N s = 4 and is generated by the method in [10]. Thus, the symmetric correlator T ( d ) is defined as: T ( d ) = N s = 2 1 X k =1 r ( d + k ) r ( d + N s k ) : (5) 3.2. Statistical Pr operty of Symmetric Corr elator As in [12], the Probability Distrib ution Function (PDF) of T ( d ) is defined as follo ws: ( d ) = N s = 2 1 X k =1 r ( d + N s = 2 k ) r ( d + N s = 2 + k ) ; (6) for j d d 0 j < L r , ( d ) follo w a comple x normal distrib ution as: ( d ) C N (0 ; K 4 r ) ; d = 2 L C N ( K h 2 ( d d 0 ) 2 x e 2 f ; K 4 r ) ; d 2 L; (7) where L r is the number of ident ical part of the preamble ( L r = N s = 2) , K = ( N s = 2 1) , 2 r =  2 x + 2 w ; = P m j h ( m ) j 2 , 2 x = 1 N s P N s 1 k =0 j x p ( k ) j 2 , 2 w is noise v ariance, and x p ( k ) denote the preamble signal in t ime domain. d 0 indicates the start of preamble ( d 0 = 0) , which corresponds to the first arri ving path and L (= ( d 0 ; d 0 + 1 ; :::; d 0 + L ch )) is multipath channel inde x. Accordingly , for correlator length ( L r > j d d 0 j ) , T ( d ) is a Rician random v ariable with PDF: f ( T ( d ); 2 ; v ( d )) = T ( d ) 2 exp ( T 2 ( d ) + v 2 ( d ) 2 2 ) I 0 ( T ( d ) v ( d ) 2 ) ; (8) where I 0 ( x ) is modified the first kind of Bassel function with order zero, v ( d ) = K j h 2 ( d d 0 ) j 2 x ; d 2 L 0 ; d = 2 L; (9) and 2 = K 4 r = 2 . 3.3. T iming Estimation Based on Statistical Change of Symmetric Corr elator From the PDF deri v ed in (8), [12] observ es the statistical change of T ( d ) upon the reception of the preamble. Then, by the Generalized Lik elihood Ratio (GLR) approach, the timing metric is defined as: M T ( d ) = exp 1 2 ( d ) + 1 I 0 p ( d ) 2 2( d ) ; (10) where ( d ) = T 2 ( d ) 2 0 ( d ) , 2 0 ( d ) = 1 2 J P J 1 k =0 T 2 ( d k ) , and J is the observ ation length for detection. Thus, the timing estimation is defined as: ^ d = ar g max | {z } d ( M 0 T ( d )) ; (11) where M 0 T ( d ) = M T ( d ) j ; T ( d ) > R 0 ; other w ise; (12) and R is the threshold, which set to a v oid F alse Alarm in Eq. (12). The Probability of F alse Alarm ( P F A ) is deri v ed from Eq. (8) at v ( d ) = 0 as: Impr o ved T iming Estimation Using Iter ative Normalization T ec hnique for OFDM ... (Suyoto) Evaluation Warning : The document was created with Spire.PDF for Python.
