## A self-coherent receiver for detection of PolMUX coherent signals |

Optics Express, Vol. 20, Issue 19, pp. 21413-21433 (2012)

http://dx.doi.org/10.1364/OE.20.021413

Acrobat PDF (1357 KB)

### Abstract

A self-coherent receiver capable of demultiplexing PolMUX-signals without an external polarization controller is presented. Training sequences are introduced to estimate the polarization rotation, and a decision feedback recursive algorithm mitigates the random walk of the recovered field. The concept is tested for a PolMUX-DQPSK modulation format where one polarization carries a normal DQPSK signal while the other polarization is encoded as a progressive phase-shift DQPSK signal. An experimental demonstration of the scheme for a 112 Gbit/s PolMUX-DQPSK signal is presented.

© 2012 OSA

## 1. Introduction

1. C. R. S. Fludger, T. Duthel, D. Van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. **26**(1), 64–72 (2008). [CrossRef]

2. X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express **16**(2), 792–803 (2008). [CrossRef] [PubMed]

8. I. Tselniker, M. Nazarathy, S.-B. Ezra, J. Li, and J. Leuthold, “Self-coherent complex field reconstruction with in-phase and quadrature delay detection without a direct-detection branch,” Opt. Express **20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

9. J. M. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. **10**(2), 259–272 (2004). [CrossRef]

8. I. Tselniker, M. Nazarathy, S.-B. Ezra, J. Li, and J. Leuthold, “Self-coherent complex field reconstruction with in-phase and quadrature delay detection without a direct-detection branch,” Opt. Express **20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

2. X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express **16**(2), 792–803 (2008). [CrossRef] [PubMed]

8. I. Tselniker, M. Nazarathy, S.-B. Ezra, J. Li, and J. Leuthold, “Self-coherent complex field reconstruction with in-phase and quadrature delay detection without a direct-detection branch,” Opt. Express **20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

10. D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).

**20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

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

## 2. PolMUX transmission and self-coherent reception

_{x}, Tx

_{y}) that carry two independent data streams,

*S*and

_{x}*S*. The signals generated by the two transmitters are orthogonally polarized. Their electric fields are denoted with

_{y}*E*and

_{x}*E*. The two signals are superimposed in a polarization beam combiner (PBC) to form the polarization multiplexed (PolMUX) signal, which is transmitted along a fiber, experiencing a random change of the state of polarization (SOP). The channel is modeled as a matrix

_{y}**C**including arbitrary polarization rotations

**R**

_{n}, arbitrary order of polarization mode dispersion (

**PMD**

_{n}

**)**, and arbitrary phase offset

**P**, as detailed in Section 2.1. In the polarization diverse self-coherent receiver, the signal is split by a polarization beam splitter (PBS) in two orthogonal linear polarizations, the output fields of which are denoted with

*E*and

_{x}*E*as generated by the random SOP change along the fiber. Both polarizations are processed in a self-coherent receiver, the optical front-end (OFE) of which can be implemented by either of two following schemes.

_{y}**Delay interferometer front-end.**In Fig. 1(b) two DIs with balanced detectors are shown. The input of each DI is either

**Optical hybrid front-end.**An equivalent alternative scheme is shown in Fig. 1(c) where a 2 × 4 optical hybrid is used similarly to a coherent receiver. In lieu of the local oscillator, the incoming signal is delayed by τ, and this copy is fed into the 2 × 4 optical hybrid in order to interfere with the original signal. Multiple variations of 2 × 4 optical hybrids exist, implemented by discrete couplers, by star-couplers [19

19. C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Monolithic demodulator for 40-Gbs DQPSK using a star coupler,” J. Lightwave Technol. **24**(1), 171–174 (2006). [CrossRef]

20. L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90° hybrids based on Silicon-on insulator 4×4 waveguide coupler,” IEEE Photon. Technol. Lett. **21**(3), 143–145 (2009). [CrossRef]

_{x}and Tx

_{y}signals and summarize the challenges that need to solve. At the end, the principle of our transmitter and receiver will be presented.

### 2.1. Channel model

*E*and

_{x}*E*represent the linearly polarized electric field components at the transmitter Tx

_{y}_{x}and Tx

_{y}. The two signals are combined at a PBC whose linear eigenstates are aligned with the polarization axes of

*E*and

_{x}*E*(blue and red coordinate systems). After the PBC, a fiber is attached. The fiber is modeled by numerous birefringent slices all of which have a different orientation of the fast and the slow axes and a different PMD. The first slice of the fiber model has linear eigenstates

_{y}*p*(

**p**arallel) and

*s*(

**s**enkrecht, perpendicular), which are rotated by an angle of

*θ*

_{1}with respect to

*E*and

_{x}*E*. The signals have to be remapped to a new coordinate system. This operation can be described by a Jones matrix

_{y}**R**

_{1}. The last slice of the fiber model has linear eigenstates

*p*′ and

*s*′. At the end of the fiber a PBS with linear polarization eigenstates

**P**as shown in Eq. (2). The rotation angle between the eigenstates of PBS and last fiber slice is

*θ*

_{n}. The coordinate system transformation is described by matrix

**R**

_{n}.

**C**[2

2. X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express **16**(2), 792–803 (2008). [CrossRef] [PubMed]

**R**

_{n}, and arbitrary order of

**PMD**, and phase offset

_{n}**P**,

**PMD**

_{n}represents the first-order PMD within the fiber. Assuming a time dependency exp(j

*ω t*) with optical angular frequency

*ω*, the differential phase shift between the two principal states of polarizations in a signal bandwidth Δ

*ω*/ (2π) is

*τ*

_{DGDn}. Additional effects could have been also included.

### 2.2. Challenges for signal recovery

_{x}and Tx

_{y}signals are undergoing SOP change in the channel. As a consequence the signals from Tx

_{x}and Tx

_{y}are mixed in the receiver. The SCD receiver needs to recover

*E*and

_{x}*E*from

_{y}*E*and

_{x}*E*. There are several challenges that need to be solved for such a SCD receiver.

_{y}**R**

_{1},

**PMD**

_{1}, and

**P**are all identity matrices. The eigenstates of PBS with matrix

**R**

_{2}are rotated with respect to the eigenstates of PBC, so that the transmitted field components

*θ*

_{2}= −45°, see Fig. 2(a) . We findAs an example, we assume QPSK where

*I*, in-phase) and imaginary part (

*Q*, quadrature phase) of the complex envelope of the carrier exp(j

*ω t*), Fig. 2(b). As an issue with the reception scheme one may notice the zeros in the Rx constellation diagrams. The zeros result from a destructive interference between

*E*and

_{x}*E*when carrying identical symbols. These zeros result in outages of the field reconstruction for

_{y}**C**in the next section and Appendix B.

### 2.3. Transmitter with differential encoding and training sequence for channel estimation

*A*(

*n*) at discrete times

*t*=

_{n}*n*τ at multiples

*n*of the symbol period τ [21

21. N. Sigron, I. Tselniker, and M. Nazarathy, “Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD),” Opt. Express **20**(3), 1981–2003 (2012). [CrossRef] [PubMed]

*S*(

*n*) = [1, j, −1, 1, −j…] and

*A*(0) = 1, we get

*A*(

*n*) = [1, j, −j, −j, −1…].

*A*(

*n*) is then modulated on an optical carrier. In a polarization multiplexed system we convey two signal streams

*A*(

_{x}*n*) and

*A*(

_{y}*n*) on the two orthogonal SOP, say, linear polarizations in

*x*and

*y*-direction. The optical signals after the modulation are denoted

### 2.4. Self-coherent receiver with decision feedback

*S*(

_{x,y}*n*). The OFE of the self-coherent receiver processes the transmitted signal

*x'*or

*y'*by interfering them with their delayed copy as shown in Fig. 1. For simplicity, we replaced the SCD Rx, i.e. the mixed analog-digital circuit of the Rx (in Fig. 1) by an equivalent digital circuit (see Fig. 4 ). In Fig. 4, we take it for granted that a DSP unit transforms the analog inputs

*t*=

*t*=

_{n}*n*τ into digital quantities

*x** denotes the complex conjugate of quantity

*x*. It should be noted that |

*A*(

_{x,y}*n*− 1)| = 1 can be chosen for signals

*S*(

_{x,y}*n*) with constant modulus such as for DQPSK. Looking at Eq. (6) we see that with this normalization

*u*(

_{x,y}*n*) =

*S*(

_{x,y}*n*), which means an ideal DQPSK detection. No polarization and field recovery algorithm is needed.

*x*and

*y*, as described by the channel model of Eq. (2). The overall system is represented by the equivalent digital scheme in Fig. 5 .

*S*and

_{x}*S*. However, these symbols are no longer simply obtained at the two DI outputs, due to polarization mixing. The challenge is to recover the fields

_{y}**20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

*x*. By repeatedly applying Eq. (8) we can recursively recover the signal field at sampling times

*t*once we have an initial estimate

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

*S*and

_{x}*S*,

_{y}*S*(

_{x}*n*) and

*S*(

_{y}*n*) may be derived for any differentially encoding modulation format including QAM, and not only for constant-modulus signals.

**20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

**20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

*g**,

*g*,

**20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

**20**(14), 15452–15473 (2012). [CrossRef] [PubMed]

**C**, and then make a decision

**C**and introducing a delay by one bit. The resulting

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

**C**. During the channel estimation, the initial symbols

*A*(8), which are translated into transmitted field quantities

_{x,y}### 2.5. Field outages caused by polarization crosstalk

*E*

_{x}_{,}

*in the*

_{y}*x*and

*y*-direction, respectively. After transmission, the fields

**C**and one polarization state only (i. e.

*E*and

_{x}*E*. In this case, if for example

_{y}_{.}, see Eq. (3). Now the quantities

*E*, Fig. 9 right column. This could be done with an additional clocked phase modulator. The resulting DQPSK phases for the symbols

_{y}*S*are 45°, 135°, −135° and −45° [22

_{y}22. X. Wei, A. H. Gnauck, D. M. Gill, X. Liu, U.-V. Koc, S. Chandrasekhar, G. Raybon, and J. Leuthold, “Optical pi/2-DPSK and its tolerance to filtering and polarization-mode dispersion,” IEEE Photon. Technol. Lett. **15**(11), 1639–1641 (2003). [CrossRef]

*S*, Fig. 9 left column. Looking at Fig. 9 and assuming that

_{x}*n*th estimates may be still in error, however, after a maximum of two erroneously detected symbols the error propagation stops and the algorithm turns back to normal operation.

## 3. Experimental setup and results

24. M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. **36**(5), 605–612 (1988). [CrossRef]

^{−9}[25

25. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photon. Technol. Lett. **24**(1), 61–63 (2012). [CrossRef]

^{5}symbols) has been used for the BER evaluation. For polarization states ‘D’ and ‘E’, the BER at OSNR 16dB is anomalously high. This could be due to the failure of the clock recovery algorithm at low OSNR.

26. A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory **29**(4), 543–551 (1983). [CrossRef]

9. J. M. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. **10**(2), 259–272 (2004). [CrossRef]

1. C. R. S. Fludger, T. Duthel, D. Van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. **26**(1), 64–72 (2008). [CrossRef]

## 4. Conclusion

## Appendix A: Signal processing of *E*(*t*) by delay interferometers

*E*(

*t*).

*E*(

*t*) therefore given at the constructive and destructive ports areIn the photodiodes the fields are converted into photo currents that are proportional to the square of the field magnitude,

*x*. After the balanced photodiode receiver, the differential output current isThis operation is performed for the in-phase (I in Fig. 1(b)) as well as for the quadrature phase DI (Q in Fig. 1(b)). Because of the π/2 phase offset, the photocurrents

*t*=

_{n}*n*τ, we can also write this equation as

## Appendix B: Channel estimation with training sequences

*A*(8) and

_{x}*A*(8) can be any symbol from the transmitted constellation. The preamble with a starting zero serves as a uniquely identifiable symbol sequence. For convenience we set

_{y}*E*=

_{x,y}*A*, i. e., we omit encoding the symbols onto an optical carrier which does not change our channel estimation process. At the receiver, we have

_{x,y}*C*, and the estimation

**C**results from Eq. (18),

**C**, its estimation

*n*= 9 can be correctly recovered. After the decision circuit (which is introduced because of practical reasons),

*C*

_{12},

*C*

_{21}→ 0, or if the polarization states are interchanged

*C*

_{11},

*C*

_{22}→ 0,In this case,

*E*(8) and

_{x}*E*(8), or they are equal to the cross-polarized transmitted fields

_{y}*E*(8) and

_{y}*E*(8). The subsequent fields

_{x}*E*

_{x}_{,}

*(9),*

_{y}*E*

_{x}_{,}

*(10),*

_{y}*…*can then be recovered as described previously.

## Acknowledgment

## References and links

1. | C. R. S. Fludger, T. Duthel, D. Van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. |

2. | X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express |

3. | N. Kikuchi, K. Mandai, K. Sekine, and S. Sasaki, “Incoherent 32-level optical multilevel signaling technologies,” J. Lightwave Technol. |

4. | J. Zhao, M. E. McCarthy, and A. D. Ellis, “Electronic dispersion compensation using full optical-field reconstruction in 10Gbit/s OOK based systems,” Opt. Express |

5. | J. Li, K. Worms, P. Vorreau, D. Hillerkuss, A. Ludwig, R. Maestle, S. Schuele, U. Hollenbach, J. Mohr, W. Freude, and J. Leuthold, “Optical vector signal analyzer based on differential direct detection,” in Proc. of IEEE Photonics Society (LEOS Annual Meeting) 2009 (Belek-Antalya, Turkey), Paper TuA4 (2009). |

6. | J. Li, K. Worms, R. Maestle, D. Hillerkuss, W. Freude, and J. Leuthold, “Free-space optical delay interferometer with tunable delay and phase,” Opt. Express |

7. | J. Li, C. Schmidt-Langhorst, R. Schmogrow, D. Hillerkuss, M. Lauermann, M. Winter, K. Worms, C. Schubert, C. Koos, W. Freude, and J. Leuthold, “Self-coherent receiver for PolMUX coherent signals,” in Proc. Optical Fiber Commun. Conf. (OFC)/Natl. Fiber Optic Eng. Conf. (NFOEC), paper OWV5 (2011). |

8. | I. Tselniker, M. Nazarathy, S.-B. Ezra, J. Li, and J. Leuthold, “Self-coherent complex field reconstruction with in-phase and quadrature delay detection without a direct-detection branch,” Opt. Express |

9. | J. M. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. |

10. | D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005). |

11. | D. van den Borne, S. L. Jansen, E. Gottwald, P. M. Krummrich, G. D. Khoe, and H. de Waardt, “1.6-b/s/Hz spectrally efficient transmission over 1700 km of SSMF using 40 × 85.6-Gb/s POLMUX-RZ-DQPSK,” J. Lightwave Technol. |

12. | A. Gnauck, G. Charlet, P. Tran, P. Winzer, C. Doerr, J. Centanni, E. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals,” J. Lightwave Technol. |

13. | M. Yagi, S. Satomi, and S. Ryu, “Field trial of 160-Gb/s, polarization-division multiplexed RZ-DQPSK transmission system using automatic polarization control,” in Proc. Optical Fiber Commun. Conf. (OFC)/Natl. Fiber Optic Eng. Conf. (NFOEC), Feb. 2008, paper OTuT7 (2008). |

14. | B. Koch, R. Noé, V. Mirvoda, D. Sandel, V. Filsinger, and K. Puntsri, “40-krad/s polarization tracking in 200-Gb/s PDM-RZ-DQPSK transmission over 430 km,” IEEE Photon. Technol. Lett. |

15. | C. R. Doerr and L. Chen, “Monolithic PDM-DQPSK receiver in silicon,” in Proc. of Eur. Conf. Optical Communication (ECOC 2010), Paper PD3.6 (2010). |

16. | S. Chandrasekhar, X. Liu, A. Konczykowska, F. Jorge, J. Dupuy, and J. Godin, “Direct detection of 107-Gb/s polarization-multiplexed RZ-DQPSK without optical polarization demultiplexing,” IEEE Photon. Technol. Lett. |

17. | R. Nagarajan, J. Rahn, M. Kato, J. Pleumeekers, D. Lambert, V. Lal, H.-S. Tsai, A. Nilsson, A. Dentai, M. Kuntz, R. Malendevich, J. Tang, J. Zhang, T. Butrie, M. Raburn, B. Little, W. Chen, G. Goldfarb, V. Dominic, B. Taylor, M. Reffle, F. Kish, and D. Welch, “10 Channel, 45.6 Gb/s per Channel, polarization-multiplexed DQPSK, InP receiver photonic integrated circuit,” J. Lightwave Technol. |

18. | S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express |

19. | C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Monolithic demodulator for 40-Gbs DQPSK using a star coupler,” J. Lightwave Technol. |

20. | L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90° hybrids based on Silicon-on insulator 4×4 waveguide coupler,” IEEE Photon. Technol. Lett. |

21. | N. Sigron, I. Tselniker, and M. Nazarathy, “Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD),” Opt. Express |

22. | X. Wei, A. H. Gnauck, D. M. Gill, X. Liu, U.-V. Koc, S. Chandrasekhar, G. Raybon, and J. Leuthold, “Optical pi/2-DPSK and its tolerance to filtering and polarization-mode dispersion,” IEEE Photon. Technol. Lett. |

23. | R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. |

24. | M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. |

25. | R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photon. Technol. Lett. |

26. | A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.5060) Fiber optics and optical communications : Phase modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: July 17, 2012

Revised Manuscript: August 20, 2012

Manuscript Accepted: August 21, 2012

Published: September 4, 2012

**Citation**

Jingshi Li, Rene Schmogrow, David Hillerkuss, Philipp C. Schindler, Moshe Nazarathy, Carsten Schmidt-Langhorst, Shalva-Ben Ezra, Igor Tselniker, Christian Koos, Wolfgang Freude, and Juerg Leuthold, "A self-coherent receiver for detection of
PolMUX coherent signals," Opt. Express **20**, 21413-21433 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-19-21413

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### References

- C. R. S. Fludger, T. Duthel, D. Van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol.26(1), 64–72 (2008). [CrossRef]
- X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express16(2), 792–803 (2008). [CrossRef] [PubMed]
- N. Kikuchi, K. Mandai, K. Sekine, and S. Sasaki, “Incoherent 32-level optical multilevel signaling technologies,” J. Lightwave Technol.26(1), 150–157 (2008). [CrossRef]
- J. Zhao, M. E. McCarthy, and A. D. Ellis, “Electronic dispersion compensation using full optical-field reconstruction in 10Gbit/s OOK based systems,” Opt. Express16(20), 15353–15365 (2008). [CrossRef] [PubMed]
- J. Li, K. Worms, P. Vorreau, D. Hillerkuss, A. Ludwig, R. Maestle, S. Schuele, U. Hollenbach, J. Mohr, W. Freude, and J. Leuthold, “Optical vector signal analyzer based on differential direct detection,” in Proc. of IEEE Photonics Society (LEOS Annual Meeting) 2009 (Belek-Antalya, Turkey), Paper TuA4 (2009).
- J. Li, K. Worms, R. Maestle, D. Hillerkuss, W. Freude, and J. Leuthold, “Free-space optical delay interferometer with tunable delay and phase,” Opt. Express19(12), 11654–11666 (2011). [CrossRef] [PubMed]
- J. Li, C. Schmidt-Langhorst, R. Schmogrow, D. Hillerkuss, M. Lauermann, M. Winter, K. Worms, C. Schubert, C. Koos, W. Freude, and J. Leuthold, “Self-coherent receiver for PolMUX coherent signals,” in Proc. Optical Fiber Commun. Conf. (OFC)/Natl. Fiber Optic Eng. Conf. (NFOEC), paper OWV5 (2011).
- I. Tselniker, M. Nazarathy, S.-B. Ezra, J. Li, and J. Leuthold, “Self-coherent complex field reconstruction with in-phase and quadrature delay detection without a direct-detection branch,” Opt. Express20(14), 15452–15473 (2012). [CrossRef] [PubMed]
- J. M. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron.10(2), 259–272 (2004). [CrossRef]
- D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
- D. van den Borne, S. L. Jansen, E. Gottwald, P. M. Krummrich, G. D. Khoe, and H. de Waardt, “1.6-b/s/Hz spectrally efficient transmission over 1700 km of SSMF using 40 × 85.6-Gb/s POLMUX-RZ-DQPSK,” J. Lightwave Technol.25(1), 222–232 (2007). [CrossRef]
- A. Gnauck, G. Charlet, P. Tran, P. Winzer, C. Doerr, J. Centanni, E. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals,” J. Lightwave Technol.26(1), 79–84 (2008). [CrossRef]
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