An Improved Doppler Frequency Offset Estimation Algorithm of OFDM System under High-speed Movement Environment

Transcription

1 JOURAL OF COMPUTERS, VOL. 8, O. 2, DECEMBER An Improved Doppler Frequeny Offset Estimation Algorithm of OFDM System under High-speed Movement Environment Yunlv Hong Department of Eletroni Engineering, Shanghai Jiao Tong University, Shanghai, China Di He Department of Eletroni Engineering, Shanghai Jiao Tong University, Shanghai, China Abstrat Orthogonal frequeny division multiplexing (OFDM is a multi-arrier digital modulation tehnique. It s liely to be used in next generation high-speed railway ommuniation system. When OFDM is used in the ommuniation of high-speed railway user s, Doppler frequeny shift will beome an important tehnial barrier, beause OFDM is sensitive to frequeny offset. Espeially in high-speed movement environment, Doppler frequeny shift an destroy the orthogonal harateristi between subarriers in OFDM system. In this paper, we analyze the performane of OFDM system in high-speed movement environment and propose a new Doppler spread estimation algorithm to improve the bit error rate (BER performane. Theoretial analysis and omputer simulations present the advantages of the proposed approah, espeially under high-speed railway environment. Index Terms High-speed movement environment, OFDM, Doppler frequeny shift, Frequeny offset estimation I. ITRODUCTIO OFDM [][2] is a multi-arrier digital modulation tehnique. Its basi idea is to divide a high speed data string to some low speed data strings, and all sub-arriers are orthogonal to eah other. It ensures very little interferene among the sub-arriers. OFDM is widely used in popular modern ommuniation system lie LTE, WLA, et. Beause of its advantages, OFDM is liely to be used in next generation high-speed railway ommuniation. However, OFDM has a big problem that the system is easy to be affeted by frequeny shift. Frequeny shift ours when an objet is moving, espeially in the high speed movement, for example the high-speed railway environment. This phenomenon is alled Doppler shift. When a train runs at 35 m/h, and OFDM system (lie LTE operates at 2.4 G frequeny point, the imum Doppler frequeny offset will be over 8 Hz. Beause of the apparent Doppler shift, the orthogonal harateristi between sub-arriers in OFDM system will be destroyed, and serious inter-carrier interferene (ICI [3] will be aused. Finally, there will be a substantial inrease in BER. Main ideas in literatures to solve this problem are divided into two types. One is the design of the Doppler frequeny offset estimation algorithm. In this type, the algorithm is based on the reeived information to obtain the estimated value of Doppler offset. Maximum lielihood estimation (MLE and minimum estimation (ME are often used in estimation algorithm [4-6]. But due to the fat that the auray or the omplexity of alulation is not very perfet, the algorithm sometimes still an t be well used in the OFDM systems. Another type is to onsider Doppler shift as a resoure of diversity. Through designing diversity reeivers, it an improve the system s performane. It mainly inludes Doppler frequeny diversity and joint multi-path Doppler diversity [7]. It was applied in CDMA system, but its further appliation to OFDM system has not been studied yet. In this paper, a novel Doppler frequeny offset estimation algorithm is proposed, whih uses the yli umulative frequeny offset estimator to mae the estimation more aurate. Setion II gives the hannel of OFDM system under high-speed environment and disusses the useful S&C algorithm and its disadvantages. Setion III presents the novel algorithm based on the improvement of S&C algorithm. Computer simulations are shown in Setion IV. And Setion V gives the onlusion. II. OFDM PERFORMACE I HIGH-SPEED MOVEMET EVIROMET The main idea of OFDM is to onvert high-speed input data to road low-speed data, and modulate low-speed data onto orthogonal sub-arriers. The transmitted signal s baseband expression in a symbol is j2 π ( t ts / T x( t = s( e,( ts t ts + T ( = where is the number of sub-arrier; s( is the transmitted symbol; T is the ode period. In every t = t s doi:.434/jp

2 392 JOURAL OF COMPUTERS, VOL. 8, O. 2, DECEMBER 23 or t = ts + T, x( t = s(. It is obvious that the adjaent sub-arriers of the entre frequeny interval is /T. Then the orthogonality within sub-arriers an be ensured. Its Figure. OFDM sub-arriers frequeny domain frequeny domain is shown in Figure. In the wireless environment, the frequeny offset aused by the movement of objetives is nown as Doppler shift, whih an be expressed as v v fd = osθ = f osθ (2 λ where is the speed of light; v is the moving speed of the reeiving antenna; f is signal s arrier frequeny; θ is the angle between the moving diretions of reeiving antenna and eletromagneti wave. In OFDM system, we suppose the imum arrier frequeny ould reah 2.6 G Hz. owadays, the speed of ommerial high-speed air vehile or railway an reah 35 m/h or even more. If the moving diretions of high-speed objetive and the eletromagneti waves are the same, it means that θ may be zero. At this time, the Doppler offset reahes its imum value, and the imum Doppler offset may reah 842 Hz. The high Doppler shift an destroy the orthogonal harateristi within sub-arriers in OFDM system, and it will ertainly lead to serious ICI. Finally, there will be a substantial inrease in BER, whih is alulated by biterror BER = bit transmitted (3 where bit error is the number of reeived error bits; bit transmitted is the total number of transmitted bits. Generally speaing, taling about the Doppler shift in high mobility environment, the hannel fading should be inorporated, and then the Doppler shift expends to a Doppler spetrum. In this paper, we thin the high-speed objetive mainly runs on the plains. In this environment, there should be only one strong diret trail and very little (maybe just one or two refletor trails, so that the affet of Doppler shift should be mainly aused by the diret trail. On other words, when a lot of refletor trails ours, whih means that the train run in the ity, the speed of train shouldn't be too fast. So at most time, there is only one diret trail, and this paper mainly disusses how to detet the diret trail's Doppler shift. Due to the sensitivity of OFDM systems to frequeny shift, the frequeny estimation problem mainly has three inds of solutions in previous researhes. They an be divided into the data-aided tehnique [8], the non dataaided tehnique [9] and those based on yli prefix (CP []. The data-aided algorithm is to add some training sequene into data for transmission. At the reeiver, one an omplete the frequeny orretion by estimating the frequeny offset of the speifi training sequene. This ind of method has muh faster proessing speed and better estimation performane than the non data-aided tehnique. Based on the unique property stated above, in the following study, it is supposed that the data-aided estimation algorithm is more suitable for high-speed movement environment, as the objetive runs fast and the environment hanges rapidly. To detet the diret trail's Doppler shift, Shmidl and Cox proposed an important algorithm in 997 []. It s a two-step algorithm and here we name it S&C algorithm for simpliity in the following analysis. It onstruts a speifi training sequene and it is sent on even subarriers. Its first half and seond half are the same. When the frequeny shift ours, the estimation of the frequeny offset an be realized aording to the strutural hange of the reeived training sequene. A lot of researhes have been arried out to the further improve this algorithm suh as referene [2]. But the algorithm in referene [2] is muh more ompliated and is not suitable for a system whih needs a rapid response. In a word, S&C based algorithm is still not good enough for OFDM system under high-speed railway environment. The analysis details an be obtained from [], here we just analyze the disadvantages for S&C algorithm applied in the high-speed OFDM system. In [] it does not give evidene that S&C an be applied in very high mobility environment. That is beause the high ICI aused by high speed annot be easily overome by adding SR. There is a formula in []: M( dopt SR ˆ = (4 M( dopt In (4, M is involved in the reeived power. It is obviously that SR and M are not seriously orrelative. It means that inreasing SR will also enhane the ICI, so the system performane will not be linearly improved with the inreasing of SR. Then we give the performane of OFDM system in high-speed movement environment. The BER performane omparison under different SR environment with the following simulation parameters are given as well, as shown in Table. Figure 2 shows that OFDM is not suitable for highspeed movement environment in the above model we proposed. The BER (red line of the OFDM system inreases to the level of when SR=dB, whih annot be aeptable in real appliations. This figure also

3 JOURAL OF COMPUTERS, VOL. 8, O. 2, DECEMBER TABLE. SIMULATIO PARAMETERS FOR FIGURE 2 Center frequeny Sub-arrier Pilot number per bandwidth symbol 2.6 GHz 5 KHz IFFT number Symbol length Modulation mode bits QPSK shows that S&C algorithm (blue line does not wor well in high mobility environment. Based on Figure 2, improvement of SR will still lead to very high BER without good enough frequeny Figure 2. BER performane omparison under different SR environment with moving speed 35 m/h and still state orretion algorithm. From above, it an be found that S&C algorithm still annot meet the demand under highspeed movement (frequeny offset is more than 8 Hz. In a word, we annot get a big offset estimation range and auray at the same time. That s the major ontradition of S&C algorithm under high-speed movement environment. III. CYCLIC CUMULATIVE DOPPLER FREQUECY OFFSET ESTIMATIO ALGORITHM From last setion, it is found that there is a ontradition between frequeny estimation range and auray. That s the biggest problem of S&C algorithm in the high-speed appliations. Here we try to improve the algorithm ombining with the high-speed movement sene. Generally, suppose the hange of moving objetive s veloity is ontinuous. And the adjoint frames will be sent in several ms if their sub-arriers bandwidth is within several KHz. And the veloity of the objetive will not hange rapidly without rash, beause the aeleration should not be over g. So we an get the onlusion that the variation of Doppler offset between adjaent symbols will not be over 2 Hz. And within 2 Hz, it is found that the S&C algorithm always performs well. Aording to above analysis, we design a yli umulative frequeny offset estimation algorithm to solve the problem that S&C algorithm has poor auray if the estimation range is beyond 2 Hz. If the aurate value of frequeny offset in one symbol period annot be got, in the next period, add an additional value to the old estimation value to mae it loser to the aurate frequeny point. Then the problem is onverted to a one dimensional searh problem. We suppose the aurate Doppler offset is between and upper bound offset, and we searh it from to upper bound offset. As already nown, if the objetive runs in 35 m/h, the Doppler offset should be over 8 Hz and less than 9 Hz, so we an set upper bound offset to be 9 Hz. In one dimensional algorithm, golden setion proves to be in useful and fast onvergene in eah iterations. In the following setions, we hoose the golden setion method to realize the estimation proess. The details of the estimation algorithm are given as follows: a When the training sequene A is sent to the estimator, alulate the frational frequeny offset and integrate frequeny offset with S&C algorithm. Set up a storage S, and put the first estimated offset f A to this storage S, and it will be used in the next round frequeny estimation. Set bound f min =, f =9. b When the training sequene B is sent to the estimator, use S&C algorithm to get new estimated offset fb enter around f A. Use golden setion method in area [ f min, f ]: b. If f b f A, set f min = f A. Otherwise, set f = f A b.2 Let λ = fmin +.328( f fmin (5 λ 2 = fmin +.68( f fmin b.3 Compare the performanes of offset λ with λ 2 in S&C algorithm. b.4 If λ performs better, let f B = λ. Otherwise, let f B = λ 2. b.5 If f fmin < ε, algorithm terminates, Otherwise go to step (b.2. As shown in (5, the proposed algorithm uses the golden setion method to obtain the linear onvergene. So after several rounds, we an get a good solution. Besides, as what analyzed above, the Doppler frequeny offset between adjaent symbols doesn t show signifiant hanges. So the whole system does not produe obvious osillations aused by frequeny hopping. This algorithm is espeially designed for high-speed movement environment. The struture of the proposed novel estimator is shown in Figure 3. Figure 3. Struture of the proposed novel estimator ow we disuss the performane of the novel designed algorithm. The transmitted signal an be expressed in time domain by T xt ( = Se ( π (6 = t j 2

4 394 JOURAL OF COMPUTERS, VOL. 8, O. 2, DECEMBER 23 where T=T s is the symbol period and T s is the sampling interval; S( is the signal. Assume Δ f is the frequeny offset, Δ is the phase offset. The signal at the reeiver an be expressed by j2πδ ft+δ y( t = x( t e + η( t (7 where η ( t is the additive noise. Remove the CP, and after the FFT hange, we an get s] e ( ( ΔfTs R ( = ( Sm e + η ' s] e sin( π ΔfTs ( ΔfTs = S ( e + sin( πδf T e s sin[ π ( Δ f T ] s ( ( Sm ( Δ ft s e + m s] η ' (8 To fous on the Doppler frequeny offset, simplify the problem by assuming the phase offset aused by the hannel an be orreted at the reeiver, so we have Δ =. Then the reeived signal R( should be sin( π ΔfTs ( ΔfTs R ( = S ( e + sin( πδfts sin[ π ( Δ f ] m Ts ( ( ΔfTs Sm ( e + η ' m s] (9 Aording to the design, the proposed novel algorithm an improve the estimation of ĝ. In this formula fˆ [ ˆ ( πt] (2 gˆ T sin( π ΔfTs is sin( φ sin( πδft sin( φ/t Δ = +. The oeffiient of the amplitude, so the S&C algorithm and the s proposed approah have the same performanes. j ( fts The same as e π Δ, by replaing Δ f, it is nearly to be e j. And the two algorithms also have the same performanes. The seond item in the right side of formula (9, say ( ( Δf s T s m sin[ π ( Δ f T ] Sm ( e s], will lead to ICI. So, we an get that system performane will not be linearly improved with the inrease of SR. That means this variable will still be the problem by replaing Δ f. The SR deterioration aused by the above formula is D nf = log + log 2 2 E b sin( πδfts sin( πδfts sin( πδfts sin( πδfts ( Aording to (9, it should be 2 2 Eb sin sin Dnf " = log + log 2gˆπ 2gˆ + π sin( + sin( ( Beause the proposed novel algorithm uses golden setion method, so after 5 rounds, Δf of the integer 4 frequeny offset should derease by.68 85% at least. Considering the osillation and deviation of alulating integer offset, there is still muh possibility to derease Δ f to a small range. At this time, the SR deterioration should be E sin 2 sin 2 nf ' log{ b D = + [ ]} log[ ] (2 Compare (2 with (, it an be found that D nf ' in (2 is muh better than D nf " in (. So the new algorithm an improve the estimation of integer offset, and derease the SR deterioration to improve the system performane. Overall, the main idea of the proposed novel algorithm is to use several symbols to improve the auray gradually. In ase the estimation value is not aurate immediately, the proposed algorithm an still ensure that the deviation will gradually redue. IV. COMPUTER SIMULATIOS The omputer simulation environment parameters are as follows: OFDM arrier frequeny is 2.6 G Hz. The sub-arrier bandwidth is 5 Hz. The length of eah symbol is 9 bits. The yli prefix length is 32. The pilot number in per symbol is. The FFT length is 256. The oding mode is interleaved oding and Viterbi oding. The modulation mode is QPSK. The hannel is seleted as AWG flat hannel. The highest movement speed is set to 35 m/h, equivalent to 842 Hz Doppler frequeny offset. The speed rises from 6 m/h to 35 m/h gradually. When the speed reahes 35 m/h, eep the estimation offset unhanged, and set the SR vary from db to +db to draw the BER urve. Figure 4. BER omparison of the S&C and proposed algorithms From the omparison in Figure 4, the performane of the proposed Cyli Cumulative algorithm (red line is still worse than urve of m/h (green line, but it is very lose to that at SR=. And omparing the red urve and blue urve, our proposed algorithm wors muh better in high-speed movement environment than the onventional S&C algorithm. V. COCLUSIO Through the theoretial analysis and omputer simulations, it an be found the existing traditional Doppler frequeny offset estimation algorithm often doesn t wor well in high-speed movement environment.

5 JOURAL OF COMPUTERS, VOL. 8, O. 2, DECEMBER In this paper, a novel yli umulative frequeny offset estimator is proposed to improve the traditional OFDM system. It not only improves the performane of the traditional S&C algorithm, but also is muh loser to the ideal state. ACKOWLEDGMET This researh wor is supported by the ational atural Siene Foundation of China (SFC under Grant o , and the Important ational Siene and Tehnology Speifi Projet of China under Grant o. 23ZX328-5, and the ational High Tehnology Researh and Development Program of China under Grant o. 23AA362, and the ZTE Corporation and University Joint Researh Projet under Grant o. One58, and the SMC-"Chen-Xing" Young Sholar Foundation of Shanghai Jiao Tong University. REFERECES [] E. ahlman. 3G evolution: HSPA and LTE for mobile broadband. Elsevier Ltd., 28. [2] S. sesia, I. Toufi, LTE - The UMTS Long Term Evolution: From Theory to Pratie, WILEY, 29. [3] R.W. Chang, R.A. Gibby, A Theoretial Study of Performane of an Orthogonal Multiplexing Data Transmission Sheme, IEEE Trans. Commu. Tehnol,vol.5, no.6, pp , 968 [4] F. Daffara, A. Chouly, Maximum lielihood frequeny detetors for orthogonal multiarrier systems, In Pro. IEEE Int.Conf. Commun, pp , 993. [5] J.van de Bee, M. Sandell, P. Borjesson. ML Estimation of time and frequeny offset in OFDM system. IEEE Trans. Signal Proessing, vol.45, no., pp.8-85, 997. [6] W.P. Hong, A Frequeny Offset Estimation Arhiteture of OFDM System in Multipath Doppler Spread Channel, Conferene Reord of the Thirty-Third Asilomar Conferene on Signals Systems, and Computers, pp.7-75, 999. [7] A.M. Sayeed, B. Aazhang, Joint multipath-doppler diversity in mobile wireless ommuniations. IEEE Trans. Commun., vol.47, no., pp.23-32, 999. [8] M.K. Simon, D. Divsalar, Doppler-orreted differential detetion of MPSK, IEEE Trans. Commun., vol.37, no.2, pp.99-9, 989. [9] U. Tureli, H. Liu, M. Zoltowsi, OFDM blind arrier offset estimation:esprit, IEEE Trans. Commun., vol.48, no.9, pp , 2. [] J.van de Bee, M. Sandell, P.O. Borjesson. ML Estimation of Time and Frequeny Offset in OFDM System, IEEE Trans. Commun., vol.45, no.7, pp.8-85, 997. [] T.M. Shmidl, D.C. Cox. Robust frequeny and timing synhronization for OFDM. IEEE Trans. Commun., vol.45, no.2, pp ,997. [2] P. Byungjoon, C. Hyunsoo, K. Changeon and H. Daes. A novel timing estimation method for OFDM systems, IEEE Globeom, vol., pp.7-2, 22. Yunlv Hong reeived the B.E. degree in information engineering from Shanghai Jiao Tong University, Shanghai, China, in 2. And he is pursuing his M.E. degree also in information engineering from Shanghai Jiao Tong University, Shanghai, China. His researh interests are in the areas of wireless ommuniations espeially LTE. Di He reeived the B.E. degree of information engineering from Huazhong University of Siene and Tehnology, Wuhan, China, in 996; the M.E. degree in ommuniations and information systems from anjing University of Posts and Teleommuniations, anjing, China, in 999; the Ph.D. degree in iruits and systems from Shanghai Jiao Tong University, Shanghai, China, in 22. From 22 to 24, he was a Postdotoral Fellow in the Department of Eletrial and Computer Engineering, University of Calgary, Calgary, AB, Canada. He is urrently an assoiate professor in the Department of Eletroni Engineering, Shanghai Jiao Tong University, Shanghai, China. His researh interests inlude wireless ommuniations espeially ognitive radio and LTE, nonlinear dynamis and its appliations in wireless ommuniations, and networ intrusion detetion. Meanwhile, Dr. He is a member of IEEE.