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1 This document is downloaded from DR-NTU, Nanyang Technological University Library, Singaore. Title Author(s) Citation Relative hase noise estimation and mitigation in Raman amlified coherent otical communication system Cheng, Jingchi; Tang, Ming; Fu, Songnian; Shum, Perry Ping; Liu, Deming; Xiang, Meng; Feng, Zhenhua; Yu, Dawei Cheng, J., Tang, M., Fu, S., Shum, P. P., Liu, D., Xiang, M., et al. (4). Relative hase noise estimation and mitigation in Raman amlified coherent otical communication system. Otics Exress, (), Date 4 URL htt://hdl.handle.net//899 Rights 4 Otical Society of America. This aer was ublished in Otics Exress and is made available as an electronic rerint (rerint) with ermission of Otical Society of America. The aer can be found at the following official DOI: [htt://dx.doi.org/.364/oe..57]. One rint or electronic coy may be made for ersonal use only. Systematic or multile reroduction, distribution to multile locations via electronic or other means, dulication of any material in this aer for a fee or for commercial uroses, or modification of the content of the aer is rohibited and is subject to enalties under law.

2 Relative hase noise estimation and mitigation in Raman amlified coherent otical communication system Jingchi Cheng,, Ming Tang,,,* Songnian Fu,, Perry Ping Shum, 3 Deming Liu,, Meng Xiang,, Zhenhua Feng,, and Dawei Yu, Wuhan National Laboratory for Otoelectronics, Huazhong University of Science and Technology, Wuhan, 4374, China National Engineering Laboratory for Next Generation Internet Access System, School of Otics and Electronic Information, Huazhong University of Science and Technology, Wuhan, 4374, China 3 Photonics Centre of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University, Singaore , Singaore * tangming@mail.hust.edu.cn Abstract: The interlay between the stochastic intensity fluctuation of Raman um laser and cross-hase modulation (XPM) effect in transmission otical fiber leads to additional hase noise, namely, relative hase noise (RPN) of signal in multi-level modulated coherent otical communication system. Both theoretical analysis and quantitative simulation have been erformed to investigate the characteristics and imact of RPN. Being low-ass in nature, RPN is different from XPM induced hase noise in PSK/OOK hybrid system, and has not been considered yet. The noise ower of RPN can accumulate incoherently along transmission links. With a roer signal model, we study the imact of RPN to the coherent otical communication system through Monte Carlo simulation. RPN will cause more cycle slis in Viterbi-and-Viterbi (V-V) hase estimation (PE), and the quantitative analysis of cycle sli robability is carried out. When using sliding window V-V without any otimization, the Q factor enalty of RPN on DQPSK signal can be as large as around 5 db in strong RPN condition. However, it can be reduced by over 3 db when using an otimal block size or otimal averaging weights. 4 Otical Society of America OCIS codes: (6.66) Coherent communications; (3.448) Otical amlifiers. References and links. G. Li, Recent advances in coherent otical communication, Adv. Ot. Photonics (), (9).. D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, Coherent detection of otical quadrature haseshift keying signals with carrier hase estimation, J. Lightwave Technol. 4(), (6). 3. S. Zhang, P. Y. Kam, J. Chen, and C. Yu, Decision-aided maximum likelihood detection in coherent otical hase-shift-keying system, Ot. Exress 7(), (9). 4. T. Tanimura, S. Oda, M. Yuki, H. Zhang, L. Li, Z. Tao, H. Nakashima, T. Hoshida, K. Nakamura, and J. C. Rasmussen, Non-linearity tolerance of direct detection and coherent receivers for 43 Gb/s RZ-DQPSK signals with co-roagating. Gb/s NRZ signals over NZ-DSF, in Tech. Digest of the Conference on Otical Fiber Communication (8), aer OTuM4. 5. Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, A simlified model for nonlinear cross-hase modulation in hybrid otical coherent system, Ot. Exress 7(6), (9). 6. L. Li, Z. Tao, S. Oda, T. Tanimura, M. Yuki, T. Hoshida, and J. C. Rasmussen, Adative otimization for digital carrier hase estimation in otical coherent receivers, in Digest IEEE/LEOS Summer Toical Meetings, Acaulco, Mexico, Jul. 8,., aer TuC L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, XPM tolerant adative carrier hase recovery for coherent receiver based on hase noise statistics monitoring, in Proc. Euroean Conference on Otical Communications (9), aer P J. Cheng, M. Tang, S. Fu, P. P. Shum, and D. Liu, Relative hase noise induced imairment in M-ary haseshift-keying coherent otical communication system using distributed fiber Raman amlifier, Ot. Lett. 38(7), (3). 9. G. P. Agrawal, Nonlinear Fiber Otics, 3rd ed. (Academic, ). # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 57

3 . C. R. S. Fludger, V. Handerek, and R. J. Mears, Pum to signal RIN transfer in Raman fiber amlifiers, J. Lightwave Technol. 9(8), 4 48 ().. M. G. Taylor, Phase estimation methods for otical coherent detection using digital signal rocessing, J. Lightwave Technol. 7(7), 9 94 (9).. G. Goldfarb and G. Li, BER estimation of QPSK homodyne detection with carrier hase estimation using digital signal rocessing, Ot. Exress 4(8), (6).. Introduction Demand for large transmission caacity has been increasing exonentially due to the raid sread of Internet services. The single channel data rate of coherent otical communication systems has been increased to Gb/s and even beyond by emloying advanced modulation formats, such as M-ary hase-shift keying (PSK) and M-ary quadrature amlitude modulation (QAM). With the digital signal rocessing (DSP) technique, linear imairments such as chromatic disersion (CD) and olarization mode disersion (PMD) can now be comensated for in the ost-signal-rocessing stage of coherent receiver []. Therefore, for multi-level modulated signal at such high bit rate, hase noise has become a major issue. So far, various kinds of DSP-based PE algorithm have been roosed, such as M-th ower [], decisionaided (DA) maximum likelihood (ML) [3] and so forth, to erform hase tracking function in the resence of laser hase noise and additive white Gaussian noise (AWGN). Besides these hase noise, XPM induced hase noise has been reorted as one of the major bottlenecks for otical coherent communication systems, esecially with PSK/OOK hybrid transmission [4], and a simlified model has been roosed [5]. Otimized PE algorithms have been resented to evaluate the imact of this very kind of hase noise [6,7]. Recently, a different kind of XPM induced hase noise, relative hase noise, has been discovered [8]. It was shown that RPN is caused by intensity fluctuation of um laser in a Raman amlified system. The noise ower of RPN in both co-uming and counter-uming configuration has been given by theoretical analysis. However, to the best of our knowledge, no quantitative simulation has been conducted to evaluate RPN induced imairment. In this aer, by roerly modeling RPN, we investigate the imact of RPN to the coherent otical communication system using Monte Carlo simulation. RPN induced cycle sli robability for QPSK signal is determined by quantitative analysis. Using two otimized V-V PE (by otimized block size and otimized averaging weights), u to 3 db Q imrovement can be achieved comared with the traditional sliding window V-V algorithm.. Relative hase noise and signal model. Relative hase noise In coherent otical communication system using multi-level modulated signal where information is modulated on signal s hase comonent, it is necessary to assess the comlex signal field to exlore the effect of um RIN transfer in coherent system with couled amlitude equations [9] ± A α ± ± ± ± + A = iγ A A. () z As As αs ± gs ± d + As = iγ s( fr) A As + A As. () z T where A and A s are the slowly varying enveloes associated with the um and signal, ± reresents co-uming and counter-uming scheme resectively, f R is the fractional Raman contribution, d =± vg vgs is the walk-off arameter, v gj is the grou velocity, γ j is the nonlinear arameter with j = or s. In co-uming configuration, T = t z/ vg, while in counter-uming configuration, T = t ( L z)/ vg. The walk-off arameter d accounts for the # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 58

4 grou-velocity mismatch between the um and signal. Since As A, we thus neglect the XPM from signal to um and the self-hase modulation (SPM) of signal. By assuming non-deletion regime of um ower, the above equations could be solved. We define RPN as [8]: δθ RPN s( f ) = θ. (3) where δθ is the mean square fluctuation of hase shift induced by um-signal XPM and θ is the mean hase shift given by: α z e θ = γ ( ). co s f R P α (4) α z α ( ) L e θ = γ counter s fr P e. α (5) Using harmonic analysis method, RPN in both co-uming and counter-uming configuration can be obtained as follows: where M ( z) + N ( z) α RPNs( f ) co = RIN ( f ). α + ( π fd ) z ( e α ) M ( z) + N ( z) α RPNs( f ) counter = RIN ( f ). α + ( π fd ) e α z ( ) (6) (7) α z M ( z) = e α sin( π fdz) + π fdcos( π fdz) π fd. (8) α N( z) = e z π fdsin( π fdz) α cos( π fdz) + α. (9) α M ( z) = e z α sin( π fdz) + π fd cos( π fdz) π fd. () α N ( z) = e z π fdsin( π fdz) + α cos( π fdz) α. () The noise ower of RPN is then given by: ν RPN θrpn ( t) RPNs( f ) θ df. ν σ = = () where ν andν are the lower and uer frequency of the receiver, resectively. In ractice, although signal is deteriorated by both intensity noise and hase noise, i.e., RIN and RPN, the latter seems to exhibit a greater influence, esecially for PSK modulated signal. In a tyical km SMF san with 8 mw Raman um ower (i.e., around.4 db Raman on-off gain), mw Raman um ower variation will cause around 5 signal hase variation, while the gain variation is less than 7%. Consequently, for simlicity, we ignore signal RIN in our simulation, so that the imact of RPN is focused on. Before introducing the signal model, it is reasonable and necessary to further discuss some of the imortant characteristics of RPN. Firstly, RPN is a stationary Gaussian random rocess, hence can be modeled as a Gaussian random variable after signal being samled by analog to digital converter (ADC). This characteristic can be roved from Eqs. (6) and (7), where the # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 59

5 first term reresents Raman um RIN, which is tyically modeled as a stationary Gaussian random rocess [], other terms are transfer function of a linear system. Secondly, the variance (i.e., noise ower) of RPN increases linearly with san number. This is because the intensity noise of Raman um lasers between each san is indeendent. As a result, the generated RPN of each san accumulate incoherently, and the total RPN is the sum of each san. Last but not least, RPN is low-ass in nature. Figure lots the transfer function of RPN, which evaluates the frequency resonse of um RIN transfer effect and determines the ower sectral density (PSD) shae of RPN. Parameters used in the calculation can be found in Table below. 5 RPN transfer function (db) counter-uming co-uming Frequency (Hz) Fig.. RPN transfer function for both co-uming and counter-uming configuration. Comared with XPM induced hase noise in PSK/OOK hybrid system, of which the cutoff frequency is tyically GHz order of magnitude [5], the cut-off frequency of RPN is fairly low: less than khz for counter-uming and several MHz for co-uming RPN. 5 (a) 5 (b) hase (rad) hase (rad) time (μs) 5 (c) time (μs) 5 (d) hase (rad) hase (rad) time (μs) time (μs) Fig.. Phase samles of (a) laser hase noise of beat linewidth of 3 khz. (b) XPM induced hase noise in PSK/OOK hybrid system. (c) co-uming RPN. (d) counter-uming RPN. Examles of four kinds of hase noise within µs time eriod shown in Fig. give us a sense of scale of how fast they change with time. In the simulation, the noise ower of three kinds of XPM induced hase noise is.3 rad, fiber disersion is 6 s/nm/km and channel # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 6

6 sacing between PSK and OOK signal is GHz. As shown here, counter-uming RPN changes so slow that can be treated as a constant in a block window of PE algorithm, thus will not affect hase tracking erformance. Nonetheless, although co-uming RPN changes slower than XPM induced hase noise in PSK/OOK hybrid system, it changes faster than laser hase noise, and will robably induce non-negligible system imairment. Therefore, in this aer, we ignore counter-uming RPN and deal with co-uming RPN only.. Signal model The received signal model in a Raman amlified coherent detection system in the resence of laser hase noise, AWGN and RPN can be written as: rk = E, ex s k j( θd, k θlw, k θrpn θrpn, k ) nk. (3) where E s, k is the symbol energy of the signal over the k-th symbol interval kts,( k + ) Ts ( T s is the symbol duration), which is assumed to be through our simulations, θ dk, and θ LW, k are the signal hase modulation and the laser hase noise, resectively, θ RPN is the average hase shift caused by um-signal XPM and is given in Eqs. (4) and (5), θ RPN, k is the zero mean Gaussian random variable RPN, n k is AWGN. We assume erfect ADC, timing synchronization, CD comensation, PMD comensation and frequency offset comensation in the DSP unit. Phase estimation is carried out indeendently for each olarization, and only one olarization is considered for simlicity. We use sliding window V-V algorithm as the basic PE algorithm. The erformance of two modified algorithms is also included. 3. Probability of cycle slis induced by RPN For V-V algorithm, the unwraing rocessing may cause cycle sliing, which will lead to catastrohic bit errors. The standard method to avoid ersistent nature of cycle slis is to use differential logical detection []. Whether to use differential logical detection or not deends on the robability of cycle sli events. An accetable cycle sli robability might be 8 []. Because RPN may cause more cycle slis, it is of necessity to first investigate the robability of cycle slis induced by RPN fitted curve sliding window VV otimal block size otimal average weight cycle sli robabiltiy variance of RPN (rad ) Fig. 3. Cycle sli robability for QPSK signal versus variance of RPN. # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 6

7 The cycle sli robability for QPSK signal using sliding window V-V is lotted in Fig. 3. In the simulation, beat linewidth is 3 khz, and signal-to-noise ratio (SNR) er bit is db, block size is ket to 55 symbols that is the otimum block size in the back-to-back (BB) case. The oints are a good fit to curves of the form: B cycle sli robability = A ex. σ RPN where A and B are constants. The fitted curve is also included in Fig. 3, from which we can see that the 8 cycle sli robability occurs at σ RPN =.4 rad. It is rather a low threshold, which is equivalent to noise ower after transmission of 4 sans of km tyical SMF, where.4 db Raman on-off gain is rovided in each san, with a co-uming um laser of 8 mw ower and db/hz um RIN. Also, because RPN can accumulate san by san incoherently, even if um laser has fairly low RIN, it is always ossible to reach the threshold in long-haul transmission. Once the threshold is reached, differential logical detection is better to be deloyed. The basic sliding window V-V could be otimized in two ways: otimizing block size [6] or otimizing averaging weights [7]. The details are included in the next art. With otimized PE algorithm, the threshold can be imroved. The simulation oints and the associated fitted curves of each otimized PE algorithm are also lotted in Fig. 3. It is found that the threshold increases to.3 rad and.58 rad for otimized block size PE and otimized averaging weights PE, resectively. The RPN noise ower threshold indicates that different modulation format should be deloyed deending on how strong the RPN is. For convenience, in this aer, we choose to use DQPSK signal regardless of weak RPN or strong RPN condition. 4. RPN estimation and mitigation In the resence of RPN, hase tracking erformance is surely degraded, inducing nonnegligible system imairment. Monte Carlo simulation based on signal model resented in section. is conducted for erformance evaluation in co-uming system, where the low ass nature of RPN is considered. One samle er symbol is used in the simulation, and BER is calculated by bit error counting. We use sliding window V-V as the basic PE algorithm to estimate the carrier hase. In V-V algorithm, the DQPSK signal samles are first oerated to 4-th ower to stri off the data information, and then averaged over the block of L symbols to obtain the estimated hase. The sliding window imlementation estimates the carrier hase symbol by symbol. Two otimized algorithms are then resented to give an imroved erformance. Parameters used in the simulation are listed in Table. Table. Simulation Parameters Parameter Value Parameter Value Signal loss. db/km San length km Pum loss.35 db/km Number of sans Symbol rate in one Pum ower 8 mw olarization 5 Gbaud Wavelength difference 3 THz Beat linewidth 3 khz Effective Raman.35 W km SNR er bit db coefficient Fractional Raman contribution Disersion.7 Simulated symbols 8 6 s/nm/km Number of oints used to calculate averaging weights 5 In our simulation, the total transmission length is km. The variances of RPN after km transmission versus um RIN is lotted in Fig. 4. (4) # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 6

8 variance of RPN (rad ) RIN of um (db/hz) Fig. 4. Variances of RPN versus um RIN. To give an intuitive understanding of RPN induced degradation, we lotted signal constellation in Fig. 5, using non-otimized sliding window V-V..5 (a).5 (b).5.5 Q Q I I Fig. 5. Signal constellation (a) back-to-back (b) with RPN, um RIN is 5 db/hz. We can see that, in the resence of RPN, the four oints in the constellation are no longer circular, but stretched in angular direction. However, the erformance can be imroved by otimizing sliding window V-V in two ways: otimizing block size or otimizing averaging weights. For block size otimization, in rincile, a larger block size can better smooth out the AWGN noise, but reduces the hase tracking caability []. For this reason, in dealing with RPN, a smaller block size is exected. Besides otimizing block size, we could also otimize the averaging weights of symbols within an average window in V-V PE. This aroach rovides the best estimation of carrier hase in the sense of minimum mean-square error (MMSE). With the rior information of carrier statistics, otimal averaging weights can be calculated using the equation resented in [7]. In consideration of RPN, suosing the symbols from L to L are used to estimate the carrier hase at time, the otimal averaging weights h( m) are: ( ) ( ) ( ) ( ) ( ) () ( ) ( ) ( ) ( ) h L R R R L R L h L+ R R R L R L =. h( L) R ( L) R ( L ) R ( ) R( L) (5) # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 63

