Abstract

We experimentally demonstrate adaptive variable-forgetting-factor (VFF) recursive-least-square frequency-domain equalization (RLS-FDE) for mode-division multiplexing. The VFF-RLS-FDE algorithm improves convergence speed as transmission distance increases. For MDM transmission over a 1,000-km few-mode fiber, the convergence speed was increased by 18.7 times in comparison with LMS-FDE. In the meantime, the convergence error performance of VFF-RLS is also much superior to LMS while fixed-forgetting-factor RLS has a 0.2 dB penalty compared with LMS. The proposed VFF-RLS algorithm achieves better performances than conventional RLS in terms of convergence speed and convergence error.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. N. Bai and G. Li, “Adaptive Frequency-Domain Equalization for Mode-Division Multiplexed Transmission,” IEEE Photonics Technol. Lett. 24(21), 1918–1921 (2012).
    [Crossref]
  2. 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]
  3. N. Bai, E. Ip, M. Li, T. Wang, and G. Li, “Experimental Demonstration of Adaptive Frequency-domain Equalization for Mode-Division Multiplexed Transmission,” in Proc. OFC/NFOEC (2013), paper OM2C.5.
    [Crossref]
  4. S. Ö. Arık, D. Askarov, and J. M. Kahn, “Adaptive Frequency-Domain Equalization in Mode-Division Multiplexing Systems,” J. Lightwave Technol. 32(10), 1841–1852 (2014).
    [Crossref]
  5. Z. Pan, Y. Weng, X. He, and J. Wang, “Adaptive frequency-domain equalization and MIMO signal processing in mode division multiplexing systems using few-mode fibers,” in Signal Processing in Photonic Communications (OSA, 2016), paper SpW2G–1.
  6. Z. Yang, J. Zhao, N. Bai, E. Ip, T. Wang, and G. Li, “Experimental demonstration of adaptive recursive least square frequency-domain equalization for long-distance mode-division multiplexed transmission,” in 2015 European Conference on Optical Communication (ECOC, 2015), paper 15636015.
    [Crossref]
  7. C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Process. Lett. 15, 597–600 (2008).
    [Crossref]
  8. J. Wang, “A variable forgetting factor RLS adaptive filtering algorithm,” in 2009 3rd IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications (IEEE, 2009), paper 11021933.
    [Crossref]
  9. D. J. Park, B. E. Jun, and J. H. Kim, “Fast tracking RLS algorithm using novel variable forgetting factor with unity zone,” Electron. Lett. 27(23), 2150–2151 (1991).
    [Crossref]
  10. S. Haykin, Adaptive Filter Theory (Prentice-Hall, 2002), Chap. 9.
  11. N. Benvenuto, Algorithms for Communications Systems and their Applications (John Wiley, 2002), Chap. 3.
  12. N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
    [Crossref]
  13. E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

2014 (1)

2012 (2)

2008 (1)

C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Process. Lett. 15, 597–600 (2008).
[Crossref]

1991 (1)

D. J. Park, B. E. Jun, and J. H. Kim, “Fast tracking RLS algorithm using novel variable forgetting factor with unity zone,” Electron. Lett. 27(23), 2150–2151 (1991).
[Crossref]

Adhikari, S.

Arik, S. Ö.

Askarov, D.

Bai, N.

N. Bai and G. Li, “Adaptive Frequency-Domain Equalization for Mode-Division Multiplexed Transmission,” IEEE Photonics Technol. Lett. 24(21), 1918–1921 (2012).
[Crossref]

Ben Yoo, S. J.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Benesty, J.

C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Process. Lett. 15, 597–600 (2008).
[Crossref]

Benitez, A. V.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Bennett, K.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Chen, H.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Ciochina, S.

C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Process. Lett. 15, 597–600 (2008).
[Crossref]

Correa, R. A.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Ercan, B.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Ferreira, F.

Fontaine, N. K.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Gruner-Nielsen, L.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Guan, B.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Hanik, N.

Hu, J.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Huang, Y.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Inan, B.

Ip, E.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Jansen, S. L.

Jun, B. E.

D. J. Park, B. E. Jun, and J. H. Kim, “Fast tracking RLS algorithm using novel variable forgetting factor with unity zone,” Electron. Lett. 27(23), 2150–2151 (1991).
[Crossref]

Kahn, J. M.

Kim, J. H.

D. J. Park, B. E. Jun, and J. H. Kim, “Fast tracking RLS algorithm using novel variable forgetting factor with unity zone,” Electron. Lett. 27(23), 2150–2151 (1991).
[Crossref]

Koreshkov, K.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Korolev, A.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Kuschnerov, M.

Li, G.

N. Bai and G. Li, “Adaptive Frequency-Domain Equalization for Mode-Division Multiplexed Transmission,” IEEE Photonics Technol. Lett. 24(21), 1918–1921 (2012).
[Crossref]

Li, M.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Lingle, R. J.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Lobato, A.

Lopez, J. E. A.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Mateo, E.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Paleologu, C.

C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Process. Lett. 15, 597–600 (2008).
[Crossref]

Park, D. J.

D. J. Park, B. E. Jun, and J. H. Kim, “Fast tracking RLS algorithm using novel variable forgetting factor with unity zone,” Electron. Lett. 27(23), 2150–2151 (1991).
[Crossref]

Ryf, R.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Scott, R. P.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Sleiffer, V. A. J. M.

Spinnler, B.

Sun, Y.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

Tanaka, A.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

van den Borne, D.

Wood, W.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Yano, Y.

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

Electron. Lett. (1)

D. J. Park, B. E. Jun, and J. H. Kim, “Fast tracking RLS algorithm using novel variable forgetting factor with unity zone,” Electron. Lett. 27(23), 2150–2151 (1991).
[Crossref]

IEEE Photonics Technol. Lett. (1)

N. Bai and G. Li, “Adaptive Frequency-Domain Equalization for Mode-Division Multiplexed Transmission,” IEEE Photonics Technol. Lett. 24(21), 1918–1921 (2012).
[Crossref]

IEEE Signal Process. Lett. (1)

C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Process. Lett. 15, 597–600 (2008).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (1)

Other (8)

N. Bai, E. Ip, M. Li, T. Wang, and G. Li, “Experimental Demonstration of Adaptive Frequency-domain Equalization for Mode-Division Multiplexed Transmission,” in Proc. OFC/NFOEC (2013), paper OM2C.5.
[Crossref]

Z. Pan, Y. Weng, X. He, and J. Wang, “Adaptive frequency-domain equalization and MIMO signal processing in mode division multiplexing systems using few-mode fibers,” in Signal Processing in Photonic Communications (OSA, 2016), paper SpW2G–1.

Z. Yang, J. Zhao, N. Bai, E. Ip, T. Wang, and G. Li, “Experimental demonstration of adaptive recursive least square frequency-domain equalization for long-distance mode-division multiplexed transmission,” in 2015 European Conference on Optical Communication (ECOC, 2015), paper 15636015.
[Crossref]

S. Haykin, Adaptive Filter Theory (Prentice-Hall, 2002), Chap. 9.

N. Benvenuto, Algorithms for Communications Systems and their Applications (John Wiley, 2002), Chap. 3.

N. K. Fontaine, R. Ryf, H. Chen, A. V. Benitez, J. E. A. Lopez, R. A. Correa, B. Guan, B. Ercan, R. P. Scott, S. J. Ben Yoo, L. Gruner-Nielsen, Y. Sun, and R. J. Lingle, “30×30 MIMO Transmission over 15 Spatial Modes,” in Proc. OFC (2015), paper PDPTh5C.1.
[Crossref]

E. Ip, M. Li, K. Bennett, Y. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λx6x19-Gbaud Wavelength-and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few-Mode Fiber with a Gain-Equalized Few-Mode EDFA,” in Proc. OFC (2013), paper PDP5A.2.

J. Wang, “A variable forgetting factor RLS adaptive filtering algorithm,” in 2009 3rd IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications (IEEE, 2009), paper 11021933.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Block diagram of the proposed RLS FDE.
Fig. 2
Fig. 2 Variable forgetting factor based on exponential envelope.
Fig. 3
Fig. 3 Convergence speed comparison between VFF-RLS/RLS and LMS: (a) MSE convergence at 600-km vs. symbols; (b) Ratio of convergence speed of LMS and VFF-RLS/RLS vs. Distance.
Fig. 4
Fig. 4 Comparison between Conventional LMS and VFF-RLS/RLS: Q2 vs. Distance.

Tables (1)

Tables Icon

Table 1 Complexity comparison between RLS and LMS

Equations (4)

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

K(k) ¯ λ 1 R(k) ¯ ¯ Y(k) ¯ 1+ λ 1 Y(k) ¯ H R(k) ¯ ¯ Y(k) ¯ .
W(k) ¯ ¯ W(k) ¯ ¯ + K(k) ¯ E(k) ¯ H .
R(k) ¯ ¯ λ 1 R(k) ¯ ¯ λ 1 K(k) ¯ Y(k) ¯ H R(k) ¯ ¯ .
λ(n)= λ max γ× 10 nτ ,

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