OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 22 — Oct. 25, 2010
  • pp: 22796–22807
« Show journal navigation

Optimized digital backward propagation for phase modulated signals in mixed-optical fiber transmission link

Rameez Asif, Chien-Yu Lin, M. Holtmannspoetter, and Bernhard Schmauss  »View Author Affiliations


Optics Express, Vol. 18, Issue 22, pp. 22796-22807 (2010)
http://dx.doi.org/10.1364/OE.18.022796


View Full Text Article

Acrobat PDF (1327 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The parametric optimization of Digital Backward Propagation (DBP) algorithm for mitigating fiber transmission impairments is proposed and numerically demonstrated for phase modulated signals in mixed-optical fiber transmission link. The optimization of parameters i.e. dispersion (D) and non-linear coefficient (γ) offer improved eye-opening (EO). We investigate the optimization of iterative and non-iterative symmetric split-step Fourier method (S-SSFM) for solving the inverse non-linear Schrödinger equation (NLSE). Optimized DBP algorithm, with step-size equal to fiber module length i.e. one calculation step per fiber span for obtaining higher computational efficiency, is implemented at the receiver as a digital signal processing (DSP) module. The system performance is evaluated by EO-improvement for diverse in-line compensation schemes. Using computationally efficient non-iterative symmetric split-step Fourier method (NIS-SSFM) upto 3.6dB referenced EO-improvement can be obtained at 6dBm signal launch power by optimizing and modifying DBP algorithm parameters, based on the characterization of the individual fiber types, in mixed-optical fiber transmission link.

© 2010 OSA

1. State of the art

Optical fiber transmission is impacted collectively by linear and non-linear impairments. Especially in advanced modulation formats, such as DPSK and DQPSK, the influence of fiber transmission impairments i.e. dispersion and non-linearities is of high interest. The most important impenetrability in achieving high spectral efficiency in long haul communication is the combine effects of fiber non-linearity and dispersion [1

1. R. Essiambre, G. Foschini, P. Winzer, G. Kramer, and E. Burrows, “The Capacity of Fiber-Optic Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuE1.

].

Various methods of compensating fiber transmission impairments have also been proposed in recent era both in optical [2

2. X. Liu, F. Buchali, and R. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009). [CrossRef]

4

4. K. Cvecek, K. Sponsel, C. Stephan, G. Onishchukov, R. Ludwig, C. Schubert, B. Schmauss, and G. Leuchs, “Phase-preserving amplitude regeneration for a WDM RZ-DPSK signal using a nonlinear amplifying loop mirror,” Opt. Express 16(3), 1923–1928 (2008). [CrossRef] [PubMed]

] and electronic domain [5

5. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]

10

10. G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photon. 1(2), 279–307 (2009). [CrossRef]

]. The implementations of all-optical methods are practically expensive, less flexible and complex to implement. On the other hand with the development of proficient real time finite impulse response (FIR) filters and coherent receivers, electronic compensation techniques have emerged as the promising techniques for long-haul optical data transmission. After coherent detection the signals can be sampled and processed by digital signal processors (DSP) to compensate fiber transmission impairments. This digital compensation is considered vital for mitigation of fiber transmission impairments as it can offer great flexibility and adaptivity.

In view of the fact that signal propagation is interpreted by non-linear Schrödinger equation (NLSE) [11

11. G. P. Agrawal, Nonlinear fiber optics (Academic Press, 1995, 2nd edn).

,12

12. R.-J. Essiambre, P. J. Winzer, W. Lee, C. A. White, E. C. Burrows, and X. Q. Wang, “Electronic predistortion and fiber nonlinearity,” IEEE Photon. Technol. Lett. 18(17), 1804–1806 (2006). [CrossRef]

], accordingly by solving the NLSE we can estimate the optical signal amplitude and phase at each point of the fiber. This influential evaluation leads towards the study of compensating algorithm for fiber transmission impairments based on the inverse mathematical solution of NLSE, which is termed as Digital Backward Propagation (DBP). Digital Backward Propagation, for mitigating fiber transmission impairments, was first studied in 2008 [13

13. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008). [CrossRef] [PubMed]

]. A number of investigations have been done on DBP algorithm with standard single mode fiber (SMF). Also its performance was analyzed with coherent detection and split-step Fourier method (SSFM) to solve NLSE [13

13. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008). [CrossRef] [PubMed]

17

17. Millar, D. S.; Makovejs, S.; Mikhailov, V.; Killey, R. I.; Bayvel, P.; Savory, S. J. “Experimental Comparison of Nonlinear Compensation in Long-Haul PDM-QPSK Transmission at 42.7 and 85.4 Gb/s”, ECOC 09, 9.4.4, 2009.

] in recent years.

Generally, split-step Fourier method (SSFM) is used in a way for DBP algorithm, which is called asymmetric SSFM (A-SSFM). A-SSFM means to perform one linear and one non-linear calculation in each computational step. The performance of DBP hereby strongly depends on the step size. Although A-SSFM saves computational cost, it was shown that symmetric SSFM (S-SSFM) with half a linear, one nonlinear and again half a linear calculation in each step has improved performance than A-SSFM [14

14. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Effects using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

,15

15. E. Ip, A. Pak Tao Lau, D. J. F. Barros, and J. M. Kahn, “Compensation of Dispersion and Nonlinearity in WDM Transmission Using Simplified Digital Backpropagation,” IEEE/LEOS Summer Topical Meetings, 2008 Digest of the.123–124, 21–23 2008.

]. S-SSFM applies two additional iterations in each step to increase accuracy as iterative S-SSFM (IS-SSFM), while there are no such iterations in non-iterative S-SSFM (NIS-SSFM) [18

18. C. Y Lin, “Michael Holtmannspoeter; M. Rameez Asif; Bernhard Schmauss; “Compensation of Transmission Imapirments by Digital Backward Propagation for Different Link Designs,” ECOC (to be published).

].

However, till date there has been no reports of DBP implementation in mixed-optical fiber transmission links, though the future optical networks are expected to be heterogeneous in terms of fiber types. The exsisting optical infrastructures may contain mixed spans of standard single mode fiber (SMF) and non-zero dispersion shifted fiber (NZDSF). When an optical signal is transmitted over such a heterogeneous fiber type network, the signal shows degraded transmission performance due to diverse accumulation of dispersion and non-linearities [19

19. S. Pachnicke, N. Hecker-Denschlag, S. Spalter, J. Reichert, and E. Voges, “Experimental verification of fast analytical models for XPM-impaired mixed-fiber transparent optical networks,” IEEE Photon. Technol. Lett. 16(5), 1400–1402 (2004). [CrossRef]

]. Therefore in these mixed-optical fiber links, it is necessary to consider the above mentioned physical constraints for efficient transmission.

The paper is organized as follows: Section 2 reviews the theory for solving inverse NLSE and describes the proposed optimization of DBP algorithm for mitigating fiber transmission impairments in mixed-optical fiber link. Section 3 illustrates the numerical model for evaluating the algorithm. Section 4 contains the results validating the efficiency of optimized DBP algorithm in mixed-optical fiber link. Conclusions of these investigations are presented in Section 5.

2. Theory

2.1. Non-linear Schrödinger equation

The propagation of optical signal is principally described by non-linear Schrödinger equation (NLSE). In the systems where polarization mode dispersion (PMD) is negligible or well confined the NLSE can be given as in Eq. (1) [11

11. G. P. Agrawal, Nonlinear fiber optics (Academic Press, 1995, 2nd edn).

].
Ez=jγ|E|2+(jβ222t2α2)E=(N^+D^)E
(1)
Whereas:

N^=jγ|E|2,D^=jβ222t2α2
(2)

Ez=(N^D^)E
(3)

Whereas: α1,β1,γ1 are the physical parameters of fiber type ‘1’ and α2,β2,γ2are the physical parameters of fiber type ‘2’. While the linear (D^) and non-linear (N^) operators in DBP for both fiber types can be solved as in Eq. (4).

