Abstract

We demonstrate crosstalk mitigation using 4×4 multiple-input-multiple-output (MIMO) equalization on an orbital angular momentum (OAM) multiplexed free-space data link with heterodyne detection. Four multiplexed OAM beams, each carrying a 20Gbit/s quadrature phase-shift keying signal, propagate through weak turbulence. The turbulence induces inter-channel crosstalk among each beam and degrades the signal performance. Experimental results demonstrate that with the assistance of MIMO processing, the signal quality and the bit-error-rate (BER) performance can be improved. The power penalty can be reduced by >4dB at a BER of 3.8×103.

© 2014 Optical Society of America

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J. Benesty and P. Duhamel, IEE Proc. F Radar Signal Process 138, 379 (1991).
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Esmaeelpour, M.

Essiambre, R.-J.

Fazal, I. M.

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Gooch, R. P.

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Hillerkuss, D.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
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H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, M. Willner, B. Erkmen, S. Dolinar, M. Lavery, M. Padgett, M. Tur, and A. Willner, Opt. Lett. 39, 197 (2014).
[CrossRef]

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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. Willner, and S. Ramachandran, Science 340, 1545 (2013).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. Ziyadi, M. R. Chitgarha, M. Neifeld, S. Dolinar, and A. Willner, in Proceedings of the European Conference and Exhibition on Optical Communication (Optical Society of America, 2013), paper Th.1.C.4.

Huebner, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
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A. Leven, N. Kaneda, and S. Corteselli, IEEE J. Sel. Top. Quantum Electron. 16, 1227 (2010).
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Kawanishi, T.

Kobayashi, T.

Koenig, S.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
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Koos, C.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. Willner, and S. Ramachandran, Science 340, 1545 (2013).
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Lavery, M.

Lavery, M. P. J.

Leach, J.

Leuthold, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
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Leven, A.

A. Leven, N. Kaneda, and S. Corteselli, IEEE J. Sel. Top. Quantum Electron. 16, 1227 (2010).
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Li, X.

Lingle, R.

Love, G. D.

Magaña-Loaiza, O.

B. Rodenburg, M. Mirhosseini, M. Malik, O. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, and R. W. Boyd, New J. Phys. 16, 033020 (2014).
[CrossRef]

Maher, L.

B. Rodenburg, M. Mirhosseini, M. Malik, O. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, and R. W. Boyd, New J. Phys. 16, 033020 (2014).
[CrossRef]

Malik, M.

B. Rodenburg, M. Mirhosseini, M. Malik, O. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, and R. W. Boyd, New J. Phys. 16, 033020 (2014).
[CrossRef]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, Nat. Commun. 4, 2781 (2013).
[CrossRef]

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, Opt. Express 20, 13195 (2012).
[CrossRef]

McCurdy, A.

McCurdy, A. H.

Meyer, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
[CrossRef]

Millar, D. S.

Mirhosseini, M.

B. Rodenburg, M. Mirhosseini, M. Malik, O. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, and R. W. Boyd, New J. Phys. 16, 033020 (2014).
[CrossRef]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, Nat. Commun. 4, 2781 (2013).
[CrossRef]

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, Opt. Express 20, 13195 (2012).
[CrossRef]

Mumtaz, S.

Nebendahl, B.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
[CrossRef]

Neifeld, M.

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. Erkmen, N. Chandrasekaran, M. Lavery, N. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. Padgett, R. Boyd, J. Shapiro, and A. Willner, Opt. Lett. 38, 4062 (2013).
[CrossRef]

H. Huang, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. Ziyadi, M. R. Chitgarha, M. Neifeld, S. Dolinar, and A. Willner, in Proceedings of the European Conference and Exhibition on Optical Communication (Optical Society of America, 2013), paper Th.1.C.4.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, Nat. Photonics 7, 354 (2013).
[CrossRef]

O’Sullivan, M.

Padgett, M.

Padgett, M. J.

Pas’ko, V.

Peckham, D. W.

Polley, A.

Ralph, S.

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

Randel, S.

Ready, M. J.

M. J. Ready and R. P. Gooch, in Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP-90), Albuquerque, NM (1990), Vol. 3, p. 1699.

Ren, Y.

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, M. Willner, B. Erkmen, S. Dolinar, M. Lavery, M. Padgett, M. Tur, and A. Willner, Opt. Lett. 39, 197 (2014).
[CrossRef]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. Erkmen, N. Chandrasekaran, M. Lavery, N. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. Padgett, R. Boyd, J. Shapiro, and A. Willner, Opt. Lett. 38, 4062 (2013).
[CrossRef]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[CrossRef]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

H. Huang, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. Ziyadi, M. R. Chitgarha, M. Neifeld, S. Dolinar, and A. Willner, in Proceedings of the European Conference and Exhibition on Optical Communication (Optical Society of America, 2013), paper Th.1.C.4.

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, Nat. Photonics 7, 354 (2013).
[CrossRef]

Robertson, D. J.

Rodenburg, B.

B. Rodenburg, M. Mirhosseini, M. Malik, O. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, and R. W. Boyd, New J. Phys. 16, 033020 (2014).
[CrossRef]

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, Opt. Express 20, 13195 (2012).
[CrossRef]

Ryf, R.

Sakaguchi, J.

Savory, S. J.

Schmogrow, R.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, IEEE Photon. Technol. Lett. 24, 61 (2012).
[CrossRef]

Shapiro, J.

Shi, Z.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, Nat. Commun. 4, 2781 (2013).
[CrossRef]

Shieh, W.

Sierra, A.

Steinhoff, N.

B. Rodenburg, M. Mirhosseini, M. Malik, O. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, and R. W. Boyd, New J. Phys. 16, 033020 (2014).
[CrossRef]

Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. Erkmen, N. Chandrasekaran, M. Lavery, N. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. Padgett, R. Boyd, J. Shapiro, and A. Willner, Opt. Lett. 38, 4062 (2013).
[CrossRef]

Taru, T.

Tur, M.

Tyler, G.

B. Rodenburg, M. Mirhosseini, M. Malik, O. Magaña-Loaiza, M. Yanakas, L. Maher, N. Steinhoff, G. Tyler, and R. W. Boyd, New J. Phys. 16, 033020 (2014).
[CrossRef]

Vasnetsov, M.

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Figures (7)

Fig. 1.
Fig. 1.

Concept of a free space communication link using OAM multiplexing. (a) Power distribution of a pure OAM mode and a distorted OAM mode. (b) Power mapping of a SDM system using multiple OAM modes. After propagating and demultiplexing, the system may suffer from crosstalk and require MIMO equalization.

Fig. 2.
Fig. 2.

Block diagram for the experimental setup. OAM, orbital angular momentum; PC, polarization controller; BPF, bandpass filter; SMF, single mode fiber; EDFA, erbium-doped fiber amplifier; OC, optical coupler; LO, local oscillator; ADC, analog to digital converter; PD, photo detector; BS, free-space beam splitter.

Fig. 3.
Fig. 3.

(a) Procedures of offline signal processing for heterodyne and MIMO equalization. (b1)–(b3) Signal spectrum of channel using heterodyne detection. (b1) Spectrum of the sampled signal. (b2) Spectrum after bandpass filtering. (b3) Spectrum after frequency shifting.

Fig. 4.
Fig. 4.

Convergent tap weights (FIR filter coefficients) of the equalizer using constant modulus algorithm (CMA). (a)–(d) The absolute value of complex taps weights of four FIR filters to equalize channels 1–4, respectively.

Fig. 5.
Fig. 5.

Recovered constellations of 20Gbit/s QPSK signal in each of the four channels with and without MIMO equalization.

Fig. 6.
Fig. 6.

Measured BER as a function of OSNR for the 20Gbit/s QPSK signal in channel 4 with =+8.

Fig. 7.
Fig. 7.

Measured EVM of the recovered QPSK signal under 29 different emulated turbulence realizations (d/r0 is 0.68).

Equations (2)

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yj=iwij*xi,
wij(k+1)=wij(k)+u·ei·yi·xiconj,

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