OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 10 — May. 7, 2012
  • pp: 10859–10869
« Show journal navigation

DSP complexity of mode-division multiplexed receivers

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  »View Author Affiliations


Optics Express, Vol. 20, Issue 10, pp. 10859-10869 (2012)
http://dx.doi.org/10.1364/OE.20.010859


View Full Text Article

Acrobat PDF (867 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

Single mode fiber (SMF) is the standard for all long haul transmission systems so far but may not be able to meet the explosively increasing capacity demand of optical communication in the near future. One of the possible solutions is to use space division multiplexing (SDM) as this is a dimension which has not been explored yet. There are different ways to achieve SDM transmission: weakly coupled multicore fibers (MCF), strongly coupled MCF, and multimode fibers (MMF). Types of MMF in which only a few modes are supported, i.e., few mode fibers (FMF), have attracted a lot of attention in the recent years [1

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]

3

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.

]. In [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.

], the transmission over 1200 km of differential group delay (DGD) compensated FMF with three-fold mode-multiplexing has been demonstrated. The FMF transmission research is looking into optical amplification as well to achieve longer transmission distances [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.

]. Recently [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]

], used inline amplifiers to transmit over 50 km FMF and [7

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.

] demonstrated transmission with the aid of Raman amplification.

2. Equalizer complexity for few mode fiber

2.1. Blind equalizers

Figure 1
Fig. 1 Block diagram of (a) SC system with TDE (b) SC system with FDE/TDE for 10 x 10 MIMO.
illustrates two common blind equalizers These schemes adaptively update the coefficients of the finite impulse response (FIR) filters in equalizer using feedback. The coefficients are assumed to be updated once per symbol duration [11

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

]. Some of the branches in the butterfly structure are not shown for simplification of the figure.

The minimum numbers of equalizer taps to compensate the CD and DGD are
NCD=τCDTnSC,
(4)
NDGD=τDGDTnSC,
(5)
where x is the ceiling function, gives the smallest integer greater than or equal to x, nSC 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

TDE uses a finite impulse response (FIR) filter to compensate for channel effects. Figure 1(a) depicts a 10 x 10 MIMO TDE. The coefficient update doubles the complexity for the common algorithms like least mean squares, constant modulus or Godard’s algorithm [11

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

]. There are ζ2 FIR filters and each FIR filter requires NCD plus NDGD taps, resulting in ζ2 times (NCD + NDGD) complex multiplications. The equalizer gives ζ times log2(M) output bits where M is the number of points in constellation. As a result a TDE with ζ tributaries have
CTDE=2ζ2(NCD+NDGD)ζlog2(M)=2ζ(NCD+NDGD)log2(M)
(6)
complex multiplications per bit.

2.1.2. Hybrid frequency domain/time domain equalizer

CFDE/TDE=ζN+2ζ(N2log2N)ζlog2M(NNCD+1)nSC+2ζNDGDlog2M=N+2(N2log2N)log2M(NNCD+1)nSC+2ζNDGDlog2M.
(7)

The Eq. (7) shows that the CD compensation part complexity is independent of number of tributaries.

2.2. Training symbol based equalizers

The key of TS based transmission is blockwise transmission. The data are sent in blocks, which can be referred to as frames as well. Each subsequent block is separated with a guardband, often referred to as cyclic prefix (CP). The TSs are used to calculate equalizer coefficients at the receiver. The CP and TS are inserted at transmitter for the TS based equalizers as shown in Fig. 2
Fig. 2 Block diagram of single carrier system with FDE for 10 x 10 MIMO.
and both add overhead to the total data rate. With each TS the the coefficients are updated at the receiver. The repetition rate RTS 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

The block diagram of FDE is shown in Fig. 2. The complexity calculation for one frame of FDE includes the 2ζ FFT complexities, calculation of channel matrices and their inverse at every channel estimation update and the multiplication of the received frame with the inverse channel matrix [11

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

]. The calculation of channel matrices result in ζ2N complex multiplications, their inverse approximately ζ3N complex multiplications [14

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

] and multiplication of the received frame with the inverse channel matrix requires ζ2N complex multiplications. The complexity of the FDE equalizer can be expressed as
CFDE=2ζ(N2log2N)+ζ2N+ζ2N+ζ3N1/RTSTfζNlog2MnSC=2(N2log2N)+ζN+ζN+ζ2N1/RTSTfNlog2MnSC.
(8)
where Tf is the time for one frame.

