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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 26 — Dec. 12, 2011
  • pp: B581–B586
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Ultra-long-haul transmission of 7×42.9 Gbit/s PS-QPSK and PDM-BPSK

Carsten Behrens, Domaniç Lavery, David S. Millar, Sergejs Makovejs, Benn C. Thomsen, Robert I. Killey, Seb J. Savory, and Polina Bayvel  »View Author Affiliations


Optics Express, Vol. 19, Issue 26, pp. B581-B586 (2011)
http://dx.doi.org/10.1364/OE.19.00B581


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Abstract

We investigated ultra-long-haul transmission of polarization-switched QPSK (PS-QPSK) and polarization-division-multiplexed BPSK (PDM-BPSK) at 42.9 Gbit/s experimentally as well as by means of computer simulations. PDM-BPSK allowed transmission distances in excess of 14,040 km to be achieved, compared to 13,640 km for PS-QPSK. However, PS-QPSK offers a significant reduction in receiver complexity due to the lower symbol-rate.

© 2011 OSA

1. Introduction

Reported experiments focusing on long-haul and ultra long-haul transmission continue to approach the theoretical linear and nonlinear transmission limits as depicted in Fig. 1
Fig. 1 Spectral efficiency versus transmission reach for various WDM-experiments employing a variety of modulation formats, fiber types and amplification techniques. The linear limit assumes ASE noise as the only limitation [1], while the nonlinear limit additionally assumes XPM to be the dominant nonlinearity [2].
. The results of the spectral efficiency versus transmission distance have been plotted to include most noteworthy wavelength-division-multiplexed (WDM) experiments, carried out with various modulation formats, as well as the theoretical linear and nonlinear limits [1

1. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).

, 2

2. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]

]. The linear limit was calculated assuming 80 km standard singlemode fiber spans, EDFA-only amplification (NF=4.5 dB) and a 50 GHz grid with full population of the C-band, while in the case of the nonlinear limit, cross phase modulation is assumed to be the dominant nonlinearity.

Figure 1 highlights that conventional modulation formats such as on-off keying (OOK) [3

3. D. G. Foursa, C. R. Davidson, M. Nissov, M. A. Mills, L. Xu, J. X. Cai, A. N. Pilipetskii, Y. Cai, C. Breverman, R. R. Cordell, T. J. Carvelli, P. C. Corbett, H. D. Kidorf, and N. S. Bergano, "2.56 Tb/s (256x10 Gb/s) transmission over 11,000 km using hybrid Raman/EDFAs with 80 nm of continuous bandwidth," in Optical Fiber Communications Conference, A. Sawchuk, ed., Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), paper FC3.

], differential phase-shift-keying (DPSK) [4

4. J. Cai, D. Foursa, L. Liu, C. Davidson, Y. Cai, W. Patterson, A. Lucero, B. Bakhshi, G. Mohs, P. Corbett, V. Gupta, W. Anderson, M. Vaa, G. Domagala, M. Mazurczyk, H. Li, M. Nissov, A. Pilipetskii, and N. Bergano, "RZ-DPSK field trial over 13,100 km of installed non slope-matched submarine fibers," in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, (2004), paper PD34.

] and polarization multiplexed binary phase-shift-keying (PDM-BPSK) [5

5. G. Charlet, M. Salsi, H. Mardoyan, P. Tran, J. Renaudier, S. Bigo, M. Astruc, P. Sillard, L. Provost, and F. Cerou, “Transmission of 81 channels at 40Gbit/s over a transpacific-distance erbium-only link, using PDM-BPSK modulation, coherent detection, and a new large effective area fibre,” in 34th European Conference on Optical Communication, 2008. ECOC 2008 (IEEE,2008), paper Th.3.E.3.

] as well as quaternary phase-shift keying (PDM-QPSK) [6

6. D. Foursa, Y. Cai, J. Cai, C. Davidson, O. Sinkin, B. Anderson, A. Lucero, A. Pilipetskii, G. Mohs, and N. Bergano, "Coherent 40 Gb/s transmission with high spectral efficiency over transpacific distance," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMI4.

] have been widely used to demonstrate transmission over distances beyond 2000 km, which is due to their increased resilience towards nonlinear distortions [7

7. C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Nonlinear Distortion in Transmission of Higher Order Modulation Formats,” IEEE Photon. Technol. Lett. 22(15), 1111–1113 (2010). [CrossRef]

] and superior sensitivity in the presence of circularly-symmetric Gaussian noise assuming a 2-dimensional channel [8

8. J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2007).

]. However, an optical wave offers 4 degrees of freedom (2 quadratures in 2 polarizations) and recent work has addressed the question of the optimum modulation format for this higher dimensional channel [9

9. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009). [CrossRef] [PubMed]

, 10

10. E. Agrell and M. Karlsson, “Power-Efficient Modulation Formats in Coherent Transmission Systems,” J. Lightwave Technol. 27(22), 5115–5126 (2009). [CrossRef]

]. After solving a 4-dimensional sphere packing problem, Karlsson and Agrell [9

9. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009). [CrossRef] [PubMed]

] arrived at a modulation format that provides an asymptotic sensitivity gain of 1.76 dB over BPSK - polarization-switched QPSK (PS-QPSK). PS-QPSK provides maximum power efficiency by transmitting a QPSK symbol in one polarization at a time, with the resultant spectral efficiency limits of 3 bit/s/Hz as opposed to 4 bit/s/Hz for PDM-QPSK and 2 bit/s/Hz for PDM-BPSK.

2. Experimental transmission setup

We used an external cavity laser at 1553 nm with a linewidth of 100 kHz surrounded by 6 DFB-lasers with 50 GHz frequency spacing to compare transmission performance of PDM-BPSK and PS-QPSK. To generate PS-QPSK, an IQ-modulator was driven at 14.3 Gbit/s with two decorrelated 215-1 long pseudo-random binary sequences (PRBS) to initially obtain QPSK. It was followed by a polarization switching stage consisting of two parallel Mach-Zehnder modulators (Fig. 2 (a)
Fig. 2 Transmitter used for WDM transmission of (a) PS-QPSK and (b) PDM-BPSK.
). The MZMs were driven at 14.3 Gbit/s with inverse data patterns, to block one or the other polarization, to generate the PS-QPSK format. In case of PDM-BPSK, the underlying BPSK constellation was generated by driving the two arms of the IQ-modulator at 21.45 Gbit/s with inverse PRBS-15 data patterns. The IQ-modulator was followed by a polarization multiplexing stage with a relative delay of 48 symbols yielding PDM-BPSK (Fig. 2 (b)). In Fig. 2 the resulting constellation diagrams of the two formats are shown, illustrating the correlation between X- (red) and Y-polarization (blue) in the case of PS-QPSK, as opposed to no correlation in the case of PDM-BPSK. For both modulation formats, even and odd channels were subsequently separated with a 50 GHz interleaver and recombined with a relative delay of 10 ns to decorrelate neighboring channels.

The WDM-signal was launched into a single-span recirculating loop with 80.24 km of standard single mode fiber (SMF) and an accumulated chromatic dispersion of 1347 ps/nm per recirculation [12

12. C. Behrens, D. Lavery, D. S. Millar, S. Makovejs, B. C. Thomsen, R. I. Killey, S. J. Savory, and P. Bayvel, "Ultra-long-haul transmission of 7×42.9Gbit/s PS-QPSK and PM-BPSK," in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Mo.2.B.2.

]. The loop was gated with two acousto-optic modulators whose insertion losses, as well as the span loss of 15.4 dB, was compensated for by EDFAs with noise figures of 4.5 dB and a fixed output power of 17 dBm. Variable optical attenuators were used to set the launch power into the span and balance the loop. A Mach-Zehnder filter was employed to flatten the gain profile of the EDFAs and avoid out of band noise accumulation.

The signal was detected with a phase and polarization-diverse coherent receiver using a pair of balanced PINs to receive each quadrature. The local oscillator was an ECL with 100 kHz linewidth whose frequency was tuned to ensure that the frequency offset did not exceed 1 GHz. The signal was digitized with a digital sampling oscilloscope with an electrical bandwidth of 16 GHz and processed offline. After the signal had been de-skewed, normalized and resampled, chromatic dispersion was compensated digitally. For PS-QPSK, a polarization-switched constant modulus algorithm equalizer with least-mean squares updating was used [13

13. D. S. Millar and S. J. Savory, “Blind adaptive equalization of polarization-switched QPSK modulation,” Opt. Express 19(9), 8533–8538 (2011). [CrossRef] [PubMed]

], followed by a modified Viterbi & Viterbi phase recovery [11

11. D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, and S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19(10), 9296–9302 (2011). [CrossRef] [PubMed]

]. In the case of PDM-BPSK, joint equalization and phase-recovery was performed in a similar manner to that described in [14

14. 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]

] for PDM-QPSK.

3. Simulation of the transmission performance

The experimental results obtained were verified by transmission simulations using MATLAB. All 7 co-polarized WDM-channels carried 215 symbols based on different pseudo-random symbol sequences. The limited transmitter bandwidth was emulated with a 5th -order electrical Bessel filter. A 2nd order Gaussian optical filter with a 3dB bandwidth of 40 GHz has been used to model the interleaver frequency response. Laser phase noise was modeled as a Wiener process and the transmitter laser linewidth was set to be 100 kHz, as in the experiments. Residual implementation penalty of the experimental setup was modeled by adding different amounts of noise to the electrical driving signals.

After transmission, the incoming signal was detected with a phase- and polarization diverse digital coherent receiver. The linewidth of the LO was set to 100 kHz and a negligible frequency offset between transmitter and LO-laser was assumed. The limited receiver bandwidth dominated by the bandwidth of the ADCs was modeled with a filter employing measured frequency responses of every channel of the digital sampling oscilloscope used in the experiment [17

17. C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express 19(14), 12879–12884 (2011). [CrossRef] [PubMed]

]. Additional quantization noise was added by simulating ADCs with an effective number of bits equal to 5. Subsequent DSP includes chromatic dispersion compensation, equalization and digital phase estimation as described in Section 2. Monte-Carlo error counting was performed to determine the BER, which serves as the performance metric to determine the achievable reach at a given launch power.

4. Transmission results at 42.9Gbit/s

Figure 3
Fig. 3 Back to back measurements of the bit-error rate with varying OSNR for (a) PDM-BPSK and (b) PS-QPSK.
shows back-to-back measurements of the receiver sensitivity for (a) PDM-BPSK and (b) PS-QPSK. The results are plotted on a double-log scale and fitted linearly to ease comparison between the formats, as well as against theoretical sensitivity limits. Single channel PDM-BPSK shows an implementation penalty of 0.4 dB at BER = 3.8 × 10−3 compared to 0.8 dB for PS-QPSK. Adding more WDM channels to the signal resulted in an additional penalty of 0.2 dB in both cases, which was due to coherent crosstalk induced by neighboring channels. Taking this into account the different implementation penalties result in a reduction of the theoretical sensitivity advantage of PS-QPSK over PDM-BPSK (0.75 dB reduces to 0.4 dB at a BER of 3.8 × 10−3).

The experimental results show lower maximum reach than predicted by the computer simulations, which we attributed to small inaccuracies such as e.g. in EDFA noise figure and nonlinear fiber coefficient, as well as the absence of a loop synchronous polarization scrambler. Furthermore, the loop has to be rebalanced for each launch power, which can affect the amount of noise added per recirculation. All these effects tend to accumulate with an increased number of recirculations, especially if, like in this case, a single span loop is used [12

12. C. Behrens, D. Lavery, D. S. Millar, S. Makovejs, B. C. Thomsen, R. I. Killey, S. J. Savory, and P. Bayvel, "Ultra-long-haul transmission of 7×42.9Gbit/s PS-QPSK and PM-BPSK," in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Mo.2.B.2.

]. However, experimental results and simulations were in good agreement concerning the general trend as well as transmission performance in the linear and nonlinear regimes.

Despite showing similar optimum launch powers of −3.5 dBm, in experiment, and −4 dBm in simulation, PS-QPSK clearly outperformed PDM-QPSK with a maximum reach of 13,640 km compared to 10,350 km, corresponding to an increase of 30% (28% in simulation). However, PDM-BPSK shows a 1-1.5 dB higher optimum launch power, which translated into 14,040 km maximum reach, corresponding to an increase of less than 3% compared to PS-QPSK (29% in simulation).

The improved sensitivity of PS-QPSK with respect to PDM-BPSK observed in the back-to-back measurements translated into a 0.4 dB improvement in the linear region of the reach curve (0.7 dB improvement with respect to PDM-QPSK). On the nonlinear part of the reach curve, PDM-BPSK was ~1.5 dB more resilient towards nonlinearities than PS-QPSK, in both experiment and simulation. However, PDM-QPSK showed a similar penalty of ~1.5 dB and 3 dB in the nonlinear region, compared to PS-QPSK and PDM-BPSK, respectively. We attributed this effect to an increased walk-off (relative to the symbol period) as a result of increasing symbol-rates: 10.7 GBd for PDM-QPSK, 14.3 GBd for PS-QPSK and 21.45 GBd for PDM-BPSK.

In terms of the DSP complexity, it is worth mentioning that the number of FIR-filter taps required to compensate for chromatic dispersion scales with the square of the symbol-rate. Therefore, PDM-BPSK requires an approximately 125% longer FIR-filter than PS-QPSK. For transmission over 170 spans this corresponds to 1498 taps as opposed to 3371 taps [18

18. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]

], which is equivalent to 2048 and 4096 taps when ceiled to the nearest power of two for implementation with the ‘overlap and save’ technique. Furthermore, the lower symbol-rate of PS-QPSK would lead to 33% lower electrical bandwidth requirements for transmitter and receiver-side electronics compared to PDM-BPSK.

5. Conclusions

Acknowledgments

The work described in this paper was carried out with the support of Huawei Technologies, EPSRC, Oclaro, Yokogawa Electric Corporation and The Royal Society.

References and links

1.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).

2.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]

3.

D. G. Foursa, C. R. Davidson, M. Nissov, M. A. Mills, L. Xu, J. X. Cai, A. N. Pilipetskii, Y. Cai, C. Breverman, R. R. Cordell, T. J. Carvelli, P. C. Corbett, H. D. Kidorf, and N. S. Bergano, "2.56 Tb/s (256x10 Gb/s) transmission over 11,000 km using hybrid Raman/EDFAs with 80 nm of continuous bandwidth," in Optical Fiber Communications Conference, A. Sawchuk, ed., Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), paper FC3.

4.

J. Cai, D. Foursa, L. Liu, C. Davidson, Y. Cai, W. Patterson, A. Lucero, B. Bakhshi, G. Mohs, P. Corbett, V. Gupta, W. Anderson, M. Vaa, G. Domagala, M. Mazurczyk, H. Li, M. Nissov, A. Pilipetskii, and N. Bergano, "RZ-DPSK field trial over 13,100 km of installed non slope-matched submarine fibers," in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, (2004), paper PD34.

5.

G. Charlet, M. Salsi, H. Mardoyan, P. Tran, J. Renaudier, S. Bigo, M. Astruc, P. Sillard, L. Provost, and F. Cerou, “Transmission of 81 channels at 40Gbit/s over a transpacific-distance erbium-only link, using PDM-BPSK modulation, coherent detection, and a new large effective area fibre,” in 34th European Conference on Optical Communication, 2008. ECOC 2008 (IEEE,2008), paper Th.3.E.3.

6.

D. Foursa, Y. Cai, J. Cai, C. Davidson, O. Sinkin, B. Anderson, A. Lucero, A. Pilipetskii, G. Mohs, and N. Bergano, "Coherent 40 Gb/s transmission with high spectral efficiency over transpacific distance," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMI4.

7.

C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Nonlinear Distortion in Transmission of Higher Order Modulation Formats,” IEEE Photon. Technol. Lett. 22(15), 1111–1113 (2010). [CrossRef]

8.

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2007).

9.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009). [CrossRef] [PubMed]

10.

E. Agrell and M. Karlsson, “Power-Efficient Modulation Formats in Coherent Transmission Systems,” J. Lightwave Technol. 27(22), 5115–5126 (2009). [CrossRef]

11.

D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, and S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19(10), 9296–9302 (2011). [CrossRef] [PubMed]

12.

C. Behrens, D. Lavery, D. S. Millar, S. Makovejs, B. C. Thomsen, R. I. Killey, S. J. Savory, and P. Bayvel, "Ultra-long-haul transmission of 7×42.9Gbit/s PS-QPSK and PM-BPSK," in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Mo.2.B.2.

13.

D. S. Millar and S. J. Savory, “Blind adaptive equalization of polarization-switched QPSK modulation,” Opt. Express 19(9), 8533–8538 (2011). [CrossRef] [PubMed]

14.

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]

15.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 1995).

16.

F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principil states of polarization in single-mode fibers,” J. Lightwave Technol. 8(8), 1162–1166 (1990). [CrossRef]

17.

C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express 19(14), 12879–12884 (2011). [CrossRef] [PubMed]

18.

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications

ToC Category:
Transmission Systems and Network Elements

History
Original Manuscript: October 3, 2011
Revised Manuscript: November 9, 2011
Manuscript Accepted: November 18, 2011
Published: November 30, 2011

Virtual Issues
European Conference on Optical Communication 2011 (2011) Optics Express

Citation
Carsten Behrens, Domaniç Lavery, David S. Millar, Sergejs Makovejs, Benn C. Thomsen, Robert I. Killey, Seb J. Savory, and Polina Bayvel, "Ultra-long-haul transmission of 7×42.9 Gbit/s PS-QPSK and PDM-BPSK," Opt. Express 19, B581-B586 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-26-B581


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References

  1. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423 (1948).
  2. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001). [CrossRef] [PubMed]
  3. D. G. Foursa, C. R. Davidson, M. Nissov, M. A. Mills, L. Xu, J. X. Cai, A. N. Pilipetskii, Y. Cai, C. Breverman, R. R. Cordell, T. J. Carvelli, P. C. Corbett, H. D. Kidorf, and N. S. Bergano, "2.56 Tb/s (256x10 Gb/s) transmission over 11,000 km using hybrid Raman/EDFAs with 80 nm of continuous bandwidth," in Optical Fiber Communications Conference, A. Sawchuk, ed., Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), paper FC3.
  4. J. Cai, D. Foursa, L. Liu, C. Davidson, Y. Cai, W. Patterson, A. Lucero, B. Bakhshi, G. Mohs, P. Corbett, V. Gupta, W. Anderson, M. Vaa, G. Domagala, M. Mazurczyk, H. Li, M. Nissov, A. Pilipetskii, and N. Bergano, "RZ-DPSK field trial over 13,100 km of installed non slope-matched submarine fibers," in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, (2004), paper PD34.
  5. G. Charlet, M. Salsi, H. Mardoyan, P. Tran, J. Renaudier, S. Bigo, M. Astruc, P. Sillard, L. Provost, and F. Cerou, “Transmission of 81 channels at 40Gbit/s over a transpacific-distance erbium-only link, using PDM-BPSK modulation, coherent detection, and a new large effective area fibre,” in 34th European Conference on Optical Communication, 2008. ECOC 2008 (IEEE,2008), paper Th.3.E.3.
  6. D. Foursa, Y. Cai, J. Cai, C. Davidson, O. Sinkin, B. Anderson, A. Lucero, A. Pilipetskii, G. Mohs, and N. Bergano, "Coherent 40 Gb/s transmission with high spectral efficiency over transpacific distance," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMI4.
  7. C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Nonlinear Distortion in Transmission of Higher Order Modulation Formats,” IEEE Photon. Technol. Lett.22(15), 1111–1113 (2010). [CrossRef]
  8. J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2007).
  9. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express17(13), 10814–10819 (2009). [CrossRef] [PubMed]
  10. E. Agrell and M. Karlsson, “Power-Efficient Modulation Formats in Coherent Transmission Systems,” J. Lightwave Technol.27(22), 5115–5126 (2009). [CrossRef]
  11. D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, and S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express19(10), 9296–9302 (2011). [CrossRef] [PubMed]
  12. C. Behrens, D. Lavery, D. S. Millar, S. Makovejs, B. C. Thomsen, R. I. Killey, S. J. Savory, and P. Bayvel, "Ultra-long-haul transmission of 7×42.9Gbit/s PS-QPSK and PM-BPSK," in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Mo.2.B.2.
  13. D. S. Millar and S. J. Savory, “Blind adaptive equalization of polarization-switched QPSK modulation,” Opt. Express19(9), 8533–8538 (2011). [CrossRef] [PubMed]
  14. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007). [CrossRef] [PubMed]
  15. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 1995).
  16. F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principil states of polarization in single-mode fibers,” J. Lightwave Technol.8(8), 1162–1166 (1990). [CrossRef]
  17. C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express19(14), 12879–12884 (2011). [CrossRef] [PubMed]
  18. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008). [CrossRef] [PubMed]

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