## 6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization |

Optics Express, Vol. 19, Issue 17, pp. 16697-16707 (2011)

http://dx.doi.org/10.1364/OE.19.016697

Acrobat PDF (1683 KB)

### Abstract

Mode-division multiplexing over 33-km few-mode fiber is investigated. It is shown that 6×6 MIMO processing can be used to almost completely compensate for crosstalk and intersymbol interference due to mode coupling in a system that transmits uncorrelated 28-GBaud QPSK signals on the six spatial and polarization modes supported by a novel few-mode fiber.

© 2011 OSA

## 1. Introduction

1. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol. **28**, 662–701 (2010). [CrossRef]

2. P. J. Winzer, “Energy-efficient optical transport capacity scaling through spatial multiplexing,” IEEE Photon. Technol. Lett. **23**, 851–853 (2011). [CrossRef]

3. P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express (to be published). [PubMed]

4. A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, and B. Jalali, “Coherent optical MIMO (COMIMO),” J. Light-wave Technol. **23**, 2410–2419 (2005). [CrossRef]

9. C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2x100Gb/s, over 40km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express (to be published). [PubMed] [PubMed]

10. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB10.

10. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in *Optical Fiber Communication Conference*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB10.

## 2. Experimental setup

### 2.1. Signal generation

### 2.2. Few-mode fiber

_{01}mode as well as the two-times degenerate LP

_{11}mode, subsequently referred to as the LP

_{11a}and the LP

_{11b}modes. The FMF has a depressed cladding index profile with a normalized frequency of

*V*≈ 5. The index profile was optimized in order to minimize and equalize the differential group delay (DGD) to less than 60 ps/km across the C-band and to effectively cut off the LP

_{21}and LP

_{02}modes. At 1550 nm, a loss of 0.21 dB/km was measured for both LP

_{01}and LP

_{11}modes, and the effective areas of the LP

_{01}and LP

_{11}modes were calculated to be approximately 155

*μ*m

^{2}and 320

*μ*m

^{2}, respectively.

_{01}mode or the LP

_{11}

*mode was launched, and the intensity profile at the fiber end facet was captured with an InGaAs infrared camera (Note that some pixels of the camera were malfunctioning). For the LP*

_{a}_{01}mode the image profile was found to be independent of polarization or fiber arrangement. When one of the LP

_{11}modes was launched, a linear combination of LP

_{11a}and LP

_{11b}was observed after propagation, and by moving the fiber, e.g., by using an arrangement of loops similar to a manual polarization controller, it was possible to generate intensity profiles similar to the expected theoretical LP

_{11}mode profiles [see Figs. 2(b) and 2(c)]. During these measurements, strong polarization dependence of the coupling between the two degenerate LP

_{11}modes was evident. Note that the arrangement of loops is only used while recording the intensity profiles with the infrared camera and not in the further measurements reported. Without the loops random linear mode combinations are captured. The crosstalk between the LP

_{01}and the LP

_{11}modes after 33-km fiber was fluctuating over time in a range of −15 to −20 dB, indicating a clear mode separation even over longer distances. In contrast, the two LP

_{11}modes are continuously mixing inside the fiber as a result of being linear combinations of the “true” fiber modes. In particular, the LP

_{01}mode corresponds to the HE

_{11}mode that can be linearly polarized either horizontally or vertically. The LP

_{11}modes are linear combinations of the TE

_{01}mode, the TM

_{01}mode, and the two times degenerate HE

_{21}mode. For a more detailed discussion of the fiber modes and their mixing properties, we refer to [11, 12].

### 2.3. Mode multiplexer

*μ*m. These collimated beams are then combined using beam splitters. Mode selectivity is achieved using phase plates. The phase plates are made of 0.7-mm thick Borosilicate glass, and the phase structure (a

*π*phase jump between two half planes) was etched using a photolithographic process. A similar principle has been previously described in [13

13. W. Q. Thornburg, B. J. Corrado, and X. D. Zhu, “Selective launching of higher-order modes into an optical fiber with an optical phase shifter,” Opt. Lett. **19**, 454–456 (1994). [CrossRef] [PubMed]

13. W. Q. Thornburg, B. J. Corrado, and X. D. Zhu, “Selective launching of higher-order modes into an optical fiber with an optical phase shifter,” Opt. Lett. **19**, 454–456 (1994). [CrossRef] [PubMed]

*f*

_{1}and

*f*

_{2}with focal lengths of 75 mm and 3.9 mm, respectively. As the MMUX design is reciprocal, the same device can also be used as mode demultiplexer. In this case the SMFs act as mode filters [15

15. O. Wallner, W. R. Leeb, and P. J. Winzer, “Minimum length of a single-mode fiber spatial filter,” J. Opt. Soc. Am. A **19**, 2445–2448 (2002). [CrossRef]

_{01}, the LP

_{11a}, and LP

_{11b}modes, respectively. The theoretically minimum coupling loss of this configuration is 5.5 dB for all three spatial modes. Crosstalk induced by the two MMUXs was measured by launching the LP

_{01}mode and measuring the power at both LP

_{11}outputs. The crosstalk, defined as the power measured at one of the two LP

_{11}ports divided by the power measured at the LP

_{01}port of the receiving MMUX was below −28 dB for both LP

_{11}modes. Thus a strong mode selectivity of the MMUX is confirmed. Further details on the MMUX design and performance are given in [16].

### 2.4. Receivers

## 3. System identification

_{01}and the LP

_{11}modes propagate with different group velocities, crosstalk and intersymbol-interference (ISI) spreading over multiple symbols can occur. Crosstalk builds up if light is coupled from one mode to another and remains there upon detection. ISI is induced if this crosstalk is coupled back to the original mode after some amount of propagation in a mode with different group velocity. This effect is similar to polarization mode dispersion (PMD) and can be fully compensated using linear MIMO equalization as long as mode dependent loss (MDL), the analogon to polarization dependent loss (PDL) in SMF, is negligible. The effects of PMD in SMFs are well understood today [18

18. J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA **97**, 4541–4550 (2000). [CrossRef] [PubMed]

*a priori*knowledge of the complex transmit pattern, the channel impulse response

**h**= [

*h*

_{0},

*h*

_{1},...,

*h*

_{2N−1}]

*can be estimated using the least-mean square (LMS) algorithm by minimizing the error*

^{T}*k*the estimate

**ĥ**

*of*

_{k}**h**is updated according to [20

20. N. Benvenuto and G. Cherubini, *Algorithms for Communications Systems and their Applications* (Wiley, 2002). [CrossRef]

*x*is the

_{k}*k*-th received sample and

**s**

*= [*

_{k}*a*, 0,

_{k}*a*

_{k}_{+1}, 0, ... ,

*a*

_{k+N−1}, 0]

*is a vector of*

^{T}*N*twofold oversampled complex transmit symbols

*a*that contribute to

_{k}*x*;

_{k}*μ*is the LMS adaptation gain.

_{Pol}) of 23 dB over the full pattern period of 2048 symbols for the first data set with 0 dBm optical power launched into the FMF per spatial mode (OSNR

_{Pol}is defined as the optical signal power of one polarization and spatial mode divided by the noise power within 0.1 nm per spatial and polarization mode). Six groups of peaks can be identified for each waveform. By correlating the pattern delays described in Sec. 2.1, individual transmit modes and thus all 36 impulse responses can be identified. Strong coupling between all modes is evident for this data set, as expected from the suboptimal settings of the MMUXs. For the received LP

_{01}modes (RX LP

_{01x}and RX LP

_{01y}) one strong peak and several lower peaks with a spacing of 16 symbols is observed. This spacing corresponds to the delay inserted at the transmitter to decorrelate the two quadratures. We hence identify these side peaks as artefacts from using a delayed copy for modulating I and Q components. The origin and impact of this artefact will be discussed in more detail in a separate paper [21]. Furthermore, two strong peaks that are spaced about 40 symbols apart are observed for the received LP

_{11b}modes (RX LP

_{11bx}and RX LP

_{11by}). This delay does not correspond to a multiple of the quadrature delay and is therefore attributed to a suboptimal adjustment of the two MMUXs separated by the 33 km of fiber. Thus, signal parts from the LP

_{01}as well as the LP

_{11}modes are detected. From the 40-symbol separation of the peaks, a DGD of 1.43 ns is concluded while 2.0 ns were expected from the fiber’s nominal modal dispersion of 60 ps/km. Before recording the second data set the adjustment of the mode multiplexer and demultiplexer was carefully optimized and the FMF input power per spatial mode was increased to 4 dBm. The resulting impulse responses are shown in Fig. 4. It can clearly be seen that the cross-coupling between the LP

_{01}mode and the LP

_{11}modes is considerably reduced, while the LP

_{11a}and LP

_{11b}modes are still strongly coupled. The artificial side peaks due to the quadrature delay are still evident.

## 4. MIMO equalization

*M*uncoupled SDM waveguides using PDM to a full 2

*M*× 2

*M*MIMO system on

*M*coupled waveguides results in a complexity increase of 4

*M*

^{2}/(4

*M*) =

*M*. Figure 5 shows a block-diagram of the network of 6×6 adaptive linear equalizers used to approach the minimum-mean-square error independently for the received soft symbols

*y*(

_{m}*k*) according to Here,

**w**

*(*

_{m,n}*k*) is the

*L*-element column vector of equalizer coefficients that undo coupling between the

*m*-th transmitted mode and the

*n*-th received mode at the

*k*-th symbol time-step and

**x**

*(*

_{n}*k*) is the vector of

*T*/2 spaced received samples contributing to

*y*(

_{m}*k*). For each of the six channels, carrier phase estimation (CPE) of

*ϕ*(

_{m}*k*) is independently performed using the fourth power algorithm [22

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

^{6}bits. For each of the 36 equalizers the estimation of the optimum coefficients is continuously updated using the LMS algorithm [20

20. N. Benvenuto and G. Cherubini, *Algorithms for Communications Systems and their Applications* (Wiley, 2002). [CrossRef]

*d*(

_{m}*k*) =

*â*(

_{m}*k*) is the

*k*-th received symbol of the

*m*-th MDM channel after hard decision, and Δ is a delay for estimating the carrier phase

*ϕ*(

_{m}*k*) over causal and anti-causal components. Figure 6 shows a detailed block diagram of the MIMO equalization algorithm described above.

^{5}symbols in order to initialize the coefficients [23

23. M. Kuschnerov, M. Chouayakh, K. Piyawanno, B. Spinnler, E. de Man, P. Kainzmaier, M. S. Alfiad, A. Napoli, and B. Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. **2**, 387–403 (2010). [CrossRef]

*a priori*knowledge of the transmitted symbols

*d*(

_{m}*k*) =

*a*(

_{m}*k*) is used and the carrier phase

*ϕ*(

_{m}*k*) is estimated from the averaged deviation with respect to the absolute phase. The algorithm’s capability to switch between data-aided and decision-directed modes of operation is indicated by the switch in Fig. 6. In order to realize this algorithm in a practical transmission system, a training pattern is required during start-up.

## 5. Transmission performance

*μ*and the averaging length and delay Δ for CPE are optimized for each point. Figure 7(a) shows the minimum achieved BERs vs. OSNR

_{Pol}using the first data set (Fig. 3) with suboptimal adjustment of the mode couplers and

*L*= 120 taps per equalizer (filled symbols). As a reference, the BERs for the back-to-back measurement of each of the six receiver channels without PDM and SDM are plotted as open symbols. Variations of these curves characterize variations of the receiver hardware (optical 90-degree hybrid, balanced photodetectors, and oscilloscope front-end). Furthermore, the theoretical limits for 28-GBaud QPSK with (dashed) and without (solid) correcting for I/Q correlation are shown. For low signal-to-noise ratios and if the equalizer length exceeds the quadrature delay some correlation is present in the signal, and the LMS algorithm can exploit this additional I/Q correlation information, leading to a reduction of the theoretical BER limit. For further discussion we refer to [21]. The results of Fig. 7(a) show that even with a suboptimal alignment of the mode couplers, BERs below 10

^{−3}can be achieved with penalties of about 2 dB for the LP

_{11}modes and about 4 dB for the two polarizations of the LP

_{01}mode, respectively.

*L*= 120 taps per equalizer. In this case the transmission penalties are considerably reduced to about 1 dB for all modes. This result demonstrates the effectiveness of MIMO equalization and the importance of accurate excitation and reception of all individual modes. Furthermore, Fig. 7(c) shows the results for the second data set with

*L*= 80 taps per equalizer. Figure 7(d) reveals that large penalties with an error floor for the LP

_{01}mode occur for

*L*= 20. We contribute this to the fact that the LP

_{01}mode (group delay

*τ*

_{01}) suffers from residual uncompensated crosstalk caused by the two LP

_{11}modes (group delay

*τ*

_{11}) if

*L*≲ |

*τ*

_{01}−

*τ*

_{11}|/(2

*T*). In contrast, each of the LP

_{11}modes receives crosstalk from one mode experiencing

*τ*

_{11}and one mode experiencing

*τ*

_{01}. Hence, one interfering mode is compensated even for small values of

*L*, resulting in a reduced crosstalk. Finally, the required OSNR

_{Pol}for a BER of 10

^{−3}is plotted vs. the number of equalizer taps in Fig. 7(e), showing that almost optimum performance is achieved for 100 taps corresponding to an equalizer length that exceeds the maximum DGD of 1.43 ns found in Sec. 3.

## 6. Conclusions

_{11}modes but also to some extent between the LP

_{11}modes and the LP

_{01}mode. A maximum DGD of 1.43 ns for the 33-km long FMF is found, corresponding to a required length of

*L*> 80

*T*/2-spaced taps, for each of the 36 equalizers at a symbol rate of 28 GBaud. Our experiments prove the principle of scaling capacity using MDM in FMF in combination with MIMO signal processing. However, a host of open questions, such as, efficient amplification schemes, optimal fiber design, hardware efficient MIMO equalization schemes, and the impact of fiber nonlinearity remain to be answered.

## References and links

1. | R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol. |

2. | P. J. Winzer, “Energy-efficient optical transport capacity scaling through spatial multiplexing,” IEEE Photon. Technol. Lett. |

3. | P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express (to be published). [PubMed] |

4. | A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, and B. Jalali, “Coherent optical MIMO (COMIMO),” J. Light-wave Technol. |

5. | C. P. Tsekrekos and A. M. J. Koonen, “Mitigation of impairments in MGDM transmission with mode-selective spatial filtering,” IEEE Photon. Technol. Lett. |

6. | S. Schöllmann, N. Schrammar, and W. Rosenkranz, “Experimental realisation of 3 x 3 MIMO system with mode group diversity multiplexing limited by modal noise,” in |

7. | N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in |

8. | A. Al Amin, A. Li, X. Chen, and W. Shieh, “LP |

9. | C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2x100Gb/s, over 40km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express (to be published). [PubMed] [PubMed] |

10. | R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in |

11. | D. Marcuse, |

12. | H. Kogelnik and P. J. Winzer are preparing a manuscript to be called “Modal birefringence in weakly guiding fibers.” |

13. | W. Q. Thornburg, B. J. Corrado, and X. D. Zhu, “Selective launching of higher-order modes into an optical fiber with an optical phase shifter,” Opt. Lett. |

14. | W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP |

15. | O. Wallner, W. R. Leeb, and P. J. Winzer, “Minimum length of a single-mode fiber spatial filter,” J. Opt. Soc. Am. A |

16. | R. Ryf, C. Bolle, and J. von Hoyningen-Huene, “Optical coupling components for spatial multiplexing in multimode fibers,” in Proceedings of European Conf. Opt. Commun . (2011), paper Th.12.B.1 (to be published). |

17. | P. J. Winzer, A. H. Gnauck, G. Raybon, M. Schnecker, and P. J. Pupalaikis, “56-Gbaud PDM-QPSK: coherent detection and 2,500-km transmission,” in |

18. | J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA |

19. | C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. (to be published). |

20. | N. Benvenuto and G. Cherubini, |

21. | A. Sierra, S. Randel, P. J. Winzer, R. Ryf, and R.-J. Essiambre are preparing a manuscript to be called “Analysis of test sequences for systems with MMSE-based equalization.” |

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

23. | M. Kuschnerov, M. Chouayakh, K. Piyawanno, B. Spinnler, E. de Man, P. Kainzmaier, M. S. Alfiad, A. Napoli, and B. Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. |

**OCIS Codes**

(030.4070) Coherence and statistical optics : Modes

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

(060.2400) Fiber optics and optical communications : Fiber properties

(060.4230) Fiber optics and optical communications : Multiplexing

**ToC Category:**

Mode-Division Multiplexing

**History**

Original Manuscript: June 10, 2011

Revised Manuscript: August 3, 2011

Manuscript Accepted: August 9, 2011

Published: August 15, 2011

**Virtual Issues**

Space Multiplexed Optical Transmission (2011) *Optics Express*

**Citation**

Sebastian Randel, Roland Ryf, Alberto Sierra, Peter J. Winzer, Alan H. Gnauck, Cristian A. Bolle, René-Jean Essiambre, David W. Peckham, Alan McCurdy, and Robert Lingle, "6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization," Opt. Express **19**, 16697-16707 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-16697

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### References

- R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol. 28, 662–701 (2010). [CrossRef]
- P. J. Winzer, “Energy-efficient optical transport capacity scaling through spatial multiplexing,” IEEE Photon. Technol. Lett. 23, 851–853 (2011). [CrossRef]
- P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express (to be published). [PubMed]
- A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, and B. Jalali, “Coherent optical MIMO (COMIMO),” J. Light-wave Technol. 23, 2410–2419 (2005). [CrossRef]
- C. P. Tsekrekos and A. M. J. Koonen, “Mitigation of impairments in MGDM transmission with mode-selective spatial filtering,” IEEE Photon. Technol. Lett. 20, 1112–1114 (2008). [CrossRef]
- S. Schöllmann, N. Schrammar, and W. Rosenkranz, “Experimental realisation of 3 x 3 MIMO system with mode group diversity multiplexing limited by modal noise,” in National Fiber Optic Engineers Conference , OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWA68.
- N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in Optical Fiber Communication Conference , OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWA4.
- A. Al Amin, A. Li, X. Chen, and W. Shieh, “LP01/LP11 dual-mode and dual-polarisation CO-OFDM transmission on two-mode fibre,” Electron. Lett. 47, 606–608 (2011). [CrossRef]
- C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2x100Gb/s, over 40km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express (to be published). [PubMed]
- R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R. Essiambre, P. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conference , OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB10.
- D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).
- H. Kogelnik and P. J. Winzer are preparing a manuscript to be called “Modal birefringence in weakly guiding fibers.”
- W. Q. Thornburg, B. J. Corrado, and X. D. Zhu, “Selective launching of higher-order modes into an optical fiber with an optical phase shifter,” Opt. Lett. 19, 454–456 (1994). [CrossRef] [PubMed]
- W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng. 45, 074602 (2006).
- O. Wallner, W. R. Leeb, and P. J. Winzer, “Minimum length of a single-mode fiber spatial filter,” J. Opt. Soc. Am. A 19, 2445–2448 (2002). [CrossRef]
- R. Ryf, C. Bolle, and J. von Hoyningen-Huene, “Optical coupling components for spatial multiplexing in multimode fibers,” in Proceedings of European Conf. Opt. Commun . (2011), paper Th.12.B.1 (to be published).
- P. J. Winzer, A. H. Gnauck, G. Raybon, M. Schnecker, and P. J. Pupalaikis, “56-Gbaud PDM-QPSK: coherent detection and 2,500-km transmission,” in Proceedings of European Conf. Opt. Commun. , (VDE-Verlag, 2009), paper PD2.7.
- J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000). [CrossRef] [PubMed]
- C. Koebele, M. Salsi, G. Charlet, and S. Bigo, “Nonlinear effects in mode division multiplexed transmission over few-mode optical fiber,” IEEE Photon. Technol. Lett. (to be published).
- N. Benvenuto and G. Cherubini, Algorithms for Communications Systems and their Applications (Wiley, 2002). [CrossRef]
- A. Sierra, S. Randel, P. J. Winzer, R. Ryf, and R.-J. Essiambre are preparing a manuscript to be called “Analysis of test sequences for systems with MMSE-based equalization.”
- A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29, 543–551 (1983). [CrossRef]
- M. Kuschnerov, M. Chouayakh, K. Piyawanno, B. Spinnler, E. de Man, P. Kainzmaier, M. S. Alfiad, A. Napoli, and B. Lankl, “Data-aided versus blind single-carrier coherent receivers,” IEEE Photon. J. 2, 387–403 (2010). [CrossRef]

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