N^=jγ|E|2,D^=jβ222t2+α2
(4)

2.2. Split-step Fourier method

It is obligatory to solve NLSE with high precision to estimate the fiber impairments such as dispersion and non-linearities during signal transmission. The well-liked method with modest computation cost and accuracy is Split-Step Fourier Method (SSFM). Mathematically it is given in Eq. (5).

E(z+h,t)=exp(h(N^+D^))E(z,t))
(5)

In the above equation ‘h’ is the propagation length through the fiber section. As described before, SSFM can be solved by using two methods i.e. asymmetric SSFM (A-SSFM) and symmetric SSFM (S-SSFM). Due to the better performance of S-SSFM [14

14. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Effects using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

], we adopt this method to implement our DBP algorithm. In S-SSFM, linear operator is split into two parts and is evaluated on both sides of non-linear operator as in Eq. (6).

E(z+h,t)=exp(hD^2)exp(hN^)exp(hD^2)E(z,t)
(6)

Two methods are adapted for computing parameters in S-SSFM. The method in which N^(z+h)is calculated by initially assuming it asN(z) then estimatingE(z+h,t), which enables a new value of N^new(z+h)and subsequently estimating Enew(z+h,t)is termed as Iterative Symmetric SSFM (IS-SSFM). The other method, which is less time consuming and has fewer computations, is based on the calculation of N^(z+h)at the middle of propagation ‘h’ is termed as Non-iterative Symmetric SSFM (NIS-SSFM). It is affirmed that by optimizing the parameters of DBP algorithm we can get the improved eye-opening (EO) and efficient mitigation. Means we have to modify the linear and non-linear operators for solving the inverse NLSE as in Eq. (7).

Ez=(N^optimizedD^optimized)E
(7)

3. Numerical model

In our numerical investigations, as in Fig. 3
Fig. 3 Numerical model of phase encoded mixed-optical fiber transmission.
, for FP we use OptiSystem 8.0 to simulate 10Gbit/s RZ-DQPSK which is driven by a continues-wave (CW) laser at a frequency of 1550nm. The data stream consists of 211-1 pseudo-random binary sequence (PRBS) and RZ pulses of 33% duty cycle. Fiber transmission channel has a total length of 800km that consists of 80km spans of combination of standard single mode fiber (SMF) and non-zero dispersion shifted fiber (NZDSF).

We evaluate the DBP algorithm performance by using diverse dispersion compensation schemes such as; post-compensation (PC), under-compensation (UC) and no-compensation (NC). For a comparative evaluation of SMF and NZDSF, we keep the parameters i.e. dispersion, attenuation and non-linear coefficient of dispersion compensating fiber (DCF) constant in the respective cases with each type of fiber. The length of DCF is not included in the total transmission length of 800km. In case of PC the chromatic dispersion is totally compensated by the in-line DCF whereas in the case of UC we use the 50% dispersion compensation, which means that there is residual dispersion in the transmission link. While in case of NC scheme there is no in-line DCF during the transmission.

The received signal is monitored as: transmitted signal (EFP) and algorithm processed signal (EDBP) as described in Fig. 3. The system performance is compared by EO gain due to DBP (dB) and referenced EO-improvement. EO gain due to DBP can be expressed as the ratio of EODBP and EOFP and mathematically can be derived as in Eq. (8).

EOgainduetoDBP(dB)=10log10[EODBP(PC,UC,NC)EOFP(PC,UC,NC)]
(8)

While the referenced EO-improvement is the analysis of the overall system performance i.e. to see the combine effect of DBP and dispersion mapping on system performance by taking the NC scheme as reference and can be expressed as the ratio of EODBP and EOFP(NC). Mathematically it is given as in Eq. (9).

referencedEOimprovement(dB)=10log10[EODBP(PC,UC,NC)EOFP(NC)]
(9)

Whereas in Eq. (8) and Eq. (9), EOFP(NC) is the optimal signal after transmission in NC scheme, when linear dispersion compensation (LDC) is applied at the end of link, as shown in Fig. 4
Fig. 4 Signal flow-chart for digital post-processing of received data.
.

4. Numerical results and discussion

For numerical investigation, optimized DBP algorithm is evaluated at signal launch powers between 3dBm to 7.5dBm where the non-linearities are more dominant and have impact on the system performance. First, the system is numerically analyzed for standalone transmissions of SMF and NZDSF over 800km length with post-, under- and no-dispersion compensation schemes.

4.1. Iterative symmetric split-step Fourier method (IS-SSFM)

Using IS-SSFM method, DBP module is implemented after the coherent detection for per span mitigation of fiber transmission impairments. The results of EO gain due to DBP as a function of DDBP and γ DBP are depicted as contour plots in Fig. 5
Fig. 5 EO gain due to DBP (dB) map as a function of dispersion DDBP and non-linear coefficient γDBP for standalone transmission over 800km at 6dBm launch power for: SMF with dispersion mapping: (a) post-compensation; (b) under-compensation; (c) no-compensation, NZDSF with dispersion mapping: (d) post-compensation; (e) under-compensation; (f) no-compensation.
.

It is evident from the results that by optimizing the parameters of DBP algorithm using IOM (as in Fig. 2(a)), we get the improved eye-opening (EO). In case of the standalone transmission of SMF over 800km with post-compensation dispersion mapping, the optimized parameters for DBP at 6dBm signal launch power are, D = 15.1ps(nm-km) and γ = 0.17(km−1.W−1), as in Fig. (5a), which are actually less than the FP parameters i.e. D = 16ps(nm-km) and γ = 1.2(km−1.W−1) due to IS-SSFM based algorithm, that has been explained previously in section 1 and 2. Also that we have used symmetric split-step Fourier method (SSFM) to numerically investigate the performance of optimized digital backward propagation (DBP). We have calculated the nonlinear phase (NLp) with a total step size, instead of effective step size in our algorithm. We have also verified that by calculating with total step size, the system gives same optimum performance as with effective step size, but the optimum gamma should be adjusted accordingly. This optimized gamma (for calculating with the total step size), denoted as γ total, is different from the gamma (for calculating with the effective step size) when the algorithm is solved with effective step size, denoted as γ eff. Besides, the γ total also needs to be adapted to step size.

We also examine the parametric optimization of DCF used in this case but it appears that DCF has no active role in the EO-improvement, so we use the same parameters of DCF in DBP as in the original FP i.e. D = −80ps(nm-km) and γ = 5.0(km−1.W−1). Similar approach is adapted to optimize the DBP parameters in under-compensation and no-compensation scheme for SMF as presented in Fig. 5(b) and Fig. 5(c) respectively. This optimization technique also stands true for standalone transmission of NZDSF fiber over 800km. The results for post-compensation, under-compensation and no-compensation scheme are depicted in Fig. 5(d), Fig. 5(e) and Fig. 5(f) respectively.

After this numerical optimization, we alter the transmission into mixed- optical fiber link i.e. by a series of SMF and NZDSF connected one after each other over a combine length of 800km.The parametric optimization of DBP using SOM (as in Fig. 2(b)) is analyzed for mixed-optical fiber link, though a complex computation of D and γ in comparison to IOM. It is identified that the optimized values of D for SMF are: D = 15.1ps(nm-km) in post-compensation dispersion scheme, D = 16ps(nm-km) in under-compensation dispersion scheme and D = 15.9ps(nm-km) in no-compensation dispersion scheme. Similarly the optimized values of D for NZDSF are: D = 4.15ps(nm-km) in post-compensation dispersion scheme, D = 3.68ps(nm-km) in under-compensation dispersion scheme and D = 4.5ps(nm-km) in no-compensation dispersion scheme. These optimized values of D are exactly the same as the optimized values in standalone transmission of SMF and NZDSF.