9 { RPN } ( ) σ ρ( m) R m = ex 6. (6) { σrpn ρ } σnδ ( ) ( ) ( ) R m = ex 6 m + 6 m. (7) where σ RPN is the variance of RPN, ( m) the variance of AWGN and δ ( m) is the delta function. We lotted otimal block size and otimal averaging weights in Figs. 6 and 7. ρ is the normalized autocorrelation of RPN, σ n is 7 6 otimal block size RIN of um (db/hz) Fig. 6. Otimal block size versus Raman um RIN..9.8 normalized weight db/hz - db/hz -5 db/hz ta index Fig. 7. Otimal averaging weights. As can be seen from Fig. 6, the otimal block size indeed decreases with the increase of um RIN (or RPN noise ower). And from Fig. 7, we find that the averaging weights difference between central symbol and neighboring symbols becomes larger in stronger RPN condition. The signal constellation at the same um RIN value as in Fig. 5(b) using two otimized PE algorithms is lotted in Fig. 8. The corresonding otimal values can be found in Figs. 6 and 7. # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 64

10 .5 (a).5 (b).5.5 Q Q I I Fig. 8. Signal constellation using (a) otimal block size (b) otimal weights. The signal constellation quality of both modified PE algorithms imroves greatly comared with non-otimized PE. The associated Q factor curve demonstrates this quantitatively as shown in Fig Q factor (db) 9 8 back to back sliding window VV otimal block size otimal average weight RIN of um (db/hz) Fig. 9. Q factor erformance versus um RIN. In the above figure, the baseline Q in BB is around.6 db. Nearly 5 db Q enalty is induced when um RIN is as high as 5 db/hz, by using traditional non-otimized sliding window V-V algorithm. It is this intolerable huge enalty that makes it essential to adot otimized PE to mitigate RPN induced imact in strong RPN condition. As is shown in Fig. 9, both of the two otimized PE rovide significant erformance imrovement. Over 3 db Q imrovement is achieved at 5 db/hz um RIN value. The corresonding Q enalty is reduced to only around db. In addition, we can find that otimal averaging weights PE outerforms otimal block size PE slightly. This is due to the fact that otimal averaging weights PE works under MMSE criterion, thereby giving the theoretically otimum erformance. 5. Conclusion In Raman amlified coherent otical communication system, the unavoidable ower fluctuation of Raman um will bring out relative hase noise to a multi-level modulated signal through um-signal XPM effect. By roerly modeling, the imact of RPN is investigated through Monte Carlo simulation. The result shows that, although RPN generated in counter-uming Raman amlifier can be ignored due to its very low cut-off frequency, RPN in co-uming configuration will introduce non-negligible imairment, hence the design of distributed Raman amlifier in coherent otical communication system should be careful. # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 65

11 The study of the occurrence of cycle slis induced by RPN indicates that if RPN noise ower reaches the threshold of accetable cycle sli robability, differential logical detection should then be deloyed. In strong RPN condition, Q factor enalty of RPN on DQPSK signal can be as large as around 5 db using non-otimized sliding window V-V. The degradation can be mitigated if we make otimizations on sliding window V-V. With otimized block size or averaging weights, more than 3 db Q imrovement can be achieved. The significant erformance enhancement shows the imortance of otimizing PE according to the RPN statistics in Raman amlified coherent otical communication system. Acknowledgments The work resented in this aer is suorted by the National Basic Research Program of China (973 Program: CB3835), the 863 High Technology Plan of China (AA3 and 3AA34), and the National Natural Science Foundation of China (NSFC) under Grant No and 633. # $5. USD Received Oct 3; revised 9 Dec 3; acceted 6 Jan 4; ublished 3 Jan 4 (C) 4 OSA 7 January 4 Vol., No. DOI:.364/OE..57 OPTICS EXPRESS 66