2.2.2. Orthogonal frequency division multiplex

Figure 3
Fig. 3 OFDM block diagram for 10 x 10 MIMO.
depicts OFDM. For OFDM, the IFFT is done at transmitter side rather than at the receiver, but other than that it has many common properties with the single carrier FDE. The complexity of OFDM is calculated similarly as FDE,

COFDM=2(N2log2N)+ζNu+ζNu+ζ2Nu1/RTSTfNulog2M.
(9)

The oversampling in OFDM is the ratio of modulated subcarriers (Nu) to all subcarriers (N).

2.2.3. Hybrid frequency division multiplex/orthogonal frequency division multiplex

The CD is statically compensated for FDE/OFDM architecture, similar to the FDE/TDE architecture shown in Fig. 4
Fig. 4 FDE/OFDM block diagram for 10 x 10 MIMO.
. As a result the CP compensates only for DMD and PMD, and becomes shorter. The complexity of FDE/OFDM is simply a sum of the separate complexity of FDE (for CD compensation) as in Eq. (7) and OFDM (for DMD and PMD compensation),
CFDE/OFDM=N1+2(N12log2N1)log2M(N1NCD+1)nOFDM'+2(N2log2N)+ζNu+ζNu+ζ2Nu1/RTSTfNulog2M,
(10)
where N1 and N are the FFT sizes of the FDE and OFDM parts respectively, nOFDM is the oversampling of OFDM including the effects of CP and TS overheads derived as
nOFDM=NuN
(11)
nOFDM'=nOFDM(1+εTS)(1+εCP),
(12)
where εTS and εCP are the TS and CP overheads respectively. The overheads εTS and εCP are

εTS=NTrainingNTrSpacing,
(13)
εCP=TCPTf.
(14)

The number of TS used in one training block spacing NTrSpacing is NTraining and the time for CP is denoted as TCP.

3. Analytical results

The parameters chosen for the analytical analysis are as follows. The net bit rate per mode is 100 Gb/s using polarization multiplexed QPSK. The FEC overhead is chosen as 11% and the combined maximum overhead for TS and CP is 10% for TS based approach. The oversampling factors for both single and multi-carrier schemes are 1.5. The PMD parameter, 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]

]. The TS based equalization technique uses one TS for FMF, which is valid under the assumption that with subcarrier multiplexing one can find orthogonal symbols [15

15. T. Schenk, RF Imperfections in High-Rate Wireless Systems (Springer, 2008).

]. Consequently, one TS is sufficient for the MIMO scenario and the TS overhead is kept as low as possible. The channel estimation is updated every 10 μs so that TSs can dynamically react to changes in optical channel [16

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.

], however, the optimum repetition rate for FMF should still be investigated. The complexity is calculated in a two-dimensional matrix, one variable is the sampling rate and the other is the size of the FFT. The maximum sampling rate is limited to 60 GS/s, compatible with the sampling rates of commercially available current analog-to-digital and digital-to-analog converters. For each configuration, we find the optimum sampling rate resulting in minimum complexity satisfying the overhead constraint.

As explained in Section 2.2, the time shift between tributaries caused by CD and DMD is compensated with the CP for the TS based equalizers. From Eq. (8) and Eq. (9), it is deduced that the FFT size is the dominating factor on complexity and the number of modes has less impact. As a result, the complexity of a TS based equalizer for FMF is not significantly different than that for SMF. On the other hand, OFDM cannot exceed a transmission distance of 689 km due to the 10% overhead constraint. The number of complex multiplications per bit at the maximum reach is and 15.6 for 6 x 6 and 19.7 for 10 x 10 case.

4. Conclusion

Acknowledgments

This work was partially supported by the European Communities 7th Framework Program under grant agreement 228033 (MODE-GAP).

References and links

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 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]

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.

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


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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]
  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. Express20(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. Express19(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.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited