## DSP complexity of mode-division multiplexed receivers |

Optics Express, Vol. 20, Issue 10, pp. 10859-10869 (2012)

http://dx.doi.org/10.1364/OE.20.010859

Acrobat PDF (867 KB)

### Abstract

The complexities of common equalizer schemes are analytically analyzed in this paper in terms of complex multiplications per bit. Based on this approach we compare the complexity of mode-division multiplexed digital signal processing algorithms with different numbers of multiplexed modes in terms of modal dispersion and distance. It is found that training symbol based equalizers have significantly lower complexity compared to blind approaches for long-haul transmission. Among the training symbol based schemes, OFDM requires the lowest complexity for crosstalk compensation in a mode-division multiplexed receiver. The main challenge for training symbol based schemes is the additional overhead required to compensate modal crosstalk, which increases the data rate. In order to achieve 2000 km transmission, the effective modal dispersion must therefore be below 6 ps/km when the OFDM specific overhead is limited to 10%. It is concluded that for few mode transmission systems the reduction of modal delay is crucial to enable long-haul performance.

© 2012 OSA

## 1. Introduction

1. P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express **19**(17), 16680–16696 (2011). [CrossRef] [PubMed]

4. S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-Multiplexed 6×20-GBd QPSK Transmission over 1200-km DGD-Compensated Few-Mode Fiber,” in *National Fiber Optic Engineers Conference*, OSA Technical Digest (Optical Society of America, 2012), paper PDP5C.5.

5. Y. Yung, S. Alam, Z. Li, A. Dhar, D. Giles, I. Giles, J. Sahu, L. Grüner-Nielsen, F. Poletti, and D. Richardson, “First demonstration of multimode amplifier for spatial division multiplexed transmission systems,” in *37th European Conference and Exposition on Optical Communications*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.K.4.

6. N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express **20**(3), 2668–2680 (2012). [CrossRef] [PubMed]

7. R. Ryf, A. Sierra, R. Essiambre, S. Randel, A. Gnauck, C. A. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, D. Peckham, A. McCurdy, and R. Lingle, “Mode-Equalized Distributed Raman Amplification in 137-km Few-Mode Fiber,” in *37th European Conference and Exposition on Optical Communications*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.K.5.

8. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express **19**(17), 16697–16707 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-17-16697. [CrossRef] [PubMed]

7. R. Ryf, A. Sierra, R. Essiambre, S. Randel, A. Gnauck, C. A. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, D. Peckham, A. McCurdy, and R. Lingle, “Mode-Equalized Distributed Raman Amplification in 137-km Few-Mode Fiber,” in *37th European Conference and Exposition on Optical Communications*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.K.5.

_{01}and LP

_{11}was 27 ps/km, after a few months the effective DGD decreased to less than 50 ps for 30 km with the help of cascading two fibers with both 1.5 ns DGD but in one of them LP

_{01}travels faster, in the other one LP

_{11}[4

4. S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-Multiplexed 6×20-GBd QPSK Transmission over 1200-km DGD-Compensated Few-Mode Fiber,” in *National Fiber Optic Engineers Conference*, OSA Technical Digest (Optical Society of America, 2012), paper PDP5C.5.

4. S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-Multiplexed 6×20-GBd QPSK Transmission over 1200-km DGD-Compensated Few-Mode Fiber,” in *National Fiber Optic Engineers Conference*, OSA Technical Digest (Optical Society of America, 2012), paper PDP5C.5.

6. N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express **20**(3), 2668–2680 (2012). [CrossRef] [PubMed]

7. R. Ryf, A. Sierra, R. Essiambre, S. Randel, A. Gnauck, C. A. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, D. Peckham, A. McCurdy, and R. Lingle, “Mode-Equalized Distributed Raman Amplification in 137-km Few-Mode Fiber,” in *37th European Conference and Exposition on Optical Communications*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.K.5.

_{01}, LP

_{11}), it is desired to increase the number of modes to further increase fiber capacity [9

9. C. Koebele, M. Salsi, L. Milord, R. Ryf, C. A. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in *37th European Conference and Exposition on Optical Communications*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

10. B. Inan, B. Spinnler, F. Ferreira, A. P. Lobato Polo, S. Adhikari, V. Sleiffer, D. van den Borne, N. Hanik, and S. L. Jansen, “Equalizer Complexity of Mode Division Multiplexed Coherent Receivers,” in *Optical Fiber Communication Conference*, OSA Technical Digest (Optical Society of America, 2012), paper OW3D.4.

11. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1180–1192 (2010). [CrossRef]

_{21}and LP

_{01}is 6 ps/km for 2000 km of 10 x 10 MIMO transmission.

## 2. Equalizer complexity for few mode fiber

11. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1180–1192 (2010). [CrossRef]

12. F. Ferreira, S. Jansen, P. Monteiro, and H. Silva, “Nonlinear semi-analytical model for simulation of few-mode fiber transmission,” IEEE Photon. Technol. Lett. **24**(4), 240–242 (2012). [CrossRef]

11. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1180–1192 (2010). [CrossRef]

_{CD}), PMD (τ

_{PMD}) and DMD (τ

_{DMD}) can be defined aswhere

*c*is the speed of light,

*D*is the chromatic dispersion parameter,

*d*is the fiber length,

*f*

_{c}is the optical carrier frequency, ∆

*f*is the signal’s spectral bandwidth;where

*p*is the PMD parameter;where χ is the DMD per km, i.e. modal dispersion. For the rest of this section, the block diagrams are depicted for a scenario with five-fold multiplexing each with two polarizations is used, over a three mode fiber (LP

_{01}, LP

_{11}, LP

_{21}). Consequently, the number of tributaries, denoted as ζ, is 10.

### 2.1. Blind equalizers

**16**(5), 1180–1192 (2010). [CrossRef]

*x*,

*n*

_{SC}is the oversampling ration for single carrier (SC),

*T*is inverse of the symbol rate. For FMF, both DMD and PMD delay contribute to DGD.

#### 2.1.1. Time domain equalizer

**16**(5), 1180–1192 (2010). [CrossRef]

^{2}FIR filters and each FIR filter requires

*N*

_{CD}plus

*N*

_{DGD}taps, resulting in ζ

*times (N*

^{2}_{CD}+ N

_{DGD}) complex multiplications. The equalizer gives

*ζ*times log

_{2}(

*M*) output bits where

*M*is the number of points in constellation. As a result a TDE with

*ζ*tributaries havecomplex multiplications per bit.

#### 2.1.2. Hybrid frequency domain/time domain equalizer

*N*in addition to the ζ

*N*complex multiplications with coefficients (

*C’11, …, C’*). The FFT complexity is

_{1010}*N*

_{CD}-1 [11

**16**(5), 1180–1192 (2010). [CrossRef]

*n*

_{sc}to 1 takes places in the TDE part, also reducing the number of useful bits from the FDE part by a factor of

*n*

_{sc}. Thus, the number of useful bits per block on all tributaries is

### 2.2. Training symbol based equalizers

*R*

_{TS}of the TS needs to be as low as possible to limit the TS-overhead, but sufficiently fast in order to react fast enough to channel dynamics. The CP must be long enough to accommodate the impact of CD and DGD in order to avoid intersymbol interference of neighboring symbols at the receiver.

#### 2.2.1. Frequency domain equalizer

**16**(5), 1180–1192 (2010). [CrossRef]

*complex multiplications, their inverse approximately ζ*

^{2}N*complex multiplications [14*

^{3}N14. D. Coppersmith and S. Winograd, “Matrix multiplication via arithmetic progressions,” J. Symbolic Comp. **9**(3), 251–280 (1990). [CrossRef]

*complex multiplications. The complexity of the FDE equalizer can be expressed aswhere*

^{2}N*T*is the time for one frame.

_{f}#### 2.2.2. Orthogonal frequency division multiplex

*N*) to all subcarriers (

_{u}*N*).

#### 2.2.3. Hybrid frequency division multiplex/orthogonal frequency division multiplex

*N*and

_{1}*N*are the FFT sizes of the FDE and OFDM parts respectively,

*n*

_{OFDM}

*is the oversampling of OFDM including the effects of CP and TS overheads derived as where ε*

_{’}_{TS}and ε

_{CP}are the TS and CP overheads respectively. The overheads ε

_{TS}and ε

_{CP}are

*N*

_{TrSpacing}is

*N*

_{Training}and the time for CP is denoted as

*T*

_{CP}.

## 3. Analytical results

*p*, is 0.02 ps/√km. The chromatic dispersion parameter,

*D*, is chosen as 20 ps/nm/km to be compatible with recent publications such as [6

6. N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express **20**(3), 2668–2680 (2012). [CrossRef] [PubMed]

16. P. M. Krummrich, E. Schmidt, W. Weiershausen, and A. Mattheus, Field Trial Results on Statistics of Fast Polarization Changes in Long Haul WDM Transmission Systems,” in *Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference*, Technical Digest (CD) (Optical Society of America, 2005), paper OThT6.

*ζ*, is 10 in Fig. 5. The blind equalizers, TDE and FDE/TDE, use more than 1000 multiplications even for a modal dispersion of 5 ps/km, which is significantly higher compared to TS based equalizers. Most of the multiplications required for FDE/TDE are caused by time domain operations. The efficiency of FDE/TDE is greatly reduced because the modal dispersion is, unlike CD, time variant and therefore cannot be compensated for with the FDE part. The TS based equalizer complexity is significantly lower; however the reach is limited by the maximum allowed overhead. Since the modal dispersion causes the need for a larger CP, the required overhead increases. Among the TS based equalizers, OFDM has the lowest complexity. However, it cannot tolerate more than a modal dispersion of 5.9 ps/km modal dispersion due to the 10% overhead constraint, where the number of complex multiplications per bit for OFDM is only 17.6.The reach of OFDM can be extended by adding the FDE block before it. The FDE block that reduces the required CP would allow the DSP to cope with higher modal dispersion, 11.2 ps/km with higher number of complex multiplications, i.e. 37.5.

*N*and the total of TS and CP overheads are shown in terms of modal dispersion in Fig. 6 for a transmission distance of 2000 km. As the CP increases due to the growing modal dispersion, the sampling rate increases in order to keep the overhead under the maximum value. When the total overhead rises to the maximum value, the FFT size is doubled to lower the overhead. The FFT size becomes 16k for OFDM at the maximum modal dispersion it can tolerate and sampling rate at this point is 47 GS/s. It should be noted that, the FFT size has to be upper limited. For example, for FDE/OFDM and a 2 ps/km modal dispersion, the optimum solution is a 2048 FFT and almost 10% overhead. However, an FFT of higher than 10000 and a overhead of less than 5% would be less optimum due to the fact that not only higher FFT size is less tolerant to phase noise but also due to the increase of the TS overhead.

*37th European Conference and Exposition on Optical Communications*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.K.5.

*N*

_{CD}and

*N*

_{DGD}for FMF increases up to 2276 taps at 2000 km for FMF whereas it does not exceed 1 for SMF where only PMD has to be compensated. The FDE/TDE equalizer complexity is highly dependent on the time domain operations which are determined by τ

_{DMD}and τ

_{PMD}. Since, τ

_{DMD}is 0 for SMF (2 x 2), the FMF results in the much higher FDE/TDE complexity. On the other hand, the complexity of FDE/TDE for SMF is only 12.7 multiplications per bit at 2000 km.

*ζ*, increase. One more time the best TS based (OFDM) and blind equalization (FDE/TDE) techniques are chosen. The transmission distance is 2000 km. The modal dispersion is 5.9 ps/km between the highest and lowest modes since this is the maximum modal dispersion that can be tolerated in order to transmit over 2000 km with OFDM for 10 x 10 case as shown in Fig. 5. In both cases the complexity increases linearly with the number of processed bits, but for FDE/TDE the complex multiplications per bit increases to 10000 as

*ζ*increases to 20 whereas for OFDM it only increases to 28. It should be noted that as

*ζ*increases, it would be more difficult to keep the modal dispersion at 5.9 ps/km.

## 4. Conclusion

_{01}and LP

_{21}is required for 2000 km of 10 x 10 MIMO transmission. The reach of OFDM cannot exceed 689 km again due to the overhead constraint for the modal dispersion of 27 ps/km between LP

_{01}and LP

_{11}. This shows that for few mode transmission systems the reduction of modal delay is essential to enable long-haul performance.

## Acknowledgments

## References and links

1. | P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express |

2. | J. D. Downie, J. Hurley, D. V. Kuksenkov, C. M. Lynn, A. E. Korolev, and V. N. Nazarov, “Transmission of 112 Gb/s PM-QPSK Signals Over up to 635 km of Multimode Optical Fiber,” in |

3. | W. Shieh, “Interaction of Laser Phase Noise with Differential-Mode-Delay in Few-mode Fiber Based MIMO Systems,” in |

4. | S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-Multiplexed 6×20-GBd QPSK Transmission over 1200-km DGD-Compensated Few-Mode Fiber,” in |

5. | Y. Yung, S. Alam, Z. Li, A. Dhar, D. Giles, I. Giles, J. Sahu, L. Grüner-Nielsen, F. Poletti, and D. Richardson, “First demonstration of multimode amplifier for spatial division multiplexed transmission systems,” in |

6. | N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express |

7. | R. Ryf, A. Sierra, R. Essiambre, S. Randel, A. Gnauck, C. A. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, D. Peckham, A. McCurdy, and R. Lingle, “Mode-Equalized Distributed Raman Amplification in 137-km Few-Mode Fiber,” in |

8. | S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express |

9. | C. Koebele, M. Salsi, L. Milord, R. Ryf, C. A. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in |

