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

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References

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  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]
  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 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Tu.5.B.6.
  3. 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.
  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., “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]
  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]
  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]
  13. N. Benvenuto and G. Cherubini, Algorithms for Communications Systems and their Applications (Wiley, 2002).
  14. D. Coppersmith and S. Winograd, “Matrix multiplication via arithmetic progressions,” J. Symbolic Comp. 9(3), 251–280 (1990).
    [CrossRef]
  15. T. Schenk, RF Imperfections in High-Rate Wireless Systems (Springer, 2008).
  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.

2012 (2)

2011 (2)

2010 (1)

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

1990 (1)

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

Bai, N.

Bickham, S.

Bolle, C. A.

Coppersmith, D.

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

Essiambre, R. J.

Ferreira, F.

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]

Foschini, G. J.

Gnauck, A. H.

Huang, Y. K.

Ip, E.

Jansen, S.

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]

Lau, A. P.

Li, G.

Li, M. J.

Liñares, J.

Lingle, R.

Lu, C.

Luo, Y.

Man Chung, K.

Mateo, E.

McCurdy, A.

Monteiro, P.

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]

Montero, C.

Moreno, V.

Peckham, D. W.

Peng, G. D.

Prieto, X.

Randel, S.

Ryf, R.

Sierra, A.

Silva, H.

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]

Spinnler, B.

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

Tam, H. Y.

Ten, S.

Tse, V.

Wang, T.

Winograd, S.

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

Winzer, P. J.

Yaman, F.

IEEE J. Sel. Top. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (1)

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]

J. Symbolic Comp. (1)

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

Opt. Express (3)

Other (10)

N. Benvenuto and G. Cherubini, Algorithms for Communications Systems and their Applications (Wiley, 2002).

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.

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.

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.

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.

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Figures (8)

Fig. 1
Fig. 1

Block diagram of (a) SC system with TDE (b) SC system with FDE/TDE for 10 x 10 MIMO.

Fig. 2
Fig. 2

Block diagram of single carrier system with FDE for 10 x 10 MIMO.

Fig. 3
Fig. 3

OFDM block diagram for 10 x 10 MIMO.

Fig. 4
Fig. 4

FDE/OFDM block diagram for 10 x 10 MIMO.

Fig. 5
Fig. 5

Complex multiplications per bit in terms of modal dispersion for 2000 km and 10 x 10 MIMO. Total overhead for cyclic prefix and training symbols is maximum 10%.

Fig. 6
Fig. 6

The sampling rate, FFT size and total OFDM overhead vs. modal dispersion for 10 x 10 MIMO and 2000 km transmission.

Fig. 7
Fig. 7

Complex multiplications per bit in terms of distance for few mode and single mode fiber.

Fig. 8
Fig. 8

Complex multiplications per bit in terms of number of tributaries for few mode fiber.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

τCD=cfc2|Dd|Δf,
τPMD=pd,
τDMD=χd,
NCD=τCDTnSC,
NDGD=τDGDTnSC,
CTDE=2ζ2(NCD+NDGD)ζlog2(M)=2ζ(NCD+NDGD)log2(M)
CFDE/TDE=ζN+2ζ(N2log2N)ζlog2M(NNCD+1)nSC+2ζNDGDlog2M=N+2(N2log2N)log2M(NNCD+1)nSC+2ζNDGDlog2M.
CFDE=2ζ(N2log2N)+ζ2N+ζ2N+ζ3N1/RTSTfζNlog2MnSC=2(N2log2N)+ζN+ζN+ζ2N1/RTSTfNlog2MnSC.
COFDM=2(N2log2N)+ζNu+ζNu+ζ2Nu1/RTSTfNulog2M.
CFDE/OFDM=N1+2(N12log2N1)log2M(N1NCD+1)nOFDM'+2(N2log2N)+ζNu+ζNu+ζ2Nu1/RTSTfNulog2M,
nOFDM=NuN
nOFDM'=nOFDM(1+εTS)(1+εCP),
εTS=NTrainingNTrSpacing,
εCP=TCPTf.

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