Abstract

Optical multiple-input multiple-output (MIMO) transmission systems generally employ minimum mean squared error time or frequency domain equalizers. Using an experimental 3-mode dual polarization coherent transmission setup, we show that the convergence time of the MMSE time domain equalizer (TDE) and frequency domain equalizer (FDE) can be reduced by approximately 50% and 30%, respectively. The criterion used to estimate the system convergence time is the time it takes for the MIMO equalizer to reach an average output error which is within a margin of 5% of the average output error after 50,000 symbols. The convergence reduction difference between the TDE and FDE is attributed to the limited maximum step size for stable convergence of the frequency domain equalizer. The adaptive step size requires a small overhead in the form of a lookup table. It is highlighted that the convergence time reduction is achieved without sacrificing optical signal-to-noise ratio performance.

© 2013 Optical Society of America

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2013

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

2011

2010

S. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

2009

2000

B. G. Choi, Y. W. Park, J. H. Choi, “The adaptive least mean square algorithm using several step size for multiuser detection,” Proc. Vehicular Technical Conference 6(6), 2822–2825 (2000).

1992

R. H. Kwong, E. W. Johnston, “A variable step size LMS algorithm,” IEEE Trans. Signal Process. 40(7), 1633–1642 (1992).
[CrossRef]

1971

Alam, S. U.

Alfiad, M. S.

Choi, B. G.

B. G. Choi, Y. W. Park, J. H. Choi, “The adaptive least mean square algorithm using several step size for multiuser detection,” Proc. Vehicular Technical Conference 6(6), 2822–2825 (2000).

Choi, J. H.

B. G. Choi, Y. W. Park, J. H. Choi, “The adaptive least mean square algorithm using several step size for multiuser detection,” Proc. Vehicular Technical Conference 6(6), 2822–2825 (2000).

de Waardt, H.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

Dhar, A.

Faruk, M. S.

Giles, D.

Giles, I. P.

Gloge, D.

Gonzalez, G.

Grüner-Nielsen, L.

Hauske, F. N.

Johnston, E. W.

R. H. Kwong, E. W. Johnston, “A variable step size LMS algorithm,” IEEE Trans. Signal Process. 40(7), 1633–1642 (1992).
[CrossRef]

Jung, Y.

Kikuchi, K.

Koonen, A. M. J.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

Kuschnerov, M.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. 27(16), 3614–3622 (2009).
[CrossRef]

Kwong, R. H.

R. H. Kwong, E. W. Johnston, “A variable step size LMS algorithm,” IEEE Trans. Signal Process. 40(7), 1633–1642 (1992).
[CrossRef]

Lankl, B.

Li, Z.

Monroy, I. T.

Napoli, A.

Okonkwo, C. M.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

Park, Y. W.

B. G. Choi, Y. W. Park, J. H. Choi, “The adaptive least mean square algorithm using several step size for multiuser detection,” Proc. Vehicular Technical Conference 6(6), 2822–2825 (2000).

Piyawanno, K.

Poletti, F.

Richardson, D. J.

Sahu, J. K.

Savory, S.

S. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

Shengkui, Z.

Z. Shengkui, M. Zhihong, K. Suiyang, “A fast variable step-size LMS algorithm with system identification,” in Proc. Second IEEE Conference on Industrial Electronics and Applications (2007), 2340–2345.

Sleiffer, V. A. J. M.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

Soriano, R. A.

Spinnler, B.

Suiyang, K.

Z. Shengkui, M. Zhihong, K. Suiyang, “A fast variable step-size LMS algorithm with system identification,” in Proc. Second IEEE Conference on Industrial Electronics and Applications (2007), 2340–2345.

van Uden, R. G. H.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

Ye, Y.

Zhang, Z.

Zhihong, M.

Z. Shengkui, M. Zhihong, K. Suiyang, “A fast variable step-size LMS algorithm with system identification,” in Proc. Second IEEE Conference on Industrial Electronics and Applications (2007), 2340–2345.

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

S. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

IEEE Photonics Technol. Lett.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, M. Kuschnerov, H. de Waardt, A. M. J. Koonen, “Single DPLL joint carrier phase compensation for few-mode fiber transmission,” IEEE Photonics Technol. Lett. 25(14), 1381–1384 (2013).
[CrossRef]

IEEE Trans. Signal Process.

R. H. Kwong, E. W. Johnston, “A variable step size LMS algorithm,” IEEE Trans. Signal Process. 40(7), 1633–1642 (1992).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Proc. Vehicular Technical Conference

B. G. Choi, Y. W. Park, J. H. Choi, “The adaptive least mean square algorithm using several step size for multiuser detection,” Proc. Vehicular Technical Conference 6(6), 2822–2825 (2000).

Other

V. A. J. M. Sleiffer, Y. Jung, B. Inan, H. Chen, R. G. H. van Uden, M. Kuschnerov, D. van den Borne, S. L. Jansen, V. Veljanovski, A. M. J. Koonen, D. J. Richardson, S. U. Alam, F. Poletti, J. K. Sahu, A. Dhar, B. Corbett, R. Winfield, A. D. Ellis, and H. de Waardt, “Mode-division-multiplexed 3x112-Gb/s DP-QPSK transmission over 80-km few-mode fiber with inline MM-EDFA and Blind DSP,” in Proc. European Conference on Optical Communication (ECOC’12) (2012), paper Tu.1.C.2.

Z. Shengkui, M. Zhihong, K. Suiyang, “A fast variable step-size LMS algorithm with system identification,” in Proc. Second IEEE Conference on Industrial Electronics and Applications (2007), 2340–2345.

R. Ryf, S. Randel, N. K. Fontaine, M. Montoliu, E. Burrows, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R. V. Jensen, and R. Lingle, “32-bit/s/Hz spectral efficiency WDM transmission over 177-km few-mode fiber,” in Proc. Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC’13) (2013), paper PDPA.1.

E. Ip, M.-J. Li, Y.-K. Huang, A. Tanaka, E. Mateo, W. Wood, J. Hu, Y. Yano, and K. Koreshkov, “146λ x 6 x 19-Gbaud wavelength- and mode-division multiplexed transmission over 10x50-Km spans of few-mode fiber with a gain-equalized few-mode EDFA,” in Proc. Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC’13) (2013), paper PDPA.2.

V. A. J. M. Sleiffer, Y. Jung, V. Veljanovski, R. G. H. van Uden, M. Kuschnerov, Q. Kang, L. Grüner-Nielsen, Y. Sun, D. J. Richardson, S. U. Alam, F. Poletti, J. K. Sahu, A. Dhar, H. Chen, B. Inan, A. M. J. Koonen, B. Corbett, R. Winfield, A. D. Ellis, and H. de Waardt, “73.7 Tb/s (96x3x256-Gb/s) mode-division-multiplexed DP-16QAM transmission with inline MM-EDFA,” in Proc. European Conference on Optical Communication (ECOC’12) (2012), paper Th.3.C.4.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, H. de Waardt, and A. M. J. Koonen, “Adaptive step size MIMO equalization for few-mode fiber transmission systems,” in Proc. European Conference on Optical Communication (ECOC’13) (2013), paper Th.2.C.2.

J. Proakis and M. Salehi, Digital Communications, 3rd ed. (McGraw-Hill Science, 2007), p. 645.

N. Benvenuto and G. Cherubini, Algorithms for Communications Systems and Their Applications (John Wiley, 2002), p. 211.

L. Grüner-Nielsen, J. W. Nicholson, K. Jespersen, Y. Sun, R. Lingle, D. Jacobsen, and B. Pálsdóttir, “Measuring distributed mode scattering in few mode fibers with high and low differential group delay,” in Proc. of IEEE Photonics Society 2012 Sumer Topical Meeting (2012), paper TuC1.3.

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