10. | B. Inan, B. Spinnler, F. Ferreira, A. P. Lobato Polo, S. Adhikari, V. Sleiffer, D. van den Borne, N. Hanik, and S. L. Jansen, “Equalizer Complexity of Mode Division Multiplexed Coherent Receivers,” in |

11. | B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. |

12. | F. Ferreira, S. Jansen, P. Monteiro, and H. Silva, “Nonlinear semi-analytical model for simulation of few-mode fiber transmission,” IEEE Photon. Technol. Lett. |

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

14. | D. Coppersmith and S. Winograd, “Matrix multiplication via arithmetic progressions,” J. Symbolic Comp. |

15. | T. Schenk, |

16. | P. M. Krummrich, E. Schmidt, W. Weiershausen, and A. Mattheus, Field Trial Results on Statistics of Fast Polarization Changes in Long Haul WDM Transmission Systems,” in |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

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

(060.4230) Fiber optics and optical communications : Multiplexing

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 23, 2012

Revised Manuscript: April 20, 2012

Manuscript Accepted: April 23, 2012

Published: April 25, 2012

**Citation**

Beril Inan, Bernhard Spinnler, Filipe Ferreira, Dirk van den Borne, Adriana Lobato, Susmita Adhikari, Vincent A. J. M. Sleiffer, Maxim Kuschnerov, Norbert Hanik, and Sander L. Jansen, "DSP complexity of mode-division multiplexed receivers," Opt. Express **20**, 10859-10869 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-10859

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### References

- P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express19(17), 16680–16696 (2011). [CrossRef] [PubMed]
- J. D. Downie, J. Hurley, D. V. Kuksenkov, C. M. Lynn, A. E. Korolev, and V. N. Nazarov, “Transmission of 112 Gb/s PM-QPSK Signals Over up to 635 km of Multimode Optical Fiber,” in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Tu.5.B.6.
- W. Shieh, “Interaction of Laser Phase Noise with Differential-Mode-Delay in Few-mode Fiber Based MIMO Systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu2C.6.
- S. Randel, R. Ryf, A. Gnauck, M. A. Mestre, C. Schmidt, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, and R. Lingle, “Mode-Multiplexed 6×20-GBd QPSK Transmission over 1200-km DGD-Compensated Few-Mode Fiber,” in National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2012), paper PDP5C.5.
- Y. Yung, S. Alam, Z. Li, A. Dhar, D. Giles, I. Giles, J. Sahu, L. Grüner-Nielsen, F. Poletti, and D. Richardson, “First demonstration of multimode amplifier for spatial division multiplexed transmission systems,” in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.K.4.
- N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express20(3), 2668–2680 (2012). [CrossRef] [PubMed]
- R. Ryf, A. Sierra, R. Essiambre, S. Randel, A. Gnauck, C. A. Bolle, M. Esmaeelpour, P. J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, D. Peckham, A. McCurdy, and R. Lingle, “Mode-Equalized Distributed Raman Amplification in 137-km Few-Mode Fiber,” in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.K.5.
- S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express19(17), 16697–16707 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-17-16697 . [CrossRef] [PubMed]
- C. Koebele, M. Salsi, L. Milord, R. Ryf, C. A. Bolle, P. Sillard, S. Bigo, and G. Charlet, “40km Transmission of Five Mode Division Multiplexed Data Streams at 100Gb/s with low MIMO-DSP Complexity,” in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.
- B. Inan, B. Spinnler, F. Ferreira, A. P. Lobato Polo, S. Adhikari, V. Sleiffer, D. van den Borne, N. Hanik, and S. L. Jansen, “Equalizer Complexity of Mode Division Multiplexed Coherent Receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW3D.4.
- B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron.16(5), 1180–1192 (2010). [CrossRef]
- F. Ferreira, S. Jansen, P. Monteiro, and H. Silva, “Nonlinear semi-analytical model for simulation of few-mode fiber transmission,” IEEE Photon. Technol. Lett.24(4), 240–242 (2012). [CrossRef]
- N. Benvenuto and G. Cherubini, Algorithms for Communications Systems and their Applications (Wiley, 2002).
- D. Coppersmith and S. Winograd, “Matrix multiplication via arithmetic progressions,” J. Symbolic Comp.9(3), 251–280 (1990). [CrossRef]
- T. Schenk, RF Imperfections in High-Rate Wireless Systems (Springer, 2008).
- P. M. Krummrich, E. Schmidt, W. Weiershausen, and A. Mattheus, Field Trial Results on Statistics of Fast Polarization Changes in Long Haul WDM Transmission Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OThT6.

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