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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 24010–24017
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Adaptive frequency-domain equalization for the transmission of the fundamental mode in a few-mode fiber

Neng Bai, Cen Xia, and Guifang Li  »View Author Affiliations


Optics Express, Vol. 20, Issue 21, pp. 24010-24017 (2012)
http://dx.doi.org/10.1364/OE.20.024010


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Abstract

We propose and experimentally demonstrate single-carrier adaptive frequency-domain equalization (SC-FDE) to mitigate multipath interference (MPI) for the transmission of the fundamental mode in a few-mode fiber. The FDE approach reduces computational complexity significantly compared to the time-domain equalization (TDE) approach while maintaining the same performance. Both FDE and TDE methods are evaluated by simulating long-haul fundamental-mode transmission using a few-mode fiber. For the fundamental mode operation, the required tap length of the equalizer depends on the differential mode group delay (DMGD) of a single span rather than DMGD of the entire link.

© 2012 OSA

1. Introduction

The exponential growth of the internet requires a drastic increase of capacity of optical fiber communication systems. However, the capacity of conventional optical transmission systems based on the single-mode fiber (SMF) has almost reached to the nonlinear Shannon limit. To further increase the capacity, few-mode fiber (FMF) transmission systems have been proposed. With a much larger effective area, nonlinear impairments in FMF transmission systems are reduced in comparison with SMF transmission, enabling higher-capacity for long-haul transmission. Recently, long-haul transmission in the fundamental mode of a FMF has proven to be feasible [1

1. F. Yaman, N. Bai, B. Zhu, T. Wang, and G. Li, “Long distance transmission in few-mode fibers,” Opt. Express 18(12), 13250–13257 (2010). [CrossRef] [PubMed]

,2

2. F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express 18(20), 21342–21349 (2010). [CrossRef] [PubMed]

]. This approach can be called fundamental mode operation (FMO) of FMF transmission. Due to the multimode nature of the FMF, one of the main impairments of FMO is multi-path interference (MPI) [3

3. J. D. Downie, J. E. 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,” Opt. Express 19(26), B363–B369 (2011). [CrossRef] [PubMed]

]. To reduce MPI, several optical solutions have been proposed and demonstrated. Center launch into the FMF has been shown to be able to selectively excite fundamental mode. Also, the FMF can be designed to support only two mode groups and provide a large enough effective index difference between the two mode groups to suppress inter-mode coupling. However, those constraints on FMF design eventually limit the effective area of FMF.

In the paper, instead of suppressing inter-mode coupling using pure optical techniques, MPI is compensated using digital signal processing (DSP)-based adaptive equalization in the electronic domain at the receiver. This approach enables more flexibility in fiber design to allow a larger number of modes and thus larger effective areas. DSP can also track the temporal variation of the fiber and adaptively optimize its performance to improve system robustness.

This paper is organized as follows: Section 2 describes the theory and complexity of SC-FDE for FMO. Section 3 presents performance analysis for both TDE and FDE in a simulated long haul FMF transmission link. In section 4, experimental verification of proposed SC-FDE is provided. Finally, section 5 concludes the paper.

2. Theory

Figure 1
Fig. 1 Block diagram of SC-FDE
shows the schematic of SC-FDE. {y(k)} and represent the input and output signal vectors. To process the input signal at 2 samples per symbol, {y(k)}is first divided to the even and odd tributaries as in [8

8. M. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers,” Opt. Express 19(13), 12789–12798 (2011). [CrossRef] [PubMed]

]. After parallelization and fast Fourier transform (FFT), {yod(k),yev(k)} are converted to the frequency domain and multiplied by {Wod(k),Wev(k)}which are the two inverted channel sub-filters. The overlap-save method is applied to perform linear convolution in the frequency domain. The overlap rate defined by the ratio of block length and filter length is set to be 2 as optimum [9

9. S. Haykin, Adaptive filter theory, 4th ed. (Prentice-Halll, 2001), Chap. 7.

]. By calculating incremental adjustments from gradient estimation, inverted channel sub-filter weights approach the optimum after a stochastic adaptation process. Gradient constraint condition is applied to enforce an accurate calculation of linear convolution. The error signal calculation depends on what type of equalization algorithm is selected. In the paper, the constant modulus algorithm (CMA) is chosen due to its simplicity. The weights of sub-filters are updated at the symbol rate. It should be noted that in a practical environment, the speed of temporal variation of the mode coupling characteristics in the fiber is much lower than the symbol rate. As a reference, for a submarine fiber cable, polarization fluctuation frequency is less than 200Hz [10

10. Y. Namihira, Y. Horiuchi, S. Ryu, K. Mochizuki, and H. Wakabayashi, “Dynamic polarization fluctuation characteristics of optical fiber submarine cables under various environmental conditions,” J. Lightwave Technol. 6(5), 728–738 (1988). [CrossRef]

] while the proposed filters are adapted at tens of GHz. Therefore, temporal variations of mode coupling can be tracked by the adaptive equalizer described here. In contrast to TDE, calculation such as correlation and convolution can be simplified to be multiplication in FDE. Additional computation for conversion between the time and frequency domain can be implemented using FFT algorithm whose complexity is only logarithm with block size. The total complexity (CP) of the algorithm can be measured by the number of complex multiplication per symbol per mode. The CPs for FDE and TDE can be expressed as
CPFDE=6log(LFDE)+10
(1)
CPTDE=2LTDE+2
(2)
where and are filter lengths of FDE and TDE, respectively.

3. Simulation for long-haul FMF transmission

Long-haul transmission simulation results are shown in Fig. 3
Fig. 3 Q2 factor Vs. OSNR.
and Fig. 4
Fig. 4 Q2 factor Vs. distance and the constellation diagrams for two Q2 values are also shown on the right hand side.
. Simulations for 30 × 100km transmission at different OSNR levels were performed. Figure 3 illustrates the result curve. The performance improvement due to adaptive DMGD/MPI equalization grows as OSNR increases, as shown in Fig. 3. Figure 4 demonstrates Q2 factor as a function of distance ranging from 100km to 5000km. Noise loading at the receiver was used to fix the OSNR at 17dB. Without DMGD equalization, system performance degrades rapidly as the transmission distance increases due to accumulated MPIs. With equalization, the performance increases as much as 7 dB in terms of Q2 factor. For all distance, both TDE and FDE have total 256 taps. At the same performance, FDE saves 88.7% computational load compared to TDE.

4. Experiment

To experimentally demonstrate SC-FDE, we use a 1 km step-index few-mode fiber with a core diameter of 13.1μm. The FMF effectively guides 2 spatial mode groups, LP01 and LP11 at 1550nm. The effective area of the fiber is 113μm2. Although only single span transmission is performed, according to section 3, for FDE or TDE, multi-span transmission can be compensated using equalizer with the same filter length as that for a single span.

4.1 Impulse response and DMGD

4.2 Transmission experiment

The transmission experimental setup is illustrated in Fig. 6
Fig. 6 Transmission experiment setup
. A 10 Gbaud/s BPSK signal was generated by using an amplitude modulator and a pattern generator. Both ends of the FMF were butt-coupled with SMFs, in the same way as in the impulse response measurement. A high precision variable attenuator and a post-amplifier were used to adjust the optical signal-to-noise ratio (OSNR) at the coherent receiver. The signal was then sent to a 90 degree hybrid followed by two photo-detectors measuring the real and imaginary parts of the complex signal. Finally, the electric waveforms were fed into a real-time oscilloscope with a 40GHz sampling rate. 5 × 105 samples were then recorded and processed offline.

As we observed in section 4.1, due to the relatively short transmission distance and low inter-mode coupling, distributed mode coupling are negligible in the fiber. To emulate multipath interference, the SMF was intentionally offset several microns to excite both LP01 and LP11 modes. The offset launch condition is equivalent to a discrete mode coupling at the beginning of the FMF. At the output end of FMF, the FMF-SMF butt coupling was also misaligned to receive powers from both the LP01 and LP11 modes. In offline DSP, both adaptive TDE and FDE were applied after clock recovery to compare the performance as well as efficiency of these two approaches. In order to compensate DMGD, the equalizers with a total tap length of 128 were used for both TDE and FDE. Due to the fact that the symbol rate for experiment is lower than that in the simulation, the total tap length is half that in the simulation. Figure 7
Fig. 7 Q2 Vs OSNR and the constellation diagrams for two Q2 values are also shown on the right hand side
shows Q2 factor as a function of OSNR at the receiver. For back-to-back measurements, center launch and offset launch without DMGD equalization, only a 16 taps adaptive finite impulse response (FIR) filter was applied to equalize the CD or other impairments such as the frequency response of modulator driver and real time oscilloscope (RTO). Due to MPI, offset launch suffered high penalty compared to center launch case. At low OSNR, the performance of offset launching with equalization is approximately equal to center launching which verifies that both TDE and FDE effectively reduced the impact of MPI. Moreover, according to Eqs. (1) and (2), the computational complexity of FDE is only 20% of TDE.

In Fig. 8
Fig. 8 Typical sub-filter (odd) tap weights for FDE.
, the complex values of a frequency domain sub-filter tap weights are plotted in the time domain. It can be observed that two distinct peaks which agree well with the impulse response measured in Fig. 5 under offset launching condition. The left main peak corresponds to the signal launched into LP01 mode while the right weak peak relates to signal coupled to LP11 mode at the beginning of the fiber. Two signal components propagate at different group velocities. The temporal separation between two dominant peaks (~3800ps) is very close to the DMGD we previously measured.

5. Conclusion

An SC-FDE algorithm for mitigating MPI in the fundamental-mode transmission in a FMF is proposed and experimentally demonstrated. It is shown that SC-FDE significantly reduces the computational complexity compared to TDE while maintaining similar equalizing performances. The FDE algorithm potentially enables enhanced the transmission capacity using ultra large effective area FMF with MPI.

References

1.

F. Yaman, N. Bai, B. Zhu, T. Wang, and G. Li, “Long distance transmission in few-mode fibers,” Opt. Express 18(12), 13250–13257 (2010). [CrossRef] [PubMed]

2.

F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express 18(20), 21342–21349 (2010). [CrossRef] [PubMed]

3.

J. D. Downie, J. E. 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,” Opt. Express 19(26), B363–B369 (2011). [CrossRef] [PubMed]

4.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-Division Multiplexing Over 96 km of Few-Mode Fiber Using Coherent 6 × 6 MIMO Processing,” J. Lightwave Technol. 30(4), 521–531 (2012). [CrossRef]

5.

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]

6.

B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. J. M. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express 20(10), 10859–10869 (2012). [CrossRef] [PubMed]

7.

N. Bai and G. Li, “Adaptive Frequency Domain Equalization for Mode-Division Multiplexed Transmission,” in IEEE Summer Topical Conference, Seattle, Paper MC4.3 (2012).

8.

M. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers,” Opt. Express 19(13), 12789–12798 (2011). [CrossRef] [PubMed]

9.

S. Haykin, Adaptive filter theory, 4th ed. (Prentice-Halll, 2001), Chap. 7.

10.

Y. Namihira, Y. Horiuchi, S. Ryu, K. Mochizuki, and H. Wakabayashi, “Dynamic polarization fluctuation characteristics of optical fiber submarine cables under various environmental conditions,” J. Lightwave Technol. 6(5), 728–738 (1988). [CrossRef]

11.

F. Yaman, E. Mateo, and T. Wang, “Impact of Modal Crosstalk and Multi-Path Interference on Few-Mode Fiber Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1D.2.

12.

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 European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 24, 2012
Revised Manuscript: June 23, 2012
Manuscript Accepted: June 23, 2012
Published: October 4, 2012

Citation
Neng Bai, Cen Xia, and Guifang Li, "Adaptive frequency-domain equalization for the transmission of the fundamental mode in a few-mode fiber," Opt. Express 20, 24010-24017 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-24010


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References

  1. F. Yaman, N. Bai, B. Zhu, T. Wang, and G. Li, “Long distance transmission in few-mode fibers,” Opt. Express18(12), 13250–13257 (2010). [CrossRef] [PubMed]
  2. F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express18(20), 21342–21349 (2010). [CrossRef] [PubMed]
  3. J. D. Downie, J. E. 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,” Opt. Express19(26), B363–B369 (2011). [CrossRef] [PubMed]
  4. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-Division Multiplexing Over 96 km of Few-Mode Fiber Using Coherent 6 × 6 MIMO Processing,” J. Lightwave Technol.30(4), 521–531 (2012). [CrossRef]
  5. 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]
  6. B. Inan, B. Spinnler, F. Ferreira, D. van den Borne, A. Lobato, S. Adhikari, V. A. J. M. Sleiffer, M. Kuschnerov, N. Hanik, and S. L. Jansen, “DSP complexity of mode-division multiplexed receivers,” Opt. Express20(10), 10859–10869 (2012). [CrossRef] [PubMed]
  7. N. Bai and G. Li, “Adaptive Frequency Domain Equalization for Mode-Division Multiplexed Transmission,” in IEEE Summer Topical Conference, Seattle, Paper MC4.3 (2012).
  8. M. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers,” Opt. Express19(13), 12789–12798 (2011). [CrossRef] [PubMed]
  9. S. Haykin, Adaptive filter theory, 4th ed. (Prentice-Halll, 2001), Chap. 7.
  10. Y. Namihira, Y. Horiuchi, S. Ryu, K. Mochizuki, and H. Wakabayashi, “Dynamic polarization fluctuation characteristics of optical fiber submarine cables under various environmental conditions,” J. Lightwave Technol.6(5), 728–738 (1988). [CrossRef]
  11. F. Yaman, E. Mateo, and T. Wang, “Impact of Modal Crosstalk and Multi-Path Interference on Few-Mode Fiber Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1D.2.
  12. 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 European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.C.3.

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