908 ISSN: 2088-8708 P F A = exp ( R 2 = 2 2 ) ; (13) if 2 replaced by 2 0 , the threshold can be obtained for the gi v en F alse Alarm rate as: R = q 2 2 0 l og P F A : (14) 3.4. The Pr oposed T iming Estimation Cho’ s technique e xploits the statistics of T ( d ) change upon the reception of t he preamble. It detects the change of parameter v ( d ) from 0 for d < d 0 to v ( d ) = K j h 2 (0) j 2 x at d = d 0 . This technique generates error in detecting the first arri ving path when the g ain on the first channel path ( j h 2 (0) j ) is much smaller than the strongest path ( j h 2 ( m ) j ) , where m is 1 ; 2 ; :::; L ch 1 . Thus, it mak es the correlation magnitude on the first arri ving path much smaller than the stronger path and causes ( d 0 ) < ( d s ) , where d s is time inde x on the stronger path. Therefore, Cho’ s detection technique f ails to detect the first arri ving path. T o o v ercome this problem, we proposed an iterati v e normalization technique to be applied to the correlator T ( d ) before the detection based on statistical change of symmetric correlator is applied. It increases the corre lation magnitude on the first arri ving path and suppress the correlation magnitude on other paths, which are associated with the time side-lobes that are sometimes can appear as the stronger path. In other w ords, we gi v e higher weighting f actor to other paths than to the first arri ving path. Hence, making the v alue of ( d 0 ) ( d s ) . Thus, Cho’ s detection technique can successfully detect the first arri ving path. Cho met hod is actually second-order normalization technique, b ut this technique can not be applied directly to the iterati v e normalization technique because it does not has a stable performa n c e when the number of iterations is increased. This is due to P ark’ s timing metric which is compliant with WMAN 802.16m [3] systems has tw o lar ge lobes so that the short of observ ation length (Cho’ s observ ation length less than or equal to the channel length) from Cho’ s method can not be used for iterati v e technique. W e set the observ ation length for iterati v e normalizat ion equal to the number of identical parts ( L r ), since the magnitude of side-lobes depend on the number of identical parts of the preamble. This is done to achie v e stable performance until q iterations. The iterati v e normalization technique Z i ( d ) is e xpressed as: Z i ( d ) = s Z 2 i 1 ( d ) 2 Z ( i 1) ( d ) ; (15) where i is the inde x of iteration and 2 Z i ( d ) is the v ariance of correlator at i iteration and is defined as: 2 Z i ( d ) = 1 N nor m N nor m 1 X k =0 Z 2 i ( d k ) ; (16) where N nor m is the observ ation length for iterati v e normalization. Our proposed method is performed as follo ws. First, we set Z 0 ( d ) = T ( d ) , and then the iteration process is applied to (15) for i = 1 to q , where q is the number of iteration. After obtaining Z q ( d ) , we set back T ( d ) = Z q ( d ) . Then, the timing estimation can be calculated using (10) and (11). Fig. 2 Sho ws the simulation result using Cho’ s method (Fig. 2(c)) compared to that using our proposed method with q = 3 (Fig. 2(d)). Those figures repre sent normalized v alue ag ainst their maximum v alue. The correct timing point d 0 (the first arri ving path) is inde x ed as 0. Under such situations, we can observ e that Cho’ s method f ails to detect the first arri ving path because the correlation magnitude on the first arri ving path much smaller than the stronger path (Fig. 2(a)), hence ( d 0 ) < ( d s ) . Meanwhile, our proposed method ca n detect the first arri ving path; this impro v ement can be inferred from the rise of the correlation magnitude v ( d 0 ) and the decrease of the correlation magnitude on other paths (Fig. 2(b)), hence ( d 0 ) ( d s ) and Cho’ s detection technique can successfully detect the first arri ving path. 4. RESUL TS AND DISCUSSION In this part, we tested the performance of the proposed method using computer simulation in the term of timing metric and measure the Mean Squared Error (MSE) of symbol timing. The MSE of symbol timing is defined as E [( t estimation t of f set ) 2 ] , which i n di cates the a v erage squared dif ference between the estimation time at recei v er and IJECE V ol. 7, No. 2, April 2017: 905 912 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 909 Figure 2. Comparison detection under the V ehicular B channel [13] with SNR = 20 dB, N s = 2048 ; and N g = 256 on symmetric correlator output ( T ( d ) ). T able 1. Comple xity Comparison Method Number of Comple x Number of Comple x Multiplication Addition P ark et al. N s = 2 N s = 2 1 Cho and P ark N s = 2 N s = 2 + J 3 Proposed with q=2 N s = 2 N s = 2 + J + 2 N nor m 5 Proposed with q=3 N s = 2 N s = 2 + J + 3 N nor m 6 the time of fset caused by transmission. W e run our simulation at sampling rate 0.1 s , CP is set to 1 = 8 of the OFDM symbol, and 16-QAM is used as data modulation. The simulation is conducted on the V ehicular B multipath channel model with v ehicle speed set to 120 km/hour [13]. Note that we use N s = 2048 under the V ehicular B channel, so that the duration of CP is longer than the duration of CIR. The CFO is modelled as uniform random v ariable distrib uted in range 3 and P F A is set to 10 6 . The observ ation length for detection is set to J = N g = 2 and the observ ation length for iterati v e normalization is set to N nor m = N s = 2 . MSE of symbol timing under the V ehicular B channel are sho wn in Fig. 3. F or that channel model, the proposed method outperforms other methods sho wn in a much smaller MSE, which indicate that the stable timing position can be accomplished with less number of preamble detection. P ark’ s method has the lo west performance, this is due to autocorrelation technique yields a delayed timing estimate. The proposed method has better performance than Cho’ s method, this is because at e v ery iteration in iterati v e no r malization technique increasing the g ain of correlation magnitude on the first arri ving path and pressing the others path g ain, while in the Cho’ s method, the detection is made without iterati v e normalization technique so that the v ery small g ain of correlation magnitude on the first arri ving path causes a f ailure in detecting the first arri ving path (the correct timing point). Note that the proposed method with q = 3 is better than the proposed method with q = 2 in the e xpense of increasing comple xity . When we increase q > 3 , we find that the performance does not significantly impro v ed. Impr o ved T iming Estimation Using Iter ative Normalization T ec hnique for OFDM ... (Suyoto) Evaluation Warning : The document was created with Spire.PDF for Python.
910 ISSN: 2088-8708 Figure 3. Performance of three methods under V ehicular B channel. The comple xity of the proposed method in comparison with the pre vious methods sho wn in the T able 1. In the proposed method with q = 2 , we need N s = 2 comple x multiplication and N s = 2 2 comple x addition to calculate T ( d ) 2 . Then, it needs 2 di vision a n d 2 N nor m 2 comple x addition to calculate iterati v e normalization. After that, it needs 1 di vision and J 1 comple x addition to obtain ( d ) . In the proposed method with q = 3 , we need N s = 2 comple x multiplication and N s = 2 2 comple x addition to calculate T ( d ) 2 . Then, it needs 3 di vision and 3 N nor m 3 comple x addition to calculate iterati v e normalization. After that, it needs 1 di vision and J 1 comple x addition to obtain ( d ) . W e can write (15) as Z 2 i ( d ) = Z 2 i 1 ( d ) 2 Z ( i 1) ( d ) so, the root equation can be a v oided and is not considered in comple xity analysis. From T able 1, we can observ e that our proposed method can be realized with comparable comple xity to the pre vious methods. Thus, our propos ed estimator can pro vide an impro v ed performance with a slight additional comple xity than pre vious methods. 5. CONCLUSION W e already proposed an impro v ement of the timing estimation based on statistical change of symmetric correlator . It uses iterati v e normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. This technique increases the detection probability and a chie v es superior estimation performance in multipath en vironments. The proposed estimator achie v es better performance than pre vious published methods as sho wn in smaller MSE. Hence, the propos ed estimator appropriate to be implemented for timing synchronization in mobile OFDM systems with high delay spread en vironment. A CKNO WLEDGEMENT The author w ould lik e to thank the Editor and anon ymous re vie wers for their helpful comments and sugges- tions in impro ving the quality of this paper and the Indonesia Endo wment Fund for Education (LPDP) for their support to our w ork in this research. REFERENCES [1] P art 11: W ireless LAN Medium Access Control (MA C) and Ph ysical Layer (PHY) Specifications, Higher -Speed Ph ysical Layer Extension in the 5 GHz Band, IEEE 802.11a, 1999. IJECE V ol. 7, No. 2, April 2017: 905 912 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 911 [2] ETSI, Di gital video broadcasting (D VB): Frame structure, channel coding and modulation for a second generation digital terrestrial tele vision broadcasting system (D VB-T2), T ech. Rep. ETSI EN 302 755 V1.1.1, Sep. 2009. [3] IEEE 802.16m-09/0034r4 IEEE 802.16m System Description Document [Draft], Dec. 2010. [4] J. A vila and K. Thenmozhi, ”Multiband OFDM for Cogniti v e Ra dio - A W ay for Cyclostationary Detection and Interference Cancellation, Internat ional Journal of Electrical and Computer Engineering (IJECE), v ol. 6, no. 4, pp. 1702-1709, August 2016. [5] Hua Hou and W ei Zhang, ”A Study of Cognit i v e T echnology OFDM Syst em and Frame Structure”, Indonesian Journal of Electrical Engineering and Computer Science, v ol. 12, no. 7, pp. 5514-5521, July 2014. [6] Y . Mostofi and D. C. Cox, ”Mathematical Analysis of The Impact of T iming Synchronization Error on The Per - formance of an OFDM System, IEEE T rans. Commun., v ol. 54, no. 2, pp. 226-230, Feb . 2006. [7] W .-L. Chin and S.-G. Chen, ”A Lo w-compple xity Minimum-interference Symbol T ime Estimation for OFDM Systems, IEICE T rans. Commun., v ol. E92-B, no. 5, May 2009. [8] T . M. Schmidl and D. C. Cox, ”Rob ust Frequenc y and T iming Synchronization for OFDM, IEEE T rans. Com- mun., v ol. 45, pp. 16131621, Dec. 1997. [9] H. Minn, M. Zeng, and V . K. Bhar g a v a, On timing of fset estimation for OFDM systems, IEEE Commun. Lett., v ol. 4, pp. 242244, July 2000. [10] B. P ark and H. Cheon, C. Kang, and D. Hong, ”A No v el T iming Estimation Method for OFDM systems, IEEE Commun. Lett., v ol. 7, pp. 239 241, May 2003. [11] G. Y i, L. Gang, and G. Jianhua, ”A No v el T iming and Frequenc y Synchronization Schem e for OFDM Systems, Consumer Electronics, IEEE T ransaction on., v ol. 54, pp. 321-325, May 2008. [12] Y .-H. Cho and D.-J. P ark, T iming Estimation Based on Statistical Change of Symmetric Correlator for OFDM Systems, IEEE Commun. Lett., v ol. 17, No. 2, pp. 397- 400, Mei. 2013. [13] Guideline for e v aluation of radio transmission technologies for IM T -2000, Recommendation ITU-R M. 1225, 1997. BIOGRAPHIES OF A UTHORS Suy oto is a researcher with Research Center for Informatics, Indonesian Institute of Sciences since 2005. He obtained bachelor and master de gree in electrical engineering from Bandung Institute of T echnology , Indonesia, in 2002 and 2009 respecti v ely . His researches are in fields of digital systems, signal processing, and wireless telecommunication. His research focuses on timing syn- chronization of high speed mobile OFDM. He is af filiated with IEEE as student member . He is currently w orking to w ard Doctoral de gree at School of El ectrical Engineering and Informatics, In- stitut T eknologi Bandung (ITB), Bandung, Indonesia. Iskandar completed his B.E. and M.E. de grees all in communications engineering from Institut T eknologi Bandung (ITB), Indonesia in 1995 and 2000, respecti v ely . In March 2007, he recei v ed his Ph.D de gree from the Graduate School of Global Information and T elecommunication Studies (GITS), W aseda Uni v ersity , Japan. Since April 1997, he joined the Department of Electrical Engi- neering, ITB, as lecturer . His major research interests are in the areas of radio propag ation, channel modelling, mobile communication, stratospheric platform, and millimetre w a v e band. Impr o ved T iming Estimation Using Iter ative Normalization T ec hnique for OFDM ... (Suyoto) Evaluation Warning : The document was created with Spire.PDF for Python.
912 ISSN: 2088-8708 Sugihartono Sugihartono recei v ed the B.E. de gree in Electrical Engineering from Institut T eknologi Bandung, Indonesia in 1973. He recei v ed master and doctor de grees from the Ecole Nationale Superieure de l’Aeronautique et de l’Espace, T oulouse, France, in 1982 and 1987 respec- ti v ely . Dr . Sugihartono is currently Associate Professor at the School of Electrical Engineering and Informatics, Institut T eknologi Bandung, Indonesia. His research interest co v ers digital communi- cation system and communication signal processing. Adit K ur niawan recei v ed B. Eng. in Electrical Engineering from Bandung Institute of T echnology , Indonesia, in 1986. He then recei v ed M. Eng. and Ph.D in T elecommuni cation Engineering from the RMIT Uni v ersity and the Uni v ersity of South Australia, respecti v ely in 1996 and 2003. He is currently Professor at School of Electrical Engineering and Informatics, Bandung Institute of T echnology , Indonesia. His research interests co v er the area of Antenna and W a v e Propag ation, and W ireless Communications. IJECE V ol. 7, No. 2, April 2017: 905 912 Evaluation Warning : The document was created with Spire.PDF for Python.