Abstract

We study the performance of various binary and nonbinary modulation methods applied to coherent laser communication through the turbulent atmosphere. We compare the spectral efficiencies and SNR efficiencies of complex modulations, and consider options for atmospheric compensation, including phase correction and diversity combining techniques. Our analysis shows that high communication rates require receivers with good sensitivity along with some technique to mitigate the effect of atmospheric fading.

© 2010 OSA

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References

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  1. J. W. Strohbehn, T. Wang, and J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10(1), 59–70 (1975).
    [CrossRef]
  2. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [CrossRef]
  3. M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  4. D. L. Fried, “Atmospheric modulation noise in an optical heterodyne receiver,” IEEE J. Quantum Electron. 3(6), 213–221 (1967).
    [CrossRef]
  5. A. Belmonte and J. Khan, “Performance of synchronous optical receivers using atmospheric compensation techniques,” Opt. Express 16(18), 14151–14162 (2008).
    [CrossRef] [PubMed]
  6. A. Belmonte and J. M. Kahn, “Capacity of coherent free-space optical links using diversity-combining techniques,” Opt. Express 17(15), 12601–12611 (2009).
    [CrossRef] [PubMed]
  7. J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Ben Roberts & Company, 2007).
  8. J. D. Parsons, “Diversity techniques in communications receivers,” in Advanced Signal Processing, D. A. Creasey, ed. (Peregrinus, 1985), Chap. 6.
  9. J. G. Proakis, and M. Salehi, Digital Communications, (Mc Graw-Hill, 2007).
  10. M. K. Simon and M.-S. Alouini, “A unified approach to the performance analysis of digital communications over generalized fading channels,” IEEE Proc. 86(9), 1860–1877 (1998).
    [CrossRef]
  11. A. Goldsmith, Wireless Communications (Cambridge University Press, 2005)
  12. J. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
    [CrossRef]

2009

2008

2004

J. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
[CrossRef]

1998

M. K. Simon and M.-S. Alouini, “A unified approach to the performance analysis of digital communications over generalized fading channels,” IEEE Proc. 86(9), 1860–1877 (1998).
[CrossRef]

1976

1975

J. W. Strohbehn, T. Wang, and J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10(1), 59–70 (1975).
[CrossRef]

1967

D. L. Fried, “Atmospheric modulation noise in an optical heterodyne receiver,” IEEE J. Quantum Electron. 3(6), 213–221 (1967).
[CrossRef]

Alouini, M.-S.

M. K. Simon and M.-S. Alouini, “A unified approach to the performance analysis of digital communications over generalized fading channels,” IEEE Proc. 86(9), 1860–1877 (1998).
[CrossRef]

Belmonte, A.

Fried, D. L.

D. L. Fried, “Atmospheric modulation noise in an optical heterodyne receiver,” IEEE J. Quantum Electron. 3(6), 213–221 (1967).
[CrossRef]

Ho, K.-P.

J. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
[CrossRef]

Kahn, J.

J. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
[CrossRef]

Kahn, J. M.

Khan, J.

Noll, R. J.

Simon, M. K.

M. K. Simon and M.-S. Alouini, “A unified approach to the performance analysis of digital communications over generalized fading channels,” IEEE Proc. 86(9), 1860–1877 (1998).
[CrossRef]

Speck, J. P.

J. W. Strohbehn, T. Wang, and J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10(1), 59–70 (1975).
[CrossRef]

Strohbehn, J. W.

J. W. Strohbehn, T. Wang, and J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10(1), 59–70 (1975).
[CrossRef]

Wang, T.

J. W. Strohbehn, T. Wang, and J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10(1), 59–70 (1975).
[CrossRef]

IEEE J. Quantum Electron.

D. L. Fried, “Atmospheric modulation noise in an optical heterodyne receiver,” IEEE J. Quantum Electron. 3(6), 213–221 (1967).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 259–272 (2004).
[CrossRef]

IEEE Proc.

M. K. Simon and M.-S. Alouini, “A unified approach to the performance analysis of digital communications over generalized fading channels,” IEEE Proc. 86(9), 1860–1877 (1998).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Radio Sci.

J. W. Strohbehn, T. Wang, and J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10(1), 59–70 (1975).
[CrossRef]

Other

A. Goldsmith, Wireless Communications (Cambridge University Press, 2005)

J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Ben Roberts & Company, 2007).

J. D. Parsons, “Diversity techniques in communications receivers,” in Advanced Signal Processing, D. A. Creasey, ed. (Peregrinus, 1985), Chap. 6.

J. G. Proakis, and M. Salehi, Digital Communications, (Mc Graw-Hill, 2007).

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

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Figures (4)

Fig. 1
Fig. 1

Bit-error probability vs. turbulence-free photons (SNR) per bit γ0 for BPSK with coherent detection and additive white Gaussian noise (AWGN). Performance is shown for different values of: (a) the number of modes J corrected by adaptive optics, and (b) the number of of branches L in the combiner. The case L = 1 corresponds to no receive diversity (green line). The area πD 2 describes the combined, multi-aperture system equivalent aperture. When no receive diversity is considered, D equals the receiver aperture diameter. Amplitude fluctuations are neglected by assuming σβ 2 = 0. Turbulence is characterized by a moderate phase coherence length r 0 such that D/r 0 = 4. In (a), the compensating phases are expansions up to tilt (J = 3), astigmatism (J = 6), and 5th-order aberrations (J = 20). The no-correction case (J = 0) is also considered. The no-turbulence, AWGN limit is indicated by black lines.

Fig. 2
Fig. 2

Bit-error probability vs. turbulence-free photons (SNR) per bit γ0/log2 M for various modulation formats and coded bits per symbol (constellation size M). Coherent detection and additive white Gaussian noise (AWGN) are assumed. Modulation type is indicated by marker style. Number of bits per symbol M is indicated by color. Performance is shown for: (a) phase compensation up to the 5th-order aberrations (J=20), and (b) a set of L=12 branches in the combiner. The area πD 2 describes the combined, multi-aperture system equivalent aperture. If no receive diversity was to be considered (L=1), D would equal the receiver aperture diameter. Amplitude fluctuations are neglected by assuming σβ 2=0. Turbulence is characterized by a moderate phase coherence length r 0 such that D/r 0=4.

Fig. 3
Fig. 3

Spectral efficiency log2(M) vs. turbulence-free photons (SNR) per bit γ0/log2 M requirement for various modulation formats with coherent detection and additive white Gaussian noise (AWGN). Modulation type is indicated by marker style. Performance is shown for different values of: (a) the number of modes J corrected by adaptive optics, and (b) the number of branches L in the combiner. The number of compensated modes J, in (a), and diversity branches L, in (b), are indicated by color. The area πD 2 describes the combined, multi-aperture system equivalent aperture. If no receive diversity was to be considered (L=1), D would equal the receiver aperture diameter. Amplitude fluctuations are neglected by assuming σβ 2=0. Turbulence is characterized by a moderate phase coherence length r 0 such that D/r 0=4. In (a), the compensating phases are expansions up to the 5th-order aberrations (J=20). The no-turbulence, AWGN limit is indicated by black lines.

Fig. 4
Fig. 4

Required receiver sensitivity at 10−9 BER as a function of data-rate for BPSK modulation at 1550-nm wavelength. Compensation method is indicated by color: Red indicates phase aberration correction and blue indicates diversity combining. When amplitude fluctuations are neglected, by assuming σβ 2=0, turbulence level is characterized by just the phase coherence length r 0 and can be indicated by the line type: Solid line indicates a coherent length such that D/r 0=2, and dashed line indicates a stronger turbulence level such that D/r 0=4. Also shown are the required receiver sensitivity when amplitude fluctuations are considered (dotted lines, for just two specific cases), AWGN limiting sensitivity (black solid line), and lines of constant power (dashed diagonals). In addition, the most relevant modal and diversity gains, along with selected phase aberration and scintillation penalties, are included in the graphic.

Tables (1)

Tables Icon

Table 1 Parameters a and b used for PSK, QAM and PAM modulation formats in Eqs. (4) and (6).

Equations (7)

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σ χ 2 = log e ( 1 + σ β 2 ) σ ϕ 2 = C j ( D r 0 ) 5 3 ,
p γ ( γ M R C ) = ( 1 + r γ ¯ ) L + 1 2 ( 1 L r ) L 1 2 exp ( L r ) exp [ ( 1 + r ) γ M R C γ ¯ ] I L 1 [ 2 L ( 1 + r ) r γ M R C γ ¯ ] ,
M ( s ) = 0 d γ exp ( s γ ) p γ ( γ ) = [ 1 + r 1 + r s γ ¯     exp ( r s γ ¯ 1 + r s γ ¯ ) ] L .
p s ( E | γ ) a π 0 π 2 d ϕ exp ( b γ sin 2 ϕ ) .
p S ( E ) = 0 d γ p S ( E | γ ) p γ ( γ ) ,
p s ( E ) = a π     0 d γ     0 π 2 d ϕ exp ( b γ sin 2 ϕ ) p γ ( γ ) = a π     0 π 2 d ϕ     M ( b sin 2 ϕ ) ,
S = R b B = R s R c log 2 M B ,

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