Abstract

We analyze the performance of adaptive field conjugation array receivers in coherent laser communications through the turbulent atmosphere. We consider coherent fiber arrays consisting of densely packed multiple subapertures, with each subaperture interfaced to a single-mode fiber. In a field conjugation fiber array, the single-mode fiber outputs are detected, and the photocurrents are adaptively co-phased and scaled, and then summed to mitigate signal fading associated with atmospheric turbulence and compensate for imperfect fiber coupling efficiency. We quantify how field conjugation processing improves performance in the presence of turbulence, as compared to a monolithic-aperture coherent receiver having an equal total cross-sectional area.

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  1. G. Li, "Recent advances in coherent optical communication," Adv. Opt. Photon. 1, 279‒307 (2009).
    [CrossRef]
  2. K. Kiasaleh, "Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence," IEEE Trans. Commun. 54, 604‒607 (2006).
    [CrossRef]
  3. T. A. Tsiftsis, "Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels," Electron. Lett. 44, 373‒375 (2008).
    [CrossRef]
  4. A. Belmonte and J. M. Kahn, "Performance of synchronous optical receivers using atmospheric compensation techniques," Opt. Express 16, 14151‒14162 (2008).
    [CrossRef] [PubMed]
  5. H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, "Optical wireless communications with heterodyne detection over turbulence channels with pointing errors," J. Lightwave Technol. 27, 4440‒4445 (2009).
    [CrossRef]
  6. E. J. Lee and V. W. Chan, "Diversity coherent and incoherent receivers for free-space optical communication in the presence and absence of interference," J. Opt. Commun. Netw. 1, 463‒483 (2009).
    [CrossRef]
  7. A. Belmonte and J. M. Kahn, "Capacity of coherent free-space optical links using diversity-combining techniques," Opt. Express 17, 12601‒12611 (2009).
    [CrossRef] [PubMed]
  8. M. Niu, J. Cheng, and J. F. Holzman, "Exact error rate analysis of equal gain and selection diversity for coherent free-space optical systems on strong turbulence channels," Opt. Express 18, 13915‒13926 (2010).
    [CrossRef] [PubMed]
  9. N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, "Polarization-multiplexed optical wireless transmission with coherent detection," J. Lightwave Technol. 28, 1218‒1227 (2010).
    [CrossRef]
  10. D. L. Fried, "Optical heterodyne detection of an atmospherically distorted signal wave front," Proc. IEEE 55, 57‒67 (1967).
    [CrossRef]
  11. R. M. Gagliardi and S. Karp, Optical Communications, John Wiley & Sons, 1995.
  12. J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications, Ben Roberts & Company, 2007.
  13. M. Nakagami, W. C. Hoffman, ed., "The m-distribution. A general formula of intensity distribution of rapid fading," Statistical Methods in Radio Wave Propagation, Pergamon Press, 1960.
  14. S. M. Aghajanzadeh and M. Uysal, "Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers," J. Opt. Commun. Netw. 2, 1087‒1094 (2010).
    [CrossRef]
  15. J. A. Buck, Fundamentals of Optical Fibers, 2nd Ed., Wiley, 2004.
  16. R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207‒211 (1976).
    [CrossRef]
  17. J. W. Strohbehn, T. Wang, and J. P. Speck, "On the probability distribution of line-of-sight fluctuations of optical signals," Radio Sci. 10, 59‒70 (1975).
    [CrossRef]
  18. V. N. Mahajan, Optical Imaging and Aberrations, Part II. Wave Diffraction Optics, SPIE Press, 2004.
  19. J. D. Parsons, D. A. Creasey, ed., "Diversity techniques in communications receivers," Advanced Signal Processing, Peregrinus, 1985, Chap. 6.
  20. V. A. Aalo, "Performance of maximal-ratio diversity systems in a correlated Nakagami-fading environment," IEEE Trans. Commun. 43, 2360‒2369 (1995).
    [CrossRef]
  21. M. Z. Win, G. Chrisikos, and J. H. Winters, "MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels," IEEE Commun. Lett. 4, 301‒303 (2000).
    [CrossRef]
  22. J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 2007.
  23. M. K. Simon and M.-S. Alouini, "A unified approach to the performance analysis of digital communications over generalized fading channels," IEEE Proc. 86, 1860‒1877 (1998).
    [CrossRef]
  24. P. J. Winzer and W. R. Leeb, "Fiber coupling efficiency for random light and its applications to lidar," Opt. Letters 23, 986‒988 (1998).
    [CrossRef]

2010 (3)

2009 (4)

2008 (2)

T. A. Tsiftsis, "Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels," Electron. Lett. 44, 373‒375 (2008).
[CrossRef]

A. Belmonte and J. M. Kahn, "Performance of synchronous optical receivers using atmospheric compensation techniques," Opt. Express 16, 14151‒14162 (2008).
[CrossRef] [PubMed]

2006 (1)

K. Kiasaleh, "Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence," IEEE Trans. Commun. 54, 604‒607 (2006).
[CrossRef]

2000 (1)

M. Z. Win, G. Chrisikos, and J. H. Winters, "MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels," IEEE Commun. Lett. 4, 301‒303 (2000).
[CrossRef]

1998 (2)

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

P. J. Winzer and W. R. Leeb, "Fiber coupling efficiency for random light and its applications to lidar," Opt. Letters 23, 986‒988 (1998).
[CrossRef]

1995 (1)

V. A. Aalo, "Performance of maximal-ratio diversity systems in a correlated Nakagami-fading environment," IEEE Trans. Commun. 43, 2360‒2369 (1995).
[CrossRef]

1976 (1)

1975 (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, 59‒70 (1975).
[CrossRef]

1967 (1)

D. L. Fried, "Optical heterodyne detection of an atmospherically distorted signal wave front," Proc. IEEE 55, 57‒67 (1967).
[CrossRef]

Aalo, V. A.

V. A. Aalo, "Performance of maximal-ratio diversity systems in a correlated Nakagami-fading environment," IEEE Trans. Commun. 43, 2360‒2369 (1995).
[CrossRef]

Aghajanzadeh, S. M.

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, 1860‒1877 (1998).
[CrossRef]

Belmonte, A.

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers, 2nd Ed., Wiley, 2004.

Chan, V. W.

Cheng, J.

Chrisikos, G.

M. Z. Win, G. Chrisikos, and J. H. Winters, "MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels," IEEE Commun. Lett. 4, 301‒303 (2000).
[CrossRef]

Cvijetic, N.

Fried, D. L.

D. L. Fried, "Optical heterodyne detection of an atmospherically distorted signal wave front," Proc. IEEE 55, 57‒67 (1967).
[CrossRef]

Gagliardi, R. M.

R. M. Gagliardi and S. Karp, Optical Communications, John Wiley & Sons, 1995.

Goodman, J. W.

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

Holzman, J. F.

Huang, Y.-K.

Kahn, J. M.

Karagiannidis, G. K.

Karp, S.

R. M. Gagliardi and S. Karp, Optical Communications, John Wiley & Sons, 1995.

Kiasaleh, K.

K. Kiasaleh, "Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence," IEEE Trans. Commun. 54, 604‒607 (2006).
[CrossRef]

Lee, E. J.

Leeb, W. R.

P. J. Winzer and W. R. Leeb, "Fiber coupling efficiency for random light and its applications to lidar," Opt. Letters 23, 986‒988 (1998).
[CrossRef]

Li, G.

Mahajan, V. N.

V. N. Mahajan, Optical Imaging and Aberrations, Part II. Wave Diffraction Optics, SPIE Press, 2004.

Nakagami, M.

M. Nakagami, W. C. Hoffman, ed., "The m-distribution. A general formula of intensity distribution of rapid fading," Statistical Methods in Radio Wave Propagation, Pergamon Press, 1960.

Niu, M.

Noll, R. J.

Parsons, J. D.

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

Proakis, J. G.

J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 2007.

Qian, D.

Salehi, M.

J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 2007.

Sandalidis, H. G.

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, 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, 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, 59‒70 (1975).
[CrossRef]

Tsiftsis, T. A.

H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, "Optical wireless communications with heterodyne detection over turbulence channels with pointing errors," J. Lightwave Technol. 27, 4440‒4445 (2009).
[CrossRef]

T. A. Tsiftsis, "Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels," Electron. Lett. 44, 373‒375 (2008).
[CrossRef]

Uysal, M.

Wang, T.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, "Polarization-multiplexed optical wireless transmission with coherent detection," J. Lightwave Technol. 28, 1218‒1227 (2010).
[CrossRef]

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

Win, M. Z.

M. Z. Win, G. Chrisikos, and J. H. Winters, "MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels," IEEE Commun. Lett. 4, 301‒303 (2000).
[CrossRef]

Winters, J. H.

M. Z. Win, G. Chrisikos, and J. H. Winters, "MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels," IEEE Commun. Lett. 4, 301‒303 (2000).
[CrossRef]

Winzer, P. J.

P. J. Winzer and W. R. Leeb, "Fiber coupling efficiency for random light and its applications to lidar," Opt. Letters 23, 986‒988 (1998).
[CrossRef]

Yu, J.

Adv. Opt. Photon. (1)

Electron. Lett. (1)

T. A. Tsiftsis, "Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels," Electron. Lett. 44, 373‒375 (2008).
[CrossRef]

IEEE Commun. Lett. (1)

M. Z. Win, G. Chrisikos, and J. H. Winters, "MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels," IEEE Commun. Lett. 4, 301‒303 (2000).
[CrossRef]

IEEE Proc. (1)

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

IEEE Trans. Commun. (2)

V. A. Aalo, "Performance of maximal-ratio diversity systems in a correlated Nakagami-fading environment," IEEE Trans. Commun. 43, 2360‒2369 (1995).
[CrossRef]

K. Kiasaleh, "Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence," IEEE Trans. Commun. 54, 604‒607 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Commun. Netw. (2)

J. Opt. Soc. Am. (1)

Opt. Express (3)

Opt. Letters (1)

P. J. Winzer and W. R. Leeb, "Fiber coupling efficiency for random light and its applications to lidar," Opt. Letters 23, 986‒988 (1998).
[CrossRef]

Proc. IEEE (1)

D. L. Fried, "Optical heterodyne detection of an atmospherically distorted signal wave front," Proc. IEEE 55, 57‒67 (1967).
[CrossRef]

Radio Sci. (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, 59‒70 (1975).
[CrossRef]

Other (7)

V. N. Mahajan, Optical Imaging and Aberrations, Part II. Wave Diffraction Optics, SPIE Press, 2004.

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

R. M. Gagliardi and S. Karp, Optical Communications, John Wiley & Sons, 1995.

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

M. Nakagami, W. C. Hoffman, ed., "The m-distribution. A general formula of intensity distribution of rapid fading," Statistical Methods in Radio Wave Propagation, Pergamon Press, 1960.

J. A. Buck, Fundamentals of Optical Fibers, 2nd Ed., Wiley, 2004.

J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 2007.

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Figures (3)

Fig. 1
Fig. 1

(Color online) A coherent free-space optical communication system is affected by atmospheric turbulence in several ways. Amplitude scintillation and phase distortion in the receiver plane lead to fluctuations in the amplitude and phase of the detected electrical signal, impairing communication system performance. Adaptive receiver arrays are considered to mitigate the impact of atmospheric turbulence. In a field conjugation fiber array, individual single-mode fiber outputs are detected, and the resulting intermediate-frequency signals are adaptively co-phased and scaled and then summed, thus mitigating amplitude and phase fluctuations caused by turbulence. We analyze coherent fiber arrays composed of L subapertures arranged in a hexagonal close-packed array.

Fig. 2
Fig. 2

(Color online) Normalized (a) mean and (b) standard deviation of SNR versus normalized receiver aperture diameter D / r 0 . The performance is shown for different numbers of subapertures L in a closely packed hexagonal coherent array. The case L = 1 corresponds to a monolithic aperture (black line). When a single aperture is considered, D describes the receiver aperture diameter. For comparison of the receiver performance between an L-element array and a single large aperture, we force the hexagonal array to be packed within the limits of the single aperture diameter D. The analysis takes account of the array fill factor and considers a coupling-geometry parameter τ for each subaperture lens equal to 1.12. Solid lines indicate that amplitude fluctuations are neglected by assuming σ β 2 = 0 . Dashed lines indicate that amplitude fluctuations are considered, assuming a scintillation index σ β 2 = 1 . In (b), the red dot-dashed line indicates the case of L = 7 subapertures with statistically independent fading.

Fig. 3
Fig. 3

(Color online) SEP versus (a) normalized receiver aperture diameter D / r 0 and (b) number of photons per symbol for QPSK with coherent detection and AWGN. The performance is shown for different numbers of subapertures L in the closely packed hexagonal coherent array. The case L = 1 corresponds to a monolithic aperture (black line). When a single aperture is considered, D describes the receiver aperture diameter. For comparison of the receiver performance between an L-element array and a single large aperture, we force the hexagonal array to be packed within the limits of the single aperture diameter D. The analysis considers the array fill factor and considers a coupling-geometry parameter for each subaperture lens of τ = 1 . 12 . In (a), the turbulence-free SNR per symbol γ 0 is proportional to the square of the aperture diameter D. For the smallest aperture considered, we assume γ 0 = 0 dB . In (b), the normalized aperture diameter is set to D / r 0 = 2 . Solid lines indicate that amplitude fluctuations are neglected by assuming σ β 2 = 0 . The upper red dot-dashed line indicates the case L = 7 considering scintillation, with scintillation index σ β 2 = 1 . The lower red dot-dashed line indicates the case L = 7 , considering scintillation, and neglecting fading correlation. Black dashed lines indicate the no-turbulence AWGN case (Eq. (33)). Black dotted lines indicate the no-turbulence AWGN case with τ = 0 , corresponding to a uniformly illuminated pupil, which corresponds to a 5-dB mean SNR improvement over the case τ = 1 . 12 .

Equations (34)

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α = 4 π D 2 d r W ( r ) E i ( r ) E m ( r )
p α ( α ) = 2 ( m N ) m α 2 m 1 Γ ( m ) exp ( m N α 2 ) ,
N = 1 α 2 ¯ ,
p γ ( γ ) = m N γ 0 m γ m 1 Γ ( m ) exp m N γ 0 γ .
M γ ( s ) = 0 d γ exp ( s γ ) p γ ( γ ) = 1 s γ 0 m N m = 1 s γ 0 m α 2 ¯ m .
γ k ¯ = Γ ( m + k ) m k Γ ( m ) γ ̄ k ,
1 m = σ γ 2 ¯ γ ¯ 2 = α 4 ¯ α 2 ¯ 2 1 .
1 m = 2 2 α ̄ 2 α 2 ¯ 2 .
E i ( r ) = exp χ ( r ) j ϕ ( r ) ,
E m ( r ) = 2 π 1 ω m exp r ω m 2 ,
α ¯ = 4 π D 2 d r W ( r ) E i ( r ) E m r ¯ = 4 π D 2 exp χ ̄ d r W ( r ) E m ( r ) exp χ ( r ) χ ̄ ¯ exp j ϕ ( r ) ¯ ,
exp ( j ϕ ) ¯ = exp 1 2 σ ϕ 2 ,
σ ϕ 2 = 1 . 0299 D r 0 5 / 3 .
χ ̄ = σ χ 2 exp χ χ ̄ ¯ = exp 1 2 σ χ 2 .
α ¯ = 1 exp τ 2 τ 2 exp 1 2 σ χ 2 exp 1 2 σ ϕ 2 .
α 2 ¯ = 4 π D 2 2 d r W ( r ) E S r E M ( r ) ¯ d r W r E S * r E M * r ¯
α 2 ¯ = 4 π D 2 2 d r d r W ( r ) W r E m ( r ) E m * r E i ( r ) E i * r ¯ .
α 2 ¯ = 4 π D 2 1 exp 2 τ 2 2 τ 2 d ρ K D ( ρ ) μ ( ρ ) .
K D ( ρ ) = 4 π D 2 d R W R + 1 2 ρ W R 1 2 ρ E m R + 1 2 ρ E m * R 1 2 ρ = 8 τ 2 exp 2 τ 2 ρ / D 2 π 1 exp 2 τ 2 0 1 ρ / D 2 d q exp 2 τ 2 q 2 0 1 q 2 ρ / D d p exp 2 τ 2 p 2
K D ( ρ ) = 2 π a cos ρ D ρ D 1 ρ D 1 2 .
μ ( ρ ) = exp χ R + 1 2 ρ + χ R 1 2 ρ ¯ j ϕ R + 1 2 ρ ϕ R 1 2 ρ ¯ = exp 1 2 D W ( ρ ) .
D W ( ρ ) = 6 . 88 ρ r 0 5 3 .
α 2 ¯ = 4 π D 2 1 exp 2 τ 2 2 τ 2 2 π 0 D ρ d ρ K D ρ μ ( ρ ) .
α 2 ¯ = 1 exp 2 τ 2 2 τ 2 1 . 09 r 0 D 2 Γ 6 5 , 1 . 08 D r 0 5 / 3 .
C α ( Δ r ) = 4 π D 2 1 exp 2 τ 2 2 τ 2 0 2 π d ϕ 0 D / 2 ρ d ρ K D ( ρ ) μ Δ r + ρ cos ϕ 2 + ρ sin ϕ 2 1 / 2 .
γ T = l = 1 L γ l = γ 0 l = 1 L α l 2 .
α = α 1 , α 2 , , α L T
C α = α α ¯ ,
C α = L 0 C α L 0 .
i = 1 L α l 2 ¯ = i = 1 L λ l .
M T ( s ) = l = 1 L M l ( s ) = l = 1 L 1 s γ 0 m λ l m .
γ ¯ = M T 0 , σ γ 2 = M T 0 M T 0 2 .
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 T ( γ ) = a π 0 π / 2 d ϕ M T b sin 2 ϕ ,