Whereas the contour plots as a function of γ DBP,SMF and γ DBP,NZDSF for mixed-optical fiber link are presented in Fig. 6
Fig. 6 EO gain due to DBP (dB) map as a function of non-linear coefficient γDBP,SMF and non-linear coefficient γDBP,NZDSF for mixed-optical fiber transmission link (series of SMF + NZDSF) over 800km at 6dBm launch power with dispersion mapping: (a) post-compensation; (b) under-compensation; (c) no-compensation.
, for post-compensation, under-compensation and no-compensation dispersion schemes. The values of optimized γ DBP,SMF and γ DBP,NZDSF using IOM and SOM are the same in case of post- and no-compensation schemes as shown in Fig. 5 and Fig. 6. Whereas the optimized values of γ DBP,SMF and γ DBP,NZDSF for under-compensation scheme slightly differ from each other in IOM and SOM optimization methods. In IOM γ DBP,SMF = 0.42(km−1.W−1) and γ DBP,NZDSF = 0.55(km−1.W−1) in comparison to SOM where γ DBP,SMF = 0.64(km−1.W−1) and γ DBP,NZDSF = 0.69(km−1.W−1). After acquiring the contour plots from both the optimization cases, IOM and SOM, we compare the system performance. We modify the DBP algorithm with the optimized values and evaluate the resultant EO-improvement. In this analysis DBP is based on IS-SSFM method. The results of EO gain due to DBP (dB) and referenced EO-improvement (dB) are given in Fig. 7
Fig. 7 Comparison of the performance of optimized DBP algorithm (IS-SSFM) for 10Gbit/s RZ-DQPSK transmission over 800km mixed-optical fiber transmission link (series of SMF + NZDSF): (a) EO gain due to DBP (dB); (b) referenced EO-improvement (dB).
.

From the investigation of the results as shown in Fig. 7, we notice considerable mitigation of fiber transmission impairments i.e. dispersion and non-linearities at high signal launch powers between 3dBm and 7.5dBm. Also that in case of post-compensation and no-compensation schemes, the optimized values of D and γ coincides for IOM and SOM. Due to this, the system performance in terms of EO-improvement is equal. While for under-compensation scheme, as previously discussed, the optimized parameters of γ from IOM and SOM are slightly divergent and we get about 0.3dB variation in the system performance in terms of EO-improvement.

By analyzing the results of EO gain due to DBP, as in Fig. 7(a), it is observed that DCF plays an important role in the performance evaluation of post-compensated system. The EO gain due to DBP in the case of NC is better than PC, is due to the absence of DCF in NC, as DCF incurs losses and higher dispersion which leads to smaller nonlinearities. So in the absence of DCF this digital compensation technique along with coherent detection helps to compensate CD without undesired effects. Whereas, the EO gain due to DBP in UC scheme is better than PC is due to the pulse compression by SPM interaction with residual dispersion that counteracts dispersive pulse broadening.

At 6dBm signal launch power the system performance in terms of referenced EO-improvement is 3.6dB for post-compensation, 2.5dB for under-compensation and 2.1dB for no-compensation scheme. This indicates that the referenced system performance for post-compensation scheme along with DBP is better than the under- and no-compensation schemes. ASE is not included in our numerical simulations. Due to this reason, at high signal launch powers i.e. 7.5dBm, we still get the efficient compensation of fiber transmission impairments and the performance is not limited by ASE-seeded non-linearities.

4.2. Non-iterative symmetric split-step Fourier method (NIS-SSFM)

To further authenticate the optimization method and system performance we also use NIS-SSFM method for implementing DBP. To summarize, we elaborate the case of the optimization of DBP parameters for standalone transmission of SMF. By using NIS-SSFM, we attain the improved eye-opening (EO) in case of post-compensation dispersion mapping at D = 15.2ps(nm-km) and γ = 0.4(km−1.W−1). In the same way we optimize NZDSF and then mix-fiber optical link containing both SMF and NZDSF by using optimization cases i.e. IOM and SOM. Interestingly it is found that the optimized parameters from both optimization techniques are the same in post-, under- and no-dispersion compensation schemes.

