Abstract

Multiple-pulse position modulation (MPPM) is an advanced modulation method for optical wireless communication (OWC), which could provide better performance when channel information is not available. We consider the evaluation of a symbol error rate (SER) expression for MPPM applied within OWC. In the proposed model, MPPM is realized by spectral-amplitude coding (SAC) with non-uniform spectral slot energies. The derived fading channel SER expression is applicable for an arbitrary fading distribution, which may be due to either atmospheric turbulence or transceiver pointing error. A detailed theoretical analysis of the SER is provided and the resulting SER expression is verified by simulation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), 5th ed.
  2. Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical wireless communications: system and channel modelling with Matlab® (CRC Press, 2012).
  3. H. M. H. Shalaby, “Efficient use of PPM in spectral-amplitude-coding optical CDMA systems,” J. Light. Technol. 30, 3512–3519 (2012).
    [Crossref]
  4. M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
    [Crossref]
  5. E. Weiss, D. Bykhovsky, and S. Arnon, “Symbol error rate model for communication using femtosecond pulses for space applications,” IEEE Photon. Technol. Lett. 28, 1286–1289 (2016).
    [Crossref]
  6. B. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007), 2nd ed.
  7. R. Rachmani, A. Zilberman, and S. Arnon, “Computer backplane with free space optical links: Air turbulence effects,” J. Light. Technol. 30, 156–162 (2012).
    [Crossref]
  8. D. Bykhovsky, D. Elmakayes, and S. Arnon, “Experimental evaluation of free space links in the presence of turbulence for server backplane,” J. Light. Technol. 33, 2923–2929 (2015).
  9. D. Elmakias, D. Bykhovsky, and S. Arnon, “Air turbulence effects on performance of optical wireless communication with crosstalk in server backplane,” Chin. Opt. Lett. 15, 020602 (2017).
    [Crossref]
  10. R. Rachmani and S. Arnon, “Server backplane with optical wavelength diversity links,” J. Light. Technol. 30, 1359–1365 (2012).
    [Crossref]
  11. S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28, 129 (2003).
    [Crossref] [PubMed]
  12. A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Light. Technol. 25, 1702–1710 (2007).
    [Crossref]
  13. H. Sandalidis, T. Tsiftsis, G. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12, 44–46 (2008).
    [Crossref]
  14. P. Kaur, V. K. Jain, and S. Kar, “Performance of free space optical links in presence of turbulence, pointing errors and adverse weather conditions,” Opt. Quantum Electron. 48, 65 (2015).
    [Crossref]
  15. F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62, 713–725 (2014).
    [Crossref]
  16. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005), 2nd ed.
    [Crossref]
  17. Y. Chen and N. Beaulieu, “Solutions to infinite integrals of Gaussian Q-function products and some applications,” IEEE Commun. Lett. 11, 853–855 (2007).
    [Crossref]
  18. T. T. Nguyen and L. Lampe, “MPPM constellation selection for free-space optical communications,” IEEE Trans. Commun. 60, 632–636 (2012).
    [Crossref]

2017 (1)

2016 (1)

E. Weiss, D. Bykhovsky, and S. Arnon, “Symbol error rate model for communication using femtosecond pulses for space applications,” IEEE Photon. Technol. Lett. 28, 1286–1289 (2016).
[Crossref]

2015 (3)

M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
[Crossref]

D. Bykhovsky, D. Elmakayes, and S. Arnon, “Experimental evaluation of free space links in the presence of turbulence for server backplane,” J. Light. Technol. 33, 2923–2929 (2015).

P. Kaur, V. K. Jain, and S. Kar, “Performance of free space optical links in presence of turbulence, pointing errors and adverse weather conditions,” Opt. Quantum Electron. 48, 65 (2015).
[Crossref]

2014 (1)

F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62, 713–725 (2014).
[Crossref]

2012 (4)

T. T. Nguyen and L. Lampe, “MPPM constellation selection for free-space optical communications,” IEEE Trans. Commun. 60, 632–636 (2012).
[Crossref]

R. Rachmani and S. Arnon, “Server backplane with optical wavelength diversity links,” J. Light. Technol. 30, 1359–1365 (2012).
[Crossref]

H. M. H. Shalaby, “Efficient use of PPM in spectral-amplitude-coding optical CDMA systems,” J. Light. Technol. 30, 3512–3519 (2012).
[Crossref]

R. Rachmani, A. Zilberman, and S. Arnon, “Computer backplane with free space optical links: Air turbulence effects,” J. Light. Technol. 30, 156–162 (2012).
[Crossref]

2008 (1)

H. Sandalidis, T. Tsiftsis, G. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12, 44–46 (2008).
[Crossref]

2007 (2)

Y. Chen and N. Beaulieu, “Solutions to infinite integrals of Gaussian Q-function products and some applications,” IEEE Commun. Lett. 11, 853–855 (2007).
[Crossref]

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Light. Technol. 25, 1702–1710 (2007).
[Crossref]

2003 (1)

Anas, S. B. A.

M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005), 2nd ed.
[Crossref]

Arnon, S.

D. Elmakias, D. Bykhovsky, and S. Arnon, “Air turbulence effects on performance of optical wireless communication with crosstalk in server backplane,” Chin. Opt. Lett. 15, 020602 (2017).
[Crossref]

E. Weiss, D. Bykhovsky, and S. Arnon, “Symbol error rate model for communication using femtosecond pulses for space applications,” IEEE Photon. Technol. Lett. 28, 1286–1289 (2016).
[Crossref]

D. Bykhovsky, D. Elmakayes, and S. Arnon, “Experimental evaluation of free space links in the presence of turbulence for server backplane,” J. Light. Technol. 33, 2923–2929 (2015).

R. Rachmani, A. Zilberman, and S. Arnon, “Computer backplane with free space optical links: Air turbulence effects,” J. Light. Technol. 30, 156–162 (2012).
[Crossref]

R. Rachmani and S. Arnon, “Server backplane with optical wavelength diversity links,” J. Light. Technol. 30, 1359–1365 (2012).
[Crossref]

S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28, 129 (2003).
[Crossref] [PubMed]

Beaulieu, N.

Y. Chen and N. Beaulieu, “Solutions to infinite integrals of Gaussian Q-function products and some applications,” IEEE Commun. Lett. 11, 853–855 (2007).
[Crossref]

Bykhovsky, D.

D. Elmakias, D. Bykhovsky, and S. Arnon, “Air turbulence effects on performance of optical wireless communication with crosstalk in server backplane,” Chin. Opt. Lett. 15, 020602 (2017).
[Crossref]

E. Weiss, D. Bykhovsky, and S. Arnon, “Symbol error rate model for communication using femtosecond pulses for space applications,” IEEE Photon. Technol. Lett. 28, 1286–1289 (2016).
[Crossref]

D. Bykhovsky, D. Elmakayes, and S. Arnon, “Experimental evaluation of free space links in the presence of turbulence for server backplane,” J. Light. Technol. 33, 2923–2929 (2015).

Chen, Y.

Y. Chen and N. Beaulieu, “Solutions to infinite integrals of Gaussian Q-function products and some applications,” IEEE Commun. Lett. 11, 853–855 (2007).
[Crossref]

Cheng, J.

F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62, 713–725 (2014).
[Crossref]

Elmakayes, D.

D. Bykhovsky, D. Elmakayes, and S. Arnon, “Experimental evaluation of free space links in the presence of turbulence for server backplane,” J. Light. Technol. 33, 2923–2929 (2015).

Elmakias, D.

Farid, A. A.

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Light. Technol. 25, 1702–1710 (2007).
[Crossref]

Ghassemlooy, Z.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical wireless communications: system and channel modelling with Matlab® (CRC Press, 2012).

Hranilovic, S.

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Light. Technol. 25, 1702–1710 (2007).
[Crossref]

Jain, V. K.

P. Kaur, V. K. Jain, and S. Kar, “Performance of free space optical links in presence of turbulence, pointing errors and adverse weather conditions,” Opt. Quantum Electron. 48, 65 (2015).
[Crossref]

Kar, S.

P. Kaur, V. K. Jain, and S. Kar, “Performance of free space optical links in presence of turbulence, pointing errors and adverse weather conditions,” Opt. Quantum Electron. 48, 65 (2015).
[Crossref]

Karagiannidis, G.

H. Sandalidis, T. Tsiftsis, G. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12, 44–46 (2008).
[Crossref]

Kaur, P.

P. Kaur, V. K. Jain, and S. Kar, “Performance of free space optical links in presence of turbulence, pointing errors and adverse weather conditions,” Opt. Quantum Electron. 48, 65 (2015).
[Crossref]

Lampe, L.

T. T. Nguyen and L. Lampe, “MPPM constellation selection for free-space optical communications,” IEEE Trans. Commun. 60, 632–636 (2012).
[Crossref]

Mahdi, M. A.

M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
[Crossref]

Mamdoohi, G.

M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
[Crossref]

Moghaddasi, M.

M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
[Crossref]

Nguyen, T. T.

T. T. Nguyen and L. Lampe, “MPPM constellation selection for free-space optical communications,” IEEE Trans. Commun. 60, 632–636 (2012).
[Crossref]

Noor, A. S. M.

M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
[Crossref]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005), 2nd ed.
[Crossref]

Popoola, W.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical wireless communications: system and channel modelling with Matlab® (CRC Press, 2012).

Proakis, J.

J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), 5th ed.

Rachmani, R.

R. Rachmani, A. Zilberman, and S. Arnon, “Computer backplane with free space optical links: Air turbulence effects,” J. Light. Technol. 30, 156–162 (2012).
[Crossref]

R. Rachmani and S. Arnon, “Server backplane with optical wavelength diversity links,” J. Light. Technol. 30, 1359–1365 (2012).
[Crossref]

Rajbhandari, S.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical wireless communications: system and channel modelling with Matlab® (CRC Press, 2012).

Saleh, B. E.

B. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007), 2nd ed.

Salehi, M.

J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), 5th ed.

Sandalidis, H.

H. Sandalidis, T. Tsiftsis, G. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12, 44–46 (2008).
[Crossref]

Shalaby, H. M. H.

H. M. H. Shalaby, “Efficient use of PPM in spectral-amplitude-coding optical CDMA systems,” J. Light. Technol. 30, 3512–3519 (2012).
[Crossref]

Teich, M. C.

B. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007), 2nd ed.

Tsiftsis, T.

H. Sandalidis, T. Tsiftsis, G. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12, 44–46 (2008).
[Crossref]

Tsiftsis, T. A.

F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62, 713–725 (2014).
[Crossref]

Uysal, M.

H. Sandalidis, T. Tsiftsis, G. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12, 44–46 (2008).
[Crossref]

Weiss, E.

E. Weiss, D. Bykhovsky, and S. Arnon, “Symbol error rate model for communication using femtosecond pulses for space applications,” IEEE Photon. Technol. Lett. 28, 1286–1289 (2016).
[Crossref]

Yang, F.

F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62, 713–725 (2014).
[Crossref]

Zilberman, A.

R. Rachmani, A. Zilberman, and S. Arnon, “Computer backplane with free space optical links: Air turbulence effects,” J. Light. Technol. 30, 156–162 (2012).
[Crossref]

Chin. Opt. Lett. (1)

IEEE Commun. Lett. (2)

H. Sandalidis, T. Tsiftsis, G. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12, 44–46 (2008).
[Crossref]

Y. Chen and N. Beaulieu, “Solutions to infinite integrals of Gaussian Q-function products and some applications,” IEEE Commun. Lett. 11, 853–855 (2007).
[Crossref]

IEEE Photon. Technol. Lett. (1)

E. Weiss, D. Bykhovsky, and S. Arnon, “Symbol error rate model for communication using femtosecond pulses for space applications,” IEEE Photon. Technol. Lett. 28, 1286–1289 (2016).
[Crossref]

IEEE Trans. Commun. (2)

T. T. Nguyen and L. Lampe, “MPPM constellation selection for free-space optical communications,” IEEE Trans. Commun. 60, 632–636 (2012).
[Crossref]

F. Yang, J. Cheng, and T. A. Tsiftsis, “Free-space optical communication with nonzero boresight pointing errors,” IEEE Trans. Commun. 62, 713–725 (2014).
[Crossref]

J. Light. Technol. (5)

H. M. H. Shalaby, “Efficient use of PPM in spectral-amplitude-coding optical CDMA systems,” J. Light. Technol. 30, 3512–3519 (2012).
[Crossref]

R. Rachmani, A. Zilberman, and S. Arnon, “Computer backplane with free space optical links: Air turbulence effects,” J. Light. Technol. 30, 156–162 (2012).
[Crossref]

D. Bykhovsky, D. Elmakayes, and S. Arnon, “Experimental evaluation of free space links in the presence of turbulence for server backplane,” J. Light. Technol. 33, 2923–2929 (2015).

R. Rachmani and S. Arnon, “Server backplane with optical wavelength diversity links,” J. Light. Technol. 30, 1359–1365 (2012).
[Crossref]

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Light. Technol. 25, 1702–1710 (2007).
[Crossref]

Opt. Commun. (1)

M. Moghaddasi, G. Mamdoohi, A. S. M. Noor, M. A. Mahdi, and S. B. A. Anas, “Development of SAC–OCDMA in FSO with multi-wavelength laser source,” Opt. Commun. 356, 282–289 (2015).
[Crossref]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

P. Kaur, V. K. Jain, and S. Kar, “Performance of free space optical links in presence of turbulence, pointing errors and adverse weather conditions,” Opt. Quantum Electron. 48, 65 (2015).
[Crossref]

Other (4)

B. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007), 2nd ed.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005), 2nd ed.
[Crossref]

J. Proakis and M. Salehi, Digital Communications (McGraw-Hill, 2007), 5th ed.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical wireless communications: system and channel modelling with Matlab® (CRC Press, 2012).

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Figures (3)

Fig. 1
Fig. 1 An illustration of different slot energies of SAC-MPPM symbol.
Fig. 2
Fig. 2 Illustration of theoretical and simulation results for (U)niform and (N)on-uniform energy spectral slots.
Fig. 3
Fig. 3 Histogram of pe values that correspond to different non-uniform energy symbols. Inset shows si coefficients used in simulation.

Equations (21)

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

W = max ( Y 1 , , Y n )
V = min ( X 1 , , X k )
Z = W V ,
p c r = P ( W < V ) = P ( Z < 0 ) = F Z ( z = 0 ) ,
F Z ( 0 ) = F W ( v ) f V ( v ) d v ,
F W ( w ) = P ( W w ) = i = 1 n P ( Y i w ) = i = 1 n F Y i ( y ) = [ Q ( w σ n ) ] n .
Q ( x ) = 1 2 π x exp ( t 2 2 ) d t .
F V ( v ) = 0 F V ( v | I ) f I ( I ) d I ,
F V ( v | I ) = P ( W w | I ) = 1 i = 1 k Q ( v s i I σ n ) .
F V ( v ) = 0 f V ( v | I ) f I ( I ) d I ,
f V ( v | I ) = v F V ( v | I ) = v i = 1 k Q ( v s i I σ n ) .
d d x [ i = 1 k f i ( x ) ] = i = 1 k [ ( j i f j ( x ) ) d d x f i ( x ) ]
d d x Q ( x a b ) = 1 b 2 π exp [ ( x a ) 2 2 b 2 ] ,
f V ( v | I ) = 1 2 π σ n i = 1 k [ j = 1 i j k Q ( v s j I σ n ) ] exp [ ( v s i I ) 2 σ n 2 ] .
p c r = 0 F W ( v ) f V ( v | I ) f I ( I ) d I d v .
p e = 1 p c r .
F V ( v | I ) = P ( V v | I ) = 1 [ Q ( v I σ n ) ] k ,
f V ( v | I ) = k 2 π σ n exp [ ( v I ) 2 2 σ n 2 ] [ Q ( v I σ n ) ] k 1 ,
f I ( I ) = 1 I 2 π σ I 2 exp { ln 2 ( I / μ ) 2 σ I 2 } , I > 0
f h ( h ) = γ 2 A 0 γ 2 h γ 2 1 , 0 h A 0
v = π a 2 w z , A 0 = [ erf ( v ) ] 2 , w z eq 2 = w z 2 π erf ( v ) 2 v exp ( v 2 ) ,

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