Abstract

In this paper, a new method of constructing three-dimensional modulation formats with constant power is introduced. Constellations designed by the method have slightly larger minimum Euclidean distances (MEDs) than the conventional ones. No repetitive algorithm to maximize MED is used so that the new method has little computational complexity. Since signal points in the new formats are distributed regularly and symmetrically, an error control coding with systematic set-partition is applicable. We also present theoretical symbol error probability (SEP) of the new constellations in an additive white Gaussian noise environment, and demonstrate that the theoretical results are accurate. As the new modulation formats have almost the same or slightly lower SEPs than the conventional ones, they are appropriate for implementing a highly reliable optical communication system.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Express 17(13), 10814–10819 (2009).
    [CrossRef] [PubMed]
  2. H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
    [CrossRef]
  3. J.-E. Porath and T. Aulin, “Design of multidimensional signal constellations,” IEE Proc.-Commun. 150(5), 317–323 (2003).
    [CrossRef]
  4. S. Benedetto and E. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
    [CrossRef]
  5. S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol. 8(7), 1127–1136 (1990).
    [CrossRef]
  6. S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
    [CrossRef]
  7. S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun. 43(2/3/4), 1591–1602 (1995).
    [CrossRef]
  8. R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun. 45(1), 95–102 (1997).
    [CrossRef]
  9. N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry.  14(3), 237–259 (1995).
  10. J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, Singapore, 2008).
  11. Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett. 14(2), 112–114 (2010).
    [CrossRef]

2010 (1)

Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett. 14(2), 112–114 (2010).
[CrossRef]

2009 (2)

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Express 17(13), 10814–10819 (2009).
[CrossRef] [PubMed]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

2003 (1)

J.-E. Porath and T. Aulin, “Design of multidimensional signal constellations,” IEE Proc.-Commun. 150(5), 317–323 (2003).
[CrossRef]

1997 (1)

R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun. 45(1), 95–102 (1997).
[CrossRef]

1995 (2)

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry.  14(3), 237–259 (1995).

S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun. 43(2/3/4), 1591–1602 (1995).
[CrossRef]

1992 (2)

S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[CrossRef]

S. Benedetto and E. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[CrossRef]

1990 (1)

S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol. 8(7), 1127–1136 (1990).
[CrossRef]

Agrell, E.

Aulin, T.

J.-E. Porath and T. Aulin, “Design of multidimensional signal constellations,” IEE Proc.-Commun. 150(5), 317–323 (2003).
[CrossRef]

Batshon, H. G.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

Benedetto, S.

S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun. 43(2/3/4), 1591–1602 (1995).
[CrossRef]

S. Benedetto and E. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[CrossRef]

Betti, S.

S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[CrossRef]

S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol. 8(7), 1127–1136 (1990).
[CrossRef]

Blaikie, R. J.

R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun. 45(1), 95–102 (1997).
[CrossRef]

Chen, Z.

Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett. 14(2), 112–114 (2010).
[CrossRef]

Choi, E. C.

Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett. 14(2), 112–114 (2010).
[CrossRef]

Conway, J. H.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry.  14(3), 237–259 (1995).

Curti, F.

S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol. 8(7), 1127–1136 (1990).
[CrossRef]

Djordjevic, I. B.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

Duff, T. D. S.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry.  14(3), 237–259 (1995).

Gough, P. T.

R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun. 45(1), 95–102 (1997).
[CrossRef]

Hardin, R. H.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry.  14(3), 237–259 (1995).

Iannone, E.

S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[CrossRef]

S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol. 8(7), 1127–1136 (1990).
[CrossRef]

Kang, S. G.

Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett. 14(2), 112–114 (2010).
[CrossRef]

Karlsson, M.

Marchis, G. D.

S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[CrossRef]

S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol. 8(7), 1127–1136 (1990).
[CrossRef]

Olmo, G.

S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun. 43(2/3/4), 1591–1602 (1995).
[CrossRef]

Poggiolini, E.

S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun. 43(2/3/4), 1591–1602 (1995).
[CrossRef]

S. Benedetto and E. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[CrossRef]

Porath, J.-E.

J.-E. Porath and T. Aulin, “Design of multidimensional signal constellations,” IEE Proc.-Commun. 150(5), 317–323 (2003).
[CrossRef]

Proakis, J. G.

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, Singapore, 2008).

Salehi, M.

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, Singapore, 2008).

Sloane, N. J. A.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry.  14(3), 237–259 (1995).

Taylor, D. P.

R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun. 45(1), 95–102 (1997).
[CrossRef]

Wang, T.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

Xu, L.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

IEE Proc.-Commun. (1)

J.-E. Porath and T. Aulin, “Design of multidimensional signal constellations,” IEE Proc.-Commun. 150(5), 317–323 (2003).
[CrossRef]

IEEE Commun. Lett. (1)

Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett. 14(2), 112–114 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

IEEE Trans. Commun. (3)

S. Benedetto and E. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun. 40(4), 708–721 (1992).
[CrossRef]

S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun. 43(2/3/4), 1591–1602 (1995).
[CrossRef]

R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun. 45(1), 95–102 (1997).
[CrossRef]

J. Lightwave Technol. (2)

S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol. 8(7), 1127–1136 (1990).
[CrossRef]

S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol. 10(12), 1985–1997 (1992).
[CrossRef]

Opt. Express (1)

Other (2)

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry.  14(3), 237–259 (1995).

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, Singapore, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Design procedure (a) the new 3-D 8-ary constellation based on 8-ary PSK (b) the new 3-D 16-ary constellation based on 16-ary PSK.

Fig. 2
Fig. 2

Decision region (a) the 8-ary constellation (b) the 16-ary constellation.

Fig. 3
Fig. 3

SEPs of the proposed modulation formats.

Fig. 4
Fig. 4

Average SERs of the proposed and the conventional constellations.

Tables (2)

Tables Icon

Table 1 Spherical coordinates of the 16-ary constellations.

Tables Icon

Table 2 MEDs of the constellations

Equations (5)

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

2 sin 2 φ ( 2 + 2 ) cos 2 φ + 2 = 0 ,
{ 2 cos 2 φ 1 + ( 2 + 2 ) cos 2 φ 2 4 = 0 , 2 cos 2 φ 1 + 2 cos φ 1 cos φ 2 + 2 sin φ 1 sin φ 2 2 = 0 ,
P s , 8 = 1 [ 1 1 2 erfc ( d m 2 N 0 ) ] 3 ,
P s , 16 = 1 1 2 erfc ( γ s ) + 1 2 cos ϕ d erfc ( γ s cos ϕ d ) exp ( γ s sin 2 ϕ d ) ,
P s = 1 1 2 erfc ( γ s ) .

Metrics