Subsequently we compare the system performance and the results are depicted as in Fig. 8
Fig. 8 Comparison of the performance of optimized DBP algorithm (NIS-SSFM) for 10Gbit/s RZ-DQPSK transmission over 800km mixed-fiber optical link (series of SMF + NZDSF): (a) EO gain due to DBP (dB); (b) referenced EO-improvement (dB).
. Fiber transmission impairments i.e. dispersion and non-linearities are effectively mitigated. We identify that NIS-SSFM based algorithm is computationally more proficient then the IS-SSFM based algorithm due to the fact that: (a) it is more robust towards the optimization of parameters using IOM and SOM. The optimization parameters are the same for post-, under- and no-compensation dispersion schemes as compared to IS-SSFM based algorithm where in case of under-compensation scheme γ values are slightly different in IOM and SOM thus giving 0.3dB decrease in system performance and (b) also NIS-SSFM based algorithm gives 1dB additional EO-improvement in case of under- and no-compensation at 7.5dBm signal launch power.

By analyzing the results from Fig. 8, the referenced system performance in terms of EO-improvement for post-compensation dispersion mapping at 6dBm signal launch power is 3.6dB. Added advantage of using NIS-SSFM is that we can adopt the optimized DBP parameters, based on the characterization of individual fiber types (IOM) present in the mixed-optical fiber transmission link, to have less computational cost.

4.3. Flexibility assessment of NIS-SSFM based DBP algorithm

The results of EO gain due to DBP (dB) and referenced EO-improvement (dB) for these span configurations are given in Fig. 9
Fig. 9 Comparison of the performance of optimized DBP algorithm (NIS-SSFM) for 10Gbit/s RZ-DQPSK transmission over 800km mixed-optical fiber link for different fiber spans configurations: (a) and (b) post-compensation; (c) and (d) under-compensation; (e) and (f) no-compensation
. All the span configurations are analyzed for post-compensation, under-compensation and no-compensation schemes. It is evident from the results that our DBP algorithm parameters are quite flexible to any change in the span configurations of the transmission link and shows efficient fiber impairment mitigation in all the cases. We also notice form Fig. 9 that additional EO-improvement is obtained, if SMF is present in the initial sections of the transmission.

5. Conclusions

To conclude, we have numerically demonstrated the parametric optimization of DBP with IS-SSFM and NIS-SSFM methods in mixed-optical fiber transmission link with phase modulated signals. DBP algorithm is implemented with step-size equal to fiber module length i.e. one calculation step per fiber span for obtaining higher computational efficiency. Optimization and modification of fiber parameters in DBP i.e. dispersion D and non-linear coefficient γ, leads to the improved eye-opening (EO). NIS-SSFM method is more robust towards the optimization of DBP parameters with diverse compensation schemes and we can get equivalent degree of EO-improvement as in IS-SSFM. Also that NIS-SSFM based DBP algorithm is more efficient in terms of computational cost. It is also observed that we can characterize the individual fiber sections and can utilize those optimized values for DBP parameters in the mixed-optical fiber link, making the algorithm simpler to implement. The referenced system performance in post-compensation scheme at 6dBm launch power is 3.6dB, which makes it more superior than the under- compensation and no-compensation schemes.

Acknowledgements

The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the framework of the excellence initiative.

References and links

1.

R. Essiambre, G. Foschini, P. Winzer, G. Kramer, and E. Burrows, “The Capacity of Fiber-Optic Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuE1.

2.

X. Liu, F. Buchali, and R. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009). [CrossRef]

3.

S. L. Jansen, et al., “Optical phase conjugation for ultra long-haul phase-shift-keyed transmission,” Lightwave Technology Journalism 24(1), 54–64 (2006). [CrossRef]

4.

K. Cvecek, K. Sponsel, C. Stephan, G. Onishchukov, R. Ludwig, C. Schubert, B. Schmauss, and G. Leuchs, “Phase-preserving amplitude regeneration for a WDM RZ-DPSK signal using a nonlinear amplifying loop mirror,” Opt. Express 16(3), 1923–1928 (2008). [CrossRef] [PubMed]

5.

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]

6.

E. M. Ip and J. M. Kahn, “Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing,” Lightwave Technology Journalism 28(4), 502–519 (2010). [CrossRef]

7.

R. I. Killey, P. M. Watts, V. Mikhailov, M. Glick, and P. Bayvel, “Electronic dispersion compensation by signal predistortion using digital Processing and a dual-drive Mach-Zehnder Modulator,” IEEE Photon. Technol. Lett. 17(3), 714–716 (2005). [CrossRef]

8.

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental Demonstration of Fiber Impairment Compensation Using the Split-Step Finite-Impulse-Response Filtering Method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008). [CrossRef]

9.

G. Goldfarb and G. Li, “Demonstration of fibre impairment compensation using split-step infinite-impulse response filtering method,” Electron. Lett. 44(13), 814–816 (2008). [CrossRef]

10.

G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photon. 1(2), 279–307 (2009). [CrossRef]

11.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, 1995, 2nd edn).

12.

R.-J. Essiambre, P. J. Winzer, W. Lee, C. A. White, E. C. Burrows, and X. Q. Wang, “Electronic predistortion and fiber nonlinearity,” IEEE Photon. Technol. Lett. 18(17), 1804–1806 (2006). [CrossRef]

13.

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008). [CrossRef] [PubMed]

14.

E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Effects using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

15.

E. Ip, A. Pak Tao Lau, D. J. F. Barros, and J. M. Kahn, “Compensation of Dispersion and Nonlinearity in WDM Transmission Using Simplified Digital Backpropagation,” IEEE/LEOS Summer Topical Meetings, 2008 Digest of the.123–124, 21–23 2008.

16.

F. Yaman and Guifang Li, “Guifang Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photon. J. 1(2), 144–152 (2009). [CrossRef]

17.

Millar, D. S.; Makovejs, S.; Mikhailov, V.; Killey, R. I.; Bayvel, P.; Savory, S. J. “Experimental Comparison of Nonlinear Compensation in Long-Haul PDM-QPSK Transmission at 42.7 and 85.4 Gb/s”, ECOC 09, 9.4.4, 2009.

18.

C. Y Lin, “Michael Holtmannspoeter; M. Rameez Asif; Bernhard Schmauss; “Compensation of Transmission Imapirments by Digital Backward Propagation for Different Link Designs,” ECOC (to be published).

19.

S. Pachnicke, N. Hecker-Denschlag, S. Spalter, J. Reichert, and E. Voges, “Experimental verification of fast analytical models for XPM-impaired mixed-fiber transparent optical networks,” IEEE Photon. Technol. Lett. 16(5), 1400–1402 (2004). [CrossRef]

20.

C. Jonas Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss; “Simple Automatic Nonlinear Compensation with Low Complexity for Implementation in Coherent Receivers,” ECOC (to be published).

21.

G. P. Agrawal, Lightwave Technology, Telecommunication Systems (John Wiley and Sons, Inc. 2005).

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4080) Fiber optics and optical communications : Modulation
(060.4230) Fiber optics and optical communications : Multiplexing
(060.4250) Fiber optics and optical communications : Networks
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: August 13, 2010
Revised Manuscript: September 10, 2010
Manuscript Accepted: October 4, 2010
Published: October 13, 2010

Citation
Rameez Asif, Chien-Yu Lin, M. Holtmannspoetter, and Bernhard Schmauss, "Optimized digital backward propagation for phase modulated signals in mixed-optical fiber transmission link," Opt. Express 18, 22796-22807 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-22796


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Essiambre, G. Foschini, P. Winzer, G. Kramer, and E. Burrows, “The Capacity of Fiber-Optic Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuE1.
  2. X. Liu, F. Buchali, and R. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009). [CrossRef]
  3. S. L. Jansen, et al., “Optical phase conjugation for ultra long-haul phase-shift-keyed transmission,” Lightwave Technology Journalism 24(1), 54–64 (2006). [CrossRef]
  4. K. Cvecek, K. Sponsel, C. Stephan, G. Onishchukov, R. Ludwig, C. Schubert, B. Schmauss, and G. Leuchs, “Phase-preserving amplitude regeneration for a WDM RZ-DPSK signal using a nonlinear amplifying loop mirror,” Opt. Express 16(3), 1923–1928 (2008). [CrossRef] [PubMed]
  5. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]
  6. E. M. Ip and J. M. Kahn, “Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing,” Lightwave Technology Journalism 28(4), 502–519 (2010). [CrossRef]
  7. R. I. Killey, P. M. Watts, V. Mikhailov, M. Glick, and P. Bayvel, “Electronic dispersion compensation by signal predistortion using digital Processing and a dual-drive Mach-Zehnder Modulator,” IEEE Photon. Technol. Lett. 17(3), 714–716 (2005). [CrossRef]
  8. G. Goldfarb, M. G. Taylor, and G. Li, “Experimental Demonstration of Fiber Impairment Compensation Using the Split-Step Finite-Impulse-Response Filtering Method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008). [CrossRef]
  9. G. Goldfarb and G. Li, “Demonstration of fibre impairment compensation using split-step infinite-impulse response filtering method,” Electron. Lett. 44(13), 814–816 (2008). [CrossRef]
  10. G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photon. 1(2), 279–307 (2009). [CrossRef]
  11. G. P. Agrawal, Nonlinear fiber optics (Academic Press, 1995, 2nd edn).
  12. R.-J. Essiambre, P. J. Winzer, W. Lee, C. A. White, E. C. Burrows, and X. Q. Wang, “Electronic predistortion and fiber nonlinearity,” IEEE Photon. Technol. Lett. 18(17), 1804–1806 (2006). [CrossRef]
  13. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008). [CrossRef] [PubMed]
  14. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Effects using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]
  15. E. Ip, A. Pak Tao Lau, D. J. F. Barros, and J. M. Kahn, “Compensation of Dispersion and Nonlinearity in WDM Transmission Using Simplified Digital Backpropagation,” IEEE/LEOS Summer Topical Meetings, 2008 Digest of the.123–124, 21–23 2008.
  16. F. Yaman and Guifang Li, “Guifang Li, “Nonlinear Impairment Compensation for Polarization-Division Multiplexed WDM Transmission Using Digital Backward Propagation,” IEEE Photon. J. 1(2), 144–152 (2009). [CrossRef]
  17. Millar, D. S.; Makovejs, S.; Mikhailov, V.; Killey, R. I.; Bayvel, P.; Savory, S. J. “Experimental Comparison of Nonlinear Compensation in Long-Haul PDM-QPSK Transmission at 42.7 and 85.4 Gb/s”, ECOC 09, 9.4.4, 2009.
  18. C. Y Lin, “Michael Holtmannspoeter; M. Rameez Asif; Bernhard Schmauss; “Compensation of Transmission Imapirments by Digital Backward Propagation for Different Link Designs,” ECOC (to be published).
  19. S. Pachnicke, N. Hecker-Denschlag, S. Spalter, J. Reichert, and E. Voges, “Experimental verification of fast analytical models for XPM-impaired mixed-fiber transparent optical networks,” IEEE Photon. Technol. Lett. 16(5), 1400–1402 (2004). [CrossRef]
  20. C. Jonas Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss; “Simple Automatic Nonlinear Compensation with Low Complexity for Implementation in Coherent Receivers,” ECOC (to be published).
  21. G. P. Agrawal, Lightwave Technology, Telecommunication Systems (John Wiley and Sons, Inc. 2005).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited