Abstract

This paper presents an analytical study of the performance of transmission control protocol (TCP) over free-space optical (FSO) turbulence channels when the automatic-repeat request, selective-repeat (ARQ-SR) scheme is employed. Different TCP versions, including Tahoe, Reno, and selective acknowledgement, are considered. In the TCP throughput analysis, a three-dimensional Markov model is used. In addition, to analyze the joint effect of ARQ-SR and FSO turbulence channels in terms of both TCP throughput and energy consumption, a newly defined joint throughput–energy-efficiency parameter is analytically derived. In the numerical results, we discuss cross-layer design strategies for the selection of FSO system parameters and the ARQ-SR scheme in order to maximize the TCP throughput and to achieve the trade-off between the energy consumption and the throughput under various conditions of the FSO turbulence channel.

© 2013 Optical Society of America

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  1. D. O’Brien and M. Katz, “Optical wireless communications within fourth-generation wireless systems,” J. Opt. Netw., vol.  4, pp. 312–322, 2005.
    [CrossRef]
  2. Z. Ghassemlooy, W. O. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB. CRC Press, Aug. 2012.
  3. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  50, pp. 1293–1300, Aug. 2002.
    [CrossRef]
  4. M. Uysal, J. T. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma–gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol.  5, pp. 1229–1233, June 2006.
    [CrossRef]
  5. X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, no. 4, pp. 540–543, Apr. 2012.
    [CrossRef]
  6. D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng., vol.  47, no. 4, 046001, Apr. 2008.
    [CrossRef]
  7. A. Khatoon, W. G. Cowley, N. Letzepis, and D. Giggenbach, “Estimation of channel parameters and background irradiance for free-space optical link,” Appl. Opt., vol.  52, no. 14, pp. 3260–3268, 2013.
    [CrossRef]
  8. W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol.  27, no. 8, pp. 967–973, Apr. 2009.
    [CrossRef]
  9. W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, “Error performance of terrestrial free space optical links with subcarrier time diversity,” IET Commun., vol.  6, no. 5, pp. 499–506, Mar. 2012.
    [CrossRef]
  10. D. A. Luong, T. C. Thang, and A. T. Pham, “Effect of avalanche photodiode and thermal noises on the performance of binary phase-shift keying/subcarrier-intensity modulation/free-space optical systems over turbulence channels,” IET Commun., vol.  7, no. 8, pp. 738–744, May 2013.
    [CrossRef]
  11. E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
    [CrossRef]
  12. C. Liu and R. Jain, “Approaches of wireless TCP enhancement and a new proposal based on congestion coherence,” in Proc. 36th Annu. Hawaii Int. Conf. on System Sciences, Jan. 2003, pp. 307–317.
  13. W. Ding and A. Jamalipour, “A new explicit loss notification with acknowledgment for wireless TCP,” in 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, Sept. 2001, vol. 1, pp. B-65–B-69.
  14. H. M. Chaskar, T. V. Lakshman, and U. Madhow, “TCP over wireless with link level error control: analysis and design methodology,” IEEE/ACM Trans. Netw., vol.  7, pp. 605–615, Oct. 1999.
    [CrossRef]
  15. L. Le, E. Hossain, and T. Le-Ngoc, “Interaction between radio link level truncated ARQ, and TCP in multi-rate wireless networks: A cross-layer performance analysis,” IET Commun., vol.  1, no. 5, pp. 821–830, Oct. 2007.
    [CrossRef]
  16. A. H. M. Mahmudul Haque, N. I. Mondal, S. K. Ghosh, and M. Z. A. Bhotto, “End to end adaptive forward error correction (FEC) for improving TCP performance over wireless wink,” in Int. Conf. on Electrical and Computer Engineering, Dec. 2006, pp. 569–572.
  17. E. J. Lee and V. W. S. Chan, “Performance of the transport layer protocol for diversity communication over the clear turbulent atmospheric optical channel,” in IEEE Int. Conf. on Communications, May 2005, vol. 1, pp. 333–339.
  18. C. Kose and T. R. Halford, “Incremental redundancy hybrid ARQ protocol design for FSO links,” in IEEE Military Communications Conf., Oct. 2009, pp. 1–7.
  19. K. Kiasaleh, “Hybrid ARQ for FSO communications through turbulent atmosphere,” IEEE Commun. Lett., vol.  14, no. 9, pp. 866–868, Sept. 2010.
    [CrossRef]
  20. A. R. Hammons and F. Davidson, “On the design of automatic repeat request protocols for turbulent free-space optical links,” in IEEE Military Communications Conf., Oct. 31–Nov. 3, 2010, pp. 808–813.
  21. B. Sikdar, S. Kalyanaraman, and K. S. Vastola, “Analytic models for the latency and steady-state throughput of TCP Tahoe, Reno, and SACK,” IEEE/ACM Trans. Netw., vol.  11, pp. 959–971, Dec. 2003.
    [CrossRef]
  22. J. G. Kim and M. M. Krunz, “Delay analysis of selective repeat ARQ for a Markovian source over a wireless channel,” IEEE Trans. Veh. Technol., vol.  49, pp. 1968–1981, Sept. 2000.
    [CrossRef]
  23. C. Casetti and M. Meo, “A new approach to model the stationary behavior of TCP connections,” in Proc. of the 19th Annu. Joint Conf. of the IEEE Computer and Communications Societies (IEEE INFOCOM), Mar. 2000, vol. 1, pp. 367–375.
  24. A. Wierman and T. Osogami, “A unified framework for modeling TCP-Vegas, TCP-SACK, and TCP-Reno,” in 11th IEEE/ACM Int. Symp. on Modeling, Analysis and Simulation of Computer Telecommunications Systems, Oct. 2003, pp. 269–278.

2013 (2)

D. A. Luong, T. C. Thang, and A. T. Pham, “Effect of avalanche photodiode and thermal noises on the performance of binary phase-shift keying/subcarrier-intensity modulation/free-space optical systems over turbulence channels,” IET Commun., vol.  7, no. 8, pp. 738–744, May 2013.
[CrossRef]

A. Khatoon, W. G. Cowley, N. Letzepis, and D. Giggenbach, “Estimation of channel parameters and background irradiance for free-space optical link,” Appl. Opt., vol.  52, no. 14, pp. 3260–3268, 2013.
[CrossRef]

2012 (2)

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, no. 4, pp. 540–543, Apr. 2012.
[CrossRef]

W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, “Error performance of terrestrial free space optical links with subcarrier time diversity,” IET Commun., vol.  6, no. 5, pp. 499–506, Mar. 2012.
[CrossRef]

2010 (1)

K. Kiasaleh, “Hybrid ARQ for FSO communications through turbulent atmosphere,” IEEE Commun. Lett., vol.  14, no. 9, pp. 866–868, Sept. 2010.
[CrossRef]

2009 (2)

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol.  27, no. 8, pp. 967–973, Apr. 2009.
[CrossRef]

2008 (1)

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng., vol.  47, no. 4, 046001, Apr. 2008.
[CrossRef]

2007 (1)

L. Le, E. Hossain, and T. Le-Ngoc, “Interaction between radio link level truncated ARQ, and TCP in multi-rate wireless networks: A cross-layer performance analysis,” IET Commun., vol.  1, no. 5, pp. 821–830, Oct. 2007.
[CrossRef]

2006 (1)

M. Uysal, J. T. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma–gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol.  5, pp. 1229–1233, June 2006.
[CrossRef]

2005 (1)

2003 (1)

B. Sikdar, S. Kalyanaraman, and K. S. Vastola, “Analytic models for the latency and steady-state throughput of TCP Tahoe, Reno, and SACK,” IEEE/ACM Trans. Netw., vol.  11, pp. 959–971, Dec. 2003.
[CrossRef]

2002 (1)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  50, pp. 1293–1300, Aug. 2002.
[CrossRef]

2000 (1)

J. G. Kim and M. M. Krunz, “Delay analysis of selective repeat ARQ for a Markovian source over a wireless channel,” IEEE Trans. Veh. Technol., vol.  49, pp. 1968–1981, Sept. 2000.
[CrossRef]

1999 (1)

H. M. Chaskar, T. V. Lakshman, and U. Madhow, “TCP over wireless with link level error control: analysis and design methodology,” IEEE/ACM Trans. Netw., vol.  7, pp. 605–615, Oct. 1999.
[CrossRef]

Ahmadi, V.

W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, “Error performance of terrestrial free space optical links with subcarrier time diversity,” IET Commun., vol.  6, no. 5, pp. 499–506, Mar. 2012.
[CrossRef]

Bayaki, E.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Bhotto, M. Z. A.

A. H. M. Mahmudul Haque, N. I. Mondal, S. K. Ghosh, and M. Z. A. Bhotto, “End to end adaptive forward error correction (FEC) for improving TCP performance over wireless wink,” in Int. Conf. on Electrical and Computer Engineering, Dec. 2006, pp. 569–572.

Casetti, C.

C. Casetti and M. Meo, “A new approach to model the stationary behavior of TCP connections,” in Proc. of the 19th Annu. Joint Conf. of the IEEE Computer and Communications Societies (IEEE INFOCOM), Mar. 2000, vol. 1, pp. 367–375.

Chan, V. W. S.

E. J. Lee and V. W. S. Chan, “Performance of the transport layer protocol for diversity communication over the clear turbulent atmospheric optical channel,” in IEEE Int. Conf. on Communications, May 2005, vol. 1, pp. 333–339.

Chaskar, H. M.

H. M. Chaskar, T. V. Lakshman, and U. Madhow, “TCP over wireless with link level error control: analysis and design methodology,” IEEE/ACM Trans. Netw., vol.  7, pp. 605–615, Oct. 1999.
[CrossRef]

Cheng, J.

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, no. 4, pp. 540–543, Apr. 2012.
[CrossRef]

Cowley, W. G.

Davidson, F.

A. R. Hammons and F. Davidson, “On the design of automatic repeat request protocols for turbulent free-space optical links,” in IEEE Military Communications Conf., Oct. 31–Nov. 3, 2010, pp. 808–813.

Ding, W.

W. Ding and A. Jamalipour, “A new explicit loss notification with acknowledgment for wireless TCP,” in 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, Sept. 2001, vol. 1, pp. B-65–B-69.

Ghassemlooy, Z.

W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, “Error performance of terrestrial free space optical links with subcarrier time diversity,” IET Commun., vol.  6, no. 5, pp. 499–506, Mar. 2012.
[CrossRef]

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol.  27, no. 8, pp. 967–973, Apr. 2009.
[CrossRef]

Z. Ghassemlooy, W. O. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB. CRC Press, Aug. 2012.

Ghosh, S. K.

A. H. M. Mahmudul Haque, N. I. Mondal, S. K. Ghosh, and M. Z. A. Bhotto, “End to end adaptive forward error correction (FEC) for improving TCP performance over wireless wink,” in Int. Conf. on Electrical and Computer Engineering, Dec. 2006, pp. 569–572.

Giggenbach, D.

A. Khatoon, W. G. Cowley, N. Letzepis, and D. Giggenbach, “Estimation of channel parameters and background irradiance for free-space optical link,” Appl. Opt., vol.  52, no. 14, pp. 3260–3268, 2013.
[CrossRef]

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng., vol.  47, no. 4, 046001, Apr. 2008.
[CrossRef]

Haas, H.

W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, “Error performance of terrestrial free space optical links with subcarrier time diversity,” IET Commun., vol.  6, no. 5, pp. 499–506, Mar. 2012.
[CrossRef]

Halford, T. R.

C. Kose and T. R. Halford, “Incremental redundancy hybrid ARQ protocol design for FSO links,” in IEEE Military Communications Conf., Oct. 2009, pp. 1–7.

Hammons, A. R.

A. R. Hammons and F. Davidson, “On the design of automatic repeat request protocols for turbulent free-space optical links,” in IEEE Military Communications Conf., Oct. 31–Nov. 3, 2010, pp. 808–813.

Henniger, H.

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng., vol.  47, no. 4, 046001, Apr. 2008.
[CrossRef]

Hossain, E.

L. Le, E. Hossain, and T. Le-Ngoc, “Interaction between radio link level truncated ARQ, and TCP in multi-rate wireless networks: A cross-layer performance analysis,” IET Commun., vol.  1, no. 5, pp. 821–830, Oct. 2007.
[CrossRef]

Jain, R.

C. Liu and R. Jain, “Approaches of wireless TCP enhancement and a new proposal based on congestion coherence,” in Proc. 36th Annu. Hawaii Int. Conf. on System Sciences, Jan. 2003, pp. 307–317.

Jamalipour, A.

W. Ding and A. Jamalipour, “A new explicit loss notification with acknowledgment for wireless TCP,” in 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, Sept. 2001, vol. 1, pp. B-65–B-69.

Kahn, J. M.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  50, pp. 1293–1300, Aug. 2002.
[CrossRef]

Kalyanaraman, S.

B. Sikdar, S. Kalyanaraman, and K. S. Vastola, “Analytic models for the latency and steady-state throughput of TCP Tahoe, Reno, and SACK,” IEEE/ACM Trans. Netw., vol.  11, pp. 959–971, Dec. 2003.
[CrossRef]

Katz, M.

Khatoon, A.

Kiasaleh, K.

K. Kiasaleh, “Hybrid ARQ for FSO communications through turbulent atmosphere,” IEEE Commun. Lett., vol.  14, no. 9, pp. 866–868, Sept. 2010.
[CrossRef]

Kim, J. G.

J. G. Kim and M. M. Krunz, “Delay analysis of selective repeat ARQ for a Markovian source over a wireless channel,” IEEE Trans. Veh. Technol., vol.  49, pp. 1968–1981, Sept. 2000.
[CrossRef]

Kose, C.

C. Kose and T. R. Halford, “Incremental redundancy hybrid ARQ protocol design for FSO links,” in IEEE Military Communications Conf., Oct. 2009, pp. 1–7.

Krunz, M. M.

J. G. Kim and M. M. Krunz, “Delay analysis of selective repeat ARQ for a Markovian source over a wireless channel,” IEEE Trans. Veh. Technol., vol.  49, pp. 1968–1981, Sept. 2000.
[CrossRef]

Lakshman, T. V.

H. M. Chaskar, T. V. Lakshman, and U. Madhow, “TCP over wireless with link level error control: analysis and design methodology,” IEEE/ACM Trans. Netw., vol.  7, pp. 605–615, Oct. 1999.
[CrossRef]

Le, L.

L. Le, E. Hossain, and T. Le-Ngoc, “Interaction between radio link level truncated ARQ, and TCP in multi-rate wireless networks: A cross-layer performance analysis,” IET Commun., vol.  1, no. 5, pp. 821–830, Oct. 2007.
[CrossRef]

Lee, E. J.

E. J. Lee and V. W. S. Chan, “Performance of the transport layer protocol for diversity communication over the clear turbulent atmospheric optical channel,” in IEEE Int. Conf. on Communications, May 2005, vol. 1, pp. 333–339.

Leitgeb, E.

W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, “Error performance of terrestrial free space optical links with subcarrier time diversity,” IET Commun., vol.  6, no. 5, pp. 499–506, Mar. 2012.
[CrossRef]

Le-Ngoc, T.

L. Le, E. Hossain, and T. Le-Ngoc, “Interaction between radio link level truncated ARQ, and TCP in multi-rate wireless networks: A cross-layer performance analysis,” IET Commun., vol.  1, no. 5, pp. 821–830, Oct. 2007.
[CrossRef]

Letzepis, N.

Li, J. T.

M. Uysal, J. T. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma–gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol.  5, pp. 1229–1233, June 2006.
[CrossRef]

Liu, C.

C. Liu and R. Jain, “Approaches of wireless TCP enhancement and a new proposal based on congestion coherence,” in Proc. 36th Annu. Hawaii Int. Conf. on System Sciences, Jan. 2003, pp. 307–317.

Luong, D. A.

D. A. Luong, T. C. Thang, and A. T. Pham, “Effect of avalanche photodiode and thermal noises on the performance of binary phase-shift keying/subcarrier-intensity modulation/free-space optical systems over turbulence channels,” IET Commun., vol.  7, no. 8, pp. 738–744, May 2013.
[CrossRef]

Madhow, U.

H. M. Chaskar, T. V. Lakshman, and U. Madhow, “TCP over wireless with link level error control: analysis and design methodology,” IEEE/ACM Trans. Netw., vol.  7, pp. 605–615, Oct. 1999.
[CrossRef]

Mahmudul Haque, A. H. M.

A. H. M. Mahmudul Haque, N. I. Mondal, S. K. Ghosh, and M. Z. A. Bhotto, “End to end adaptive forward error correction (FEC) for improving TCP performance over wireless wink,” in Int. Conf. on Electrical and Computer Engineering, Dec. 2006, pp. 569–572.

Mallik, R. K.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Meo, M.

C. Casetti and M. Meo, “A new approach to model the stationary behavior of TCP connections,” in Proc. of the 19th Annu. Joint Conf. of the IEEE Computer and Communications Societies (IEEE INFOCOM), Mar. 2000, vol. 1, pp. 367–375.

Mondal, N. I.

A. H. M. Mahmudul Haque, N. I. Mondal, S. K. Ghosh, and M. Z. A. Bhotto, “End to end adaptive forward error correction (FEC) for improving TCP performance over wireless wink,” in Int. Conf. on Electrical and Computer Engineering, Dec. 2006, pp. 569–572.

Niu, M.

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, no. 4, pp. 540–543, Apr. 2012.
[CrossRef]

O’Brien, D.

Osogami, T.

A. Wierman and T. Osogami, “A unified framework for modeling TCP-Vegas, TCP-SACK, and TCP-Reno,” in 11th IEEE/ACM Int. Symp. on Modeling, Analysis and Simulation of Computer Telecommunications Systems, Oct. 2003, pp. 269–278.

Pham, A. T.

D. A. Luong, T. C. Thang, and A. T. Pham, “Effect of avalanche photodiode and thermal noises on the performance of binary phase-shift keying/subcarrier-intensity modulation/free-space optical systems over turbulence channels,” IET Commun., vol.  7, no. 8, pp. 738–744, May 2013.
[CrossRef]

Popoola, W.

W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, “Error performance of terrestrial free space optical links with subcarrier time diversity,” IET Commun., vol.  6, no. 5, pp. 499–506, Mar. 2012.
[CrossRef]

Popoola, W. O.

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol.  27, no. 8, pp. 967–973, Apr. 2009.
[CrossRef]

Z. Ghassemlooy, W. O. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB. CRC Press, Aug. 2012.

Rajbhandari, S.

Z. Ghassemlooy, W. O. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB. CRC Press, Aug. 2012.

Schober, R.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Sikdar, B.

B. Sikdar, S. Kalyanaraman, and K. S. Vastola, “Analytic models for the latency and steady-state throughput of TCP Tahoe, Reno, and SACK,” IEEE/ACM Trans. Netw., vol.  11, pp. 959–971, Dec. 2003.
[CrossRef]

Song, X.

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, no. 4, pp. 540–543, Apr. 2012.
[CrossRef]

Thang, T. C.

D. A. Luong, T. C. Thang, and A. T. Pham, “Effect of avalanche photodiode and thermal noises on the performance of binary phase-shift keying/subcarrier-intensity modulation/free-space optical systems over turbulence channels,” IET Commun., vol.  7, no. 8, pp. 738–744, May 2013.
[CrossRef]

Uysal, M.

M. Uysal, J. T. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma–gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol.  5, pp. 1229–1233, June 2006.
[CrossRef]

Vastola, K. S.

B. Sikdar, S. Kalyanaraman, and K. S. Vastola, “Analytic models for the latency and steady-state throughput of TCP Tahoe, Reno, and SACK,” IEEE/ACM Trans. Netw., vol.  11, pp. 959–971, Dec. 2003.
[CrossRef]

Wierman, A.

A. Wierman and T. Osogami, “A unified framework for modeling TCP-Vegas, TCP-SACK, and TCP-Reno,” in 11th IEEE/ACM Int. Symp. on Modeling, Analysis and Simulation of Computer Telecommunications Systems, Oct. 2003, pp. 269–278.

Yu, M.

M. Uysal, J. T. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma–gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol.  5, pp. 1229–1233, June 2006.
[CrossRef]

Zhu, X.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  50, pp. 1293–1300, Aug. 2002.
[CrossRef]

Appl. Opt. (1)

IEEE Commun. Lett. (2)

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, no. 4, pp. 540–543, Apr. 2012.
[CrossRef]

K. Kiasaleh, “Hybrid ARQ for FSO communications through turbulent atmosphere,” IEEE Commun. Lett., vol.  14, no. 9, pp. 866–868, Sept. 2010.
[CrossRef]

IEEE Trans. Commun. (2)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  50, pp. 1293–1300, Aug. 2002.
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

IEEE Trans. Veh. Technol. (1)

J. G. Kim and M. M. Krunz, “Delay analysis of selective repeat ARQ for a Markovian source over a wireless channel,” IEEE Trans. Veh. Technol., vol.  49, pp. 1968–1981, Sept. 2000.
[CrossRef]

IEEE Trans. Wireless Commun. (1)

M. Uysal, J. T. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma–gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol.  5, pp. 1229–1233, June 2006.
[CrossRef]

IEEE/ACM Trans. Netw. (2)

H. M. Chaskar, T. V. Lakshman, and U. Madhow, “TCP over wireless with link level error control: analysis and design methodology,” IEEE/ACM Trans. Netw., vol.  7, pp. 605–615, Oct. 1999.
[CrossRef]

B. Sikdar, S. Kalyanaraman, and K. S. Vastola, “Analytic models for the latency and steady-state throughput of TCP Tahoe, Reno, and SACK,” IEEE/ACM Trans. Netw., vol.  11, pp. 959–971, Dec. 2003.
[CrossRef]

IET Commun. (3)

L. Le, E. Hossain, and T. Le-Ngoc, “Interaction between radio link level truncated ARQ, and TCP in multi-rate wireless networks: A cross-layer performance analysis,” IET Commun., vol.  1, no. 5, pp. 821–830, Oct. 2007.
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Network scenario with a TCP connection over a FSO link.

Fig. 2.
Fig. 2.

Markov chain model for Wmax=8 and the number of increasing timeouts limited to six.

Fig. 3.
Fig. 3.

Throughput versus the peak transmitted power (Ps) for different TCP versions when Cn2=5×1015m2/3, L=1200m, and no ARQ-SR.

Fig. 4.
Fig. 4.

Throughput versus the peak transmitted power (Ps) for different values of M and L when Cn2=5×1015m2/3.

Fig. 5.
Fig. 5.

Throughput versus the peak transmitted power (Ps) for different values of M and L when Cn2=9×1015m2/3.

Fig. 6.
Fig. 6.

Throughput versus the peak transmitted power (Ps) for different values of M and L when Cn2=4×1014m2/3.

Fig. 7.
Fig. 7.

Joint throughput–energy efficiency versus the peak transmitted power (Ps) for different turbulence strengths when L=1200m and M=6.

Fig. 8.
Fig. 8.

Joint throughput–energy efficiency versus the peak transmitted power (Ps) for different channel distances when Cn2=9×1015m2/3 and M=6.

Fig. 9.
Fig. 9.

Optimal peak transmitted power versus the channel distance (L) for different turbulence strengths when M=6.

Tables (1)

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TABLE I System Parameters and Constants

Equations (34)

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fX(x)=12πσsxexp[(lnx+σs2/2)22σs2],
σs2=exp[0.49σR2(1+0.18d2+0.56σR12/5)7/6+0.51σR2(1+0.9d2+0.62d2σR12/5)5/6]1.
σR2=1.23Cn2k7/6L11/6,
fX(x)=2(αβ)(α+β)/2Γ(α)Γ(β)x(α+β)/21Kαβ(2αβx),
α={exp[0.49σR2(1+1.11σR12/5)7/6]1}1,β={exp[0.51σR2(1+0.69σR12/5)5/6]1}1.
Pw(i)=(wi)[1(1PFSO)(1Pwire)]i×[(1PFSO)(1Pwire)]w1.
PFSO=1(1PfM+1)Nf,
Pf=1(1Pe)Lf,
Pe=0Q(SNR×x)fX(x)dx,
Q(y)=12πyexp(y22)dy,
SNR=(mRPsa4σN)2,
Pe=0Q(SNR×x)×12πσsxexp[(lnx+σs2/2)22σs2]dx.
Pe=1πQ[SNR×exp(2σsyσs2/2)]×exp(y2)dy.
g(y)exp(y2)dyi=N;i0Nwig(yi),
Pe1πi=N;i0NwiQ[SNR×exp(2σsyiσs2/2)].
Pe=0Q(SNR×x)×2(αβ)(α+β)/2Γ(α)Γ(β)x(α+β)/21Kαβ(2αβx)dx.
Kv(y)=π2sin(πv))p=0[(y/2)2pvΓ(pv+1)p!(y/2)2p+vΓ(p+v+1)p!],vZ,|y|<.
Pe=A(α,β