Phase Noise Jitter Synchronization for Coherent Optical OFDM via Pilot-Data-Aided and Wiener Filter

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1 Computer and Information Science; Vol. 7, No. 2; 2014 ISSN E-ISSN Publihed by Canadian Center of Science and Education Phae Noie Jitter Synchronization for Coherent Optical OFDM via Pilot-Data-Aided and Wiener Filter Jean emga 1, Liu Deming 1, Mahamadou Hamidine 2, Zhang Minming 1 & Carine H. Maiawe 3 1 National Engineering Laboratory for Next Generation Internet Acce Sytem, School of Optical and Electronic Information Engineering, Huazhong Univerity of Science and echnology, Wuhan, China 2 Wuhan National Laboratory of Optoelectronic, School of Optical and Electronic Information Engineering, Huazhong Univerity of Science and echnology, Honghan,Wuhuan, Hubei, China 3 Department of Computer Science and elecommunication, Higher intitute of Sahel, Univerity of Maroua, Cameroon Correpondence: Jean emga, National Engineering Laboratory for Next Generation Internet Acce Sytem, School of Optical and Electronic Information Engineering, Huazhong Univerity of Science and echnology, Wuhan , China. el: jeantemga@gmail.com Received: February 15, 2014 Accepted: March 25, 2014 Online Publihed: April 22, 2014 doi: /ci.v7n2p56 URL: Abtract We invetigate a carrier phae jitter ynchronization technique for quare M-ary quadrature amplitude modulation (M-QAM) coherent optical orthogonal frequency diviion multiplexing (CO-OFDM) ignal employing a unique pilot ytem deign, Feed forward maximum likelihood phae etimator a well a Wiener filter-type Minimum Mean quare error (MMSE) interpolator. he wiener filter relie upon Kolmogorov type to interpolate the etimated phae noie with M tap. A 20 Gb/ CO-OFDM via 4-QAM, 16-QAM, 64-QAM then 256-QAM modulation i applied a imulation model in Optiytem. Sytem efficiency i evaluated throughout phae root mean quare error (RMSE) calculated in degree. A comparative invetigation of four different modulation technique found that 4-QAM perform with good RMSE veru the ret of quare M-QAM. A free-noie receiver, a pilot aided feed forward maximum likelihood (PA-FF-ML) receiver and a PA-FF-ML with MMSE (PA-FF-ML-MMSE) are compared. PA-FF-ML-MMSE exhibited uperior performance rather than receiver uing jut PA-FF-ML. Keyword: coherent optical OFDM, local ocillator laer, pilot data aided, MMSE, M-QAM 1. Introduction o meet the riing interet in the capacity and data-rate requirement in optical communication ytem, CO-OFDM ytem have captivated a vat involvement in recent year (Shieh, 2008). hi i certainly imply becaue it offer the following feature; high pectral efficiency in electrical in addition to optical domain, diperion inenitivity, a well a computation efficiency (Shieh & Athaudage, 2006). In contrat, the major iue of CO-OFDM i the fact that the phae noie of the local ocillator and ampling frequency need to be compenated for, ince thee problem caue it to be vulnerable to ynchronization error compared to the ingle-carrier method (Pollet, Van Bladel, & Moeneclaey, 1995; Shieh & Athaudage, 2006). In previou reearch (Minming, Deming, & He, 2012), it wa indicated that frequency clock error and local ocillator laer phae noie are the caue of phae jitter in CO-OFDM ytem. Conequently, detail information of phae jitter ynchronization in CO-OFDM ignal deerve careful attention. In conventional CO-OFDM ytem, there are three tep of CO-OFDM ynchronization (Shieh & Djordjevic, 2009): timing ynchronization, frequency ynchronization, and ubcarrier recovery. he firt couple of tep are uually carried out in the time domain, whilt the lat tep perform in the frequency domain. Schmidl and Cox (Schmidl & Cox, 1997) made ue of correlation property of periodical training ymbol for timing and frequency etimation. In thi particular approach, timing metric carrie a plateau, reulting in a large variance in ymbol timing etimation. In the ame ene, Minn propoed a imilar method with a harper timing metric to reduce the uncertainly of timing etimation (Minn, Bhargava, & Letaief, 2003), but the etimation variance remain large in the diperive 56

2 Computer and Information Science Vol. 7, No. 2; 2014 channel. An impule-like hape at the correct ymbol timing point to correct Minn method wa propoed by Park (Park, Cheon, Kang, & Hong, 2003). hi dicloed ambiguity introduce by ide lobe of timing metric. o ynchronize frequency offet, Morelli ued a training ymbol to cover the maximum etimation range (Morelli & Mengali, 1999). Yet, the training ymbol neceitated an exceptional deign, implementing multiple identical ection to provide an adequate etimation range. he challenge of ubcarrier recovery include channel etimation and phae etimation. William Shied propoed a method uing pilot-aided (PA) and maximum-likelihood (ML) deciion feedback (PA ML-DF) (Shieh, ucker, Chen, Yi, & Pendock, 2007). hi proce economize bandwidth due to the fact that very few ubcarrier are ued in the form of pilot-aided for phae compenation. It demontrate a reliable performance with a light ize of CD. However, ince the carrier frequency raie, the involvement of the CD i ignificant and the laer ocillator phae noie tart to become much higher. hi degrade the efficiency of carrier frequency recovery and reult in exceive phae jitter a well a cycle lip impact in the receiver, thu requiring new and fater tracking cheme. Local Ocillator (LO) laer phae mialigned i frequently etimated by cyclic prefix or preamble. hi need either a long cyclic prefix or hort preamble pacing, but it coniderably enhance the complexity of the tranmitter ince extra computation are required to be performed to get the LO offet etimate. Moreover, averaging of the etimate i required to improve the reliability, which diminihe the peed with which LO change could be tracked. hi paper propoe for the firt time, a new phae jitter ynchronization baed on a novel pilot inertion approach, ML etimator and MMSE interpolator. he phae jitter ynchronization a well a the phae RMSE performance of the propoed method i evaluated on a CO-OFDM ytem at 20 Gb/ by numerical imulation. Simulation outcome verify the effectivene of the propoed ynchronization technique and how better compenation performance. hi paper i organized a follow. Section II decribe the ytem being conidered. In Section III, the propoed ynchronization method i preented. Section IV provide the imulation reult, performance evaluation, and dicuion. Finally, our concluion are given in Section V. 2. Simulation Sytem Model In thi reearch, we propoed a unique OFDM frame tructure uing pilot ignal for phae noie ynchronization. Pilot are dipoed diagonally a preented in the Figure 1. heir poition are decribed by the following formula, p p ki, mn ki, m being an integer and k 1; N, i 1; N Xki,, ik 2m1, XkN, b k1, k 2 m, i Nb k1, b. N i the OFDM ymbol number in one OFDM frame and N the Number of ubcarrier in one OFDM ymbol. b (1) frequency preamble th k th i ubcarrier N c ubcarrier time Figure 1. Data tructure of CO-OFDM frame 57

3 Computer and Information Science Vol. 7, No. 2; 2014 A conceptual diagram of our CO-OFDM imulation ytem i preented in Figure 2. A decribed in previou reearch (Minming et al., 2012), the received waveform in the frequency domain in the preence of ocillator laer phae noie i given by the following equation, R () k H () k X () k I () k N (2) m 0 m m m m Where N 1 j2πln 1 e j[ LD ( t) LD ] e 0 (3) N n0 N1 N1 m m m km k0, km n0 I H ( k) X ( k) e j2π ( km) n N (4) 0 i the optical phae noie at the tranmitter and the receiver including optical and radio frequency (RF) local ocillator phae noie. X ( ) m k i the tranmitted baeband OFDM ignal. H ( ) m k i the impule repone function of the fiber chromatic diperion (CD). N m i the noie that come from the amplified pontaneou emiion (ASE) noie of the optical amplifier (OA) in the optical fiber link. We do not conider nonlinearity and polarization mode diperion effect in thi paper. Conidering the aumption of free inter-ymbol interference (ISI) and perfect fat-fourier-tranform (FF) window and frequency ynchronization, Equation (2) can be written a follow, R ( k) H ( k) X ( k) N (5) m 0 m m m A hown in Figure 2, local ocillator phae noie ynchronization happen at the receiver uing Matlab component. Re LPF SMF Im LPF Laer1 LPF LPF Laer2 Figure 2. Simulation diagram of complete CO-OFDM with phae jitter noie ynchronization S/P, erial-to-parallel; DAC, digital-to-analogue converter; LPF, low-pa filter; I/Q, inphae/quadrature; BPF, bandpa filter; OBPF, optical bandpa filter 58

4 Computer and Information Science Vol. 7, No. 2; Propoed Synchronization Scheme he propoed phae noie jitter ynchronization ued in thi paper i illutrated in Figure 3. he propoed algorithm target are optical coherent communication ytem operating with a high level of tranmitter/ receiver local laer. he propoed ynchronization algorithm make ue of regularly inerted pilot ymbol which provide good carrier frequency and phae noie etimate with low jitter and no cycle lip. Square M-QAM contellation are ued becaue they are eaier to generate and are optimally immune againt additive white Gauian noie (AWGN) (Pfau, Hoffmann, & Noé, 2009). he ynchronization i achieved in four tep: pilot extraction, feed forward maximum likelihood (FF-ML) and linear interpolation, Wiener interpolation uing the minimum mean quare error (MMSE). he proce preent carrier phae jitter ynchronization baed upon pilot data aided carrier of a received optical OFDM ignal Rn bearing ignal field conited of N pilot of the pilot et, N ymbol of the ymbol et S. N i the c number of data ubcarrier per ymbol. n, are repectively the ubcarrier index and ymbol index. he particularity i a couple of interpolation level wherein the firt i founded on Wiener filter applying the Minimum Mean Square Error (MMSE) and the following accomplihe the linear interpolation. Figure 3 i an illutration of our ynchronization technique aociated with the following algorithm: - Pilot ignal extraction; - Calculation of an unwrapped time phae etimate (1 L) by Feed Forward Maximum Likelihood algorithm over the group of pilot ubcarrier ; - -Interpolation of mentioned unwrapped time etimate for conecutive ignal ymbol 1,2,..., with a wiener interpolator owning tap to achieve interpolated phae etimate via Minimum Mean Square Error (MMSE); - -Supply linear interpolation between mentioned interpolated phae etimate to achieve phae correction etimate (1 L) over the data ubcarrier; - -Calculation from mentioned phae correction etimate (1 L) a phae correction j e to apply to mentioned OFDM ignal R n. ht () x() t. R() t 1 R( n) -jθ e f Figure 3. Carrier phae jitter ynchronization technique tructure in coherent optical OFDM receiver x, tranceiver; LO, local ocillator; ADC, analog digital converter; FF, fat fourier tranform; FF-ML, feed forward maximum likelihood Rn to achieve a phae corrected input ignal for the hi correction i going to be applied to the input ignal data ymbol ignal. he pilot ymbol ignal do not ever neceitate being phae corrected, ince they are eliminated at the input of the ymbol de-mapper. he four tep of ynchronization, pilot extraction, FF-ML, Wiener interpolation (MMSE) a well a linear interpolation are outlined in the next paragraph. 3.1 Pilot Extraction Pilot are extracted after FF. hey do not need being phae corrected, ince they are eliminated at the output of the FF. iming recovery hould preferably be ideally fixed and inter ymbol interference i ignored. Phyical layer frame alignment i uppoed to be known to the receiver uch that the pilot ymbol could be extracted in their appropriate poition. 59

5 Computer and Information Science Vol. 7, No. 2; Unwrapped Phae Etimation over Feed Forward Maximum Likelihood (FF-ML) o etimate the phae noie jitter, we reolved to employ Maximum Likelihood (ML) etimator becaue the tranmit pilot ymbol i known. In other hand, a the et of pilot P i hort, from a few data to a few ymbol, a Feed Forward (FF) method i recommended to improve the required etimation proce. he maximum likelihood of phae noie jitter i provided by the following algebraic operation: N p ( p) ( p) ( p) arg C ( k) S ( k) (6) k0 ( ) 1 p C r( t i ) ( ) 0 S k dt ( p deignate the conjugate of C ) ( k ) which deignate the pilot carrier ymbol that are overhead (they do not carry any information content). ( p Once a ignal ample S ) () k correponding to a pilot ignal reache the receiver, it retrieved by the receiver and then ample by ample the above formula i computed. In event the pilot ymbol are mall a well a the phae proce quite low, the time variation property of the carrier phae i motly ignored. Under thi hypothei and with relatively high optical ignal-to-noie ratio, it might be demontrated that the ML etimated phae noie could be written a, ( p) N I (7) deignate the actual phae value. With N I being the zero-mean Gauian noie contribution to phae etimate, with variance, N ( p ) I (8) 2 LpE / N0 which i independent from quare M-QAM modulation contellation. 3.3 Phae Noie Interpolation by Wiener Filter Uing MMSE and Linear Interpolation he further tep i the thoughtfulne of an interpolation technique where the interpolant in a given lot are computed with a higher order interpolation function. But the choice of the interpolation technique depend on the econd effect of linear impairment uch a frequency clock error which would add a linear time varying term into the phae noie which i eaily interpolated by Wiener filter uing MMSE. hat i why in thi paper, we invetigate on MMSE to derive an optimum interpolator. hi kind of interpolation ha already been ued in wirele communication for fading channel (Li, 2000) to deal with fat varying fading proce and omehow in optical communication (Ip & Kahn, 2007). In that work a oft-deciion phae-etimation tage followed by hard-deciion etimation of the carrier phae and the tranmitted ymbol are ued. he author modeled phae noie a a Wiener proce and expreed that the optimal hard-deciion phae etimator i a linear filter. he effect of a nonzero frequency offet between tranmitter and LO laer were invetigated and found to be harmful to ytem performance. A numerical ocillator ha been ued to track the low component of laer frequency drift. However the numerical ocillator component i another jitter ource (Demir, 2006). In our tak we improved the approach of phae noie interpolation employing pilot tructured a in Figure 1 then conducted over with the FF-ML phae etimation algorithm. Wiener-Hopf equation i ued to pecify the coefficient for optimum linear etimation wherein implifying aumption are baed on Wiener-Kolmogorov model for interpolation with M tap. Since the pilot pacing i non-equiditant (ee Figure 1), for convenient notation, we preent here the vector p which hold in all time indice k K in addition to a vector that containing all time indice. p k K d : p [ p1,..., p k ], d [ d p 1,..., d k ] d ( p) We conidered the FF ML of etimated phae noie. We derived a et of filter with coefficient Ck, opt ( m ) (one filter for each ymbol in time in one frame) uch that the phae interpolant over the frame i: 60

6 Computer and Information Science Vol. 7, No. 2; 2014 M ( ll k ) C ( m) [( l m). L ] (9) k, opt mm hee interpolant are optimum in the ene that they minimize the mean quare error (MSE). M k. opt mm ( k ) E{ ( l. L k ) C ( m) [( lm). L] } (10) Uing the orthogonality principle (Cioffi, Dudevoir, Vedat, & Forney Jr, 1995), the optimum coefficient are conidered to be the olution to the et of equation: for p 0, 1,..., M and k 0,1..., L 1. Introducing the autocorrelation of (. ll ) * E{ ( ll. k ) ( ll. k ) ( l p). L} 0 (11) R ( pl) E{ [( l p). L] [ l. L]} (12) And the autocorrelation of (. ll ) and (. ll ). Yielding to Wiener-Holf equation M R ( pl) E{ [( l p). L] [ l. L]} (13) Ck. opt( m) R ( ml pl) R ( k pl) (14) mm hee equation can be written in matrix form a, Where And R p0, 1,..., M, k 0,1,..., L 1 kopt,, 0,1,..., 1 k R C r k L (15) r [ R ( kml ), R ( k( M 1) L ),..., R ( k),..., R ( k ML )] (16) k C [ C ( M), C ( M 1),..., C (0),..., C ( M)] (17) kopt, kopt, kopt, kopt, kopt, R ( ML ML) R (( M 1) L ML)... R ( ML ML ) R ( ML ( M 1) L) R (( M 1) L ( M 1) L)... R ( ML ( M 1) L) R ( ML ML) R (( M 1) L ML)... R ( ML ML) R (0) R ( L )... R (2 ML ) R ( L) R (0)... R (2ML 1) = R (2 ML) R (2ML 1)... R (0) Earlier, it ha been howed that the etimated value of phae noie may be written a, (. ll) (. ll) Nl(. ll). Uing thi equation, autocorrelation and cro correlation function can be put in the following form, So the previou matrix formulation can be written a, 1 R ( pl ) R ( pl) ( p) 2 LE p / N0 R ( pl ) R ( pl ) 2 (18) (19) 61

7 Computer and Information Science Vol. 7, No. 2; R ICkopt, r, k 0,1,..., L 1 k 2 / LE p N0 hi matrix can eaily be olved by a matrix inverion for every k 0,1,2,..., L 1. 1 Ckopt, R r, k 0,1,..., L 1 k 2 / LE p N0 hi equation mean that the optimum coefficient (M tap) of Wiener filter rely on the autocorrelation function of the phae noie jitter and on the ignal-to-noie ratio. We can eaily derive now the expreion of the minimum value of mean quare error a a reult of the interpolation of the Wiener filter with previou coefficient C k, opt. Accomplihing thi we rewrite the MSE equation matrix form, compute the expectation and then exploit the orthogonality principle to get, he average of the mean quare error ( k) (in 1 ( k) R (0) r C R (0) r R r k 0,1,..., L 1 1 k kopt, k k 2 LE p / N0 2 dg 1 unit) over the OFDM frame can be computed by: L 1 1 ( k) (23) L k 0 he root mean quare (RMSE) of phae error i given by, 4. Simulation Reult and Dicuion Simulation parameter are ummarized in able 1. (20) (21) (22) RMSE (degree) (24) able 1. CO-OFDM imulation ytem parameter Parameter Value Bit rate 20Gb/ ranmiion ditance 1000km Average pan lo 16dB Average diperion D 18p/nm/km PDM coefficient 0.07p/km OFDM ymbol number 1000 Subcarrier per ymbol 128 FF point 1024 Sampling rate 20GS/ (ampling period 1/=0.05n) Symbol period 25.8n Guard time 3.5n Filter tap number M 20 Figure 4 illutrate the OSNR veru phae jitter RMSE for different quare QAM modulation cheme. We oberve the uperior performance of 4-QAM (or QPSK) compared to other modulation cheme. 62

8 Computer and Information Science Vol. 7, No. 2; OSNR 4-QAM OSNR 16-QAM OSNR 64-QAM OSNR 256-QAM 5 OSNR (db) Phae Jitter RMSE Figure 4. Influence of phae noie jitter on OSNR of quare M-QAM able 2 how the M-QAM phae jitter performance. We noticed that the RMSE attain a maximum phae jitter RMS (degree) of 5.75 degree for 256-QAM then decreae to 3 degree for 4-QAM. hi reveal the better performance of 4-QAM compared to three other m-qam cheme. able 2. Phae jitter RMSE requirement for different m-qam to limit the performance degradation to 1-dB OSNR Modulation contellation Phae jitter RMS (degree) 4-QAM (QPSK) 3 16-QAM QAM QAM 5.75 Figure 5 diplay the RMSE phae jitter of the PA-FF-ML algorithm for different OSNR value (12 db, 7 db and 2 db). In other word, thi figure i a comparion of different OSNR when PA-FF-ML algorithm i ued. A oberved the performance i undoubtedly far better for higher OSNR. It moreover noted that the performance i relatively good in the cae that the number of ymbol increae above RMSE(degree) 14 OSNR(12dB) 13 OSNR(7dB) 12 OSNR(2dB) OFDM ymbol length Figure 5. Root Mean Square Error (RMSE) a function of OFDM ymbol length for different value of OSNR for PA FF ML he following Figure 6 diplay the imulation that had been run to acce the efficiency of PA FF ML employing Wiener filter. In comparion with Figure 5, one could check that the efficiency improvement are really big for the entire et of analyzed ymbol length. A an illutration, the RMSE of OSNR (12 db) dotted line in Figure 6 i uperior to the one in Figure 5 with very nearly 1 degree. 63

9 Computer and Information Science Vol. 7, No. 2; 2014 RMSE(degree) OFDM ymbol length OSNR(12dB) OSNR (7dB) OSNR (2dB) Figure 6. Root Mean Square Error (RMSE) a function of OFDM ymbol length for different value of OSNR for PA FF ML uing Wiener filter Figure 7 diplay the RMSE phae jitter of the ynchronization algorithm for different value of OSNR with pilot ymbol length. A oberved the performance i more effective for OSNR = 12 db and then relatively invariable for every OSNR when the pilot ymbol number get to 20. RMSE(degree) Figure 7. RMSE veru pilot ymbol number 7.0 OSRN(12dB) 6.5 OSNR(7dB) 6.0 OSNR(2dB) Pilot ymbol length L p for different OSNR value (2 db, 7 db, and 12 db) 5 Phae Jitter RMSE RMSE Wiener filter tap Figure 8. RMSE (degree) veru M filter tap 64

10 Computer and Information Science Vol. 7, No. 2; 2014 hi figure diplay the dependency of the phae RMSE to the number of tap of the Wiener filter (2M+1). A certainly a we have oberved, the RMSE decreae while M increae up to a place in which the phae noie i not more correlated at all o that there i not any poitive apect of the interpolation proce. In thi cae, the RMSE function tend to be a flat line when the tap number attain 10. For thi reaon, the RMSE function could poibly be a flat line once the tap reache a certain number. In Figure 8, thi number could be 10 tap. Figure 9 and 10 illutrate the RMSE of the phae jitter performance of the three ditinct receiver cheme (ideal receiver, PA-FF-ML and PA-FF-ML with MMSE) repectively for OSNR=7dB and OSNR= 2dB. A oberved in both cae, the performance begin to be moderately beneficial at very long ymbol length (higher than 1000ymbol). hi indicate a relative enitivity to ampling frequency error. Ideal receiver ignifie the receiver i noie-free. It i apparent that it achieve much better. he principal purpoe would be to do a comparion of PA-FF-ML and PA-FF-ML-MMSE. Figure 9 and 10 revealed outtanding efficiency of PA-FF-ML-MMSE in comparion with PA-FF-ML. One oberved an effective performance of PA-FF-ML-MMSE in Figure 9. hi i certainly becaue of the reaon that OSNR i larger (7 db) in Figure Ideal receiver (IR) PA-FF-ML PA-FF-ML with MMSE RMSE (degree) OFDM ymbol length Figure 9. Comparion of free noie receiver (IR), pilot data aided feed forward maximum likelihood (PA FFML) and pilot data aided FFML employing wiener interpolator (MMSE) at OSNR = 7 db RMSE (degree) OFDM ymbol length Ideal receiver (IR) PA-FF-ML PA-FF-ML with MMSE Figure 10. Comparion of free noie receiver (IR), pilot data aided feed forward maximum likelihood (PA FFML) and pilot data aided FFML with wiener interpolator (MMSE) at OSNR = 2 db 5. Concluion hi paper propoed a unique carrier phae jitter ynchronization technique baed upon pilot data-aided feed forward maximum likelihood etimation (PA-FF-ML) and Wiener interpolator containing M tap to acquire 65

11 Computer and Information Science Vol. 7, No. 2; 2014 interpolated phae etimate having a minimum mean quare error interpolator (MMSE). Computation confirmed that the M tap coefficient and RMSE are a function of the autocorrelation of the phae a well a of the ignal-to-noie ratio. he imulation reult confirmed that the ynchronization approach offer better accurate phae jitter etimation. A comparion between four quare QAM modulation, wa produced, after which it had been verified that for 1dB OSNR, 4-QAM achieve far better (3 degree) in comparion with 16-QAM (4.5 degree), 64-QAM (5.5 degree) and then 256-QAM (5.75 degree). An evaluation of OSNR of PA-FF-ML method and PA-FF-ML which make ue of MMSE method, ha proven the outtanding reult of the lat one. Somewhat far, the dependency of RMSE with pilot ymbol number and tap number ha confirmed that the ytem performance might be good for no le than 20 pilot ymbol number and 10 tap number. By the end a tudy of the three variou receiver cheme i preented for 7dB and 2dB OSNR. Once more PA-FF-ML uing MMSE ha proven an appropriate efficiency. Acknowledgement hi work wa upported by the National Natural Science Foundation of China. he author alo acknowledge Dr. Deng Lei at National Engineering Laboratory for Next Generation Internet Acce Sytem, School of Optical and Electronic Information Engineering, Huazhong Univerity of Science and echnology, for the numerou uggetion and guidance for the completion of thi work. Reference Cioffi, J. M., Dudevoir, G. P., Vedat, E. M., & Forney Jr, G. D. (1995). MMSE deciion-feedback equalizer and coding. I. Equalization reult. Communication, IEEE ranaction on, 43(10), Demir, A. (2006). Computing iming Jitter From Phae Noie Spectra for Ocillator and Phae-Locked Loop With White and 1/f noie. Circuit and Sytem I: Regular Paper, IEEE ranaction on, 53(9), Ip, E., & Kahn, J. M. (2007). Feedforward carrier recovery for coherent optical communication. Journal of Lightwave echnology, 25(9), Li, Y. (2000). Pilot-ymbol-aided channel etimation for OFDM in wirele ytem. Vehicular echnology, IEEE ranaction on, 49(4), Minming, Z., Deming, L., & He, W. (2012). Performance Analyi of Coherent Optical OFDM with Weiner Phae Noie jitter. Paper preented at the Information Optoelectronic, Nanofabrication and eting. Minn, H., Bhargava, V. K., & Letaief, K. B. (2003). A robut timing and frequency ynchronization for OFDM ytem. Wirele Communication, IEEE ranaction on, 2(4), Morelli, M., & Mengali, U. (1999). An improved frequency offet etimator for OFDM application. Paper preented at the Communication heory Mini-Conference, Park, B., Cheon, H., Kang, C., & Hong, D. (2003). A novel timing etimation method for OFDM ytem. Communication Letter, IEEE, 7(5), Pfau,., Hoffmann, S., & Noé, R. (2009). Hardware-Efficient Coherent Digital Receiver Concept With Feedforward Carrier Recovery for $ M $-QAM Contellation. Journal of Lightwave echnology, 27(8), Pollet,., Van Bladel, M., & Moeneclaey, M. (1995). BER enitivity of OFDM ytem to carrier frequency offet and Wiener phae noie. Communication, IEEE ranaction on, 43(234), Schmidl,. M., & Cox, D. C. (1997). Robut frequency and timing ynchronization for OFDM. Communication, IEEE ranaction on, 45(12), Shieh, W. (2008). Maximum-likelihood phae and channel etimation for coherent optical OFDM. Photonic echnology Letter, IEEE, 20(8), Shieh, W., & Athaudage, C. (2006). Coherent optical orthogonal frequency diviion multiplexing. Electronic Letter, 42(10), Shieh, W., & Djordjevic, I. (2009). OFDM for optical communication: Acce Online via Elevier. 66

12 Computer and Information Science Vol. 7, No. 2; 2014 Shieh, W., ucker, R. S., Chen, W., Yi, X., & Pendock, G. (2007). Optical performance monitoring in coherent optical OFDM ytem. Opt. Expre, 15(2), Copyright Copyright for thi article i retained by the author(), with firt publication right granted to the journal. hi i an open-acce article ditributed under the term and condition of the Creative Common Attribution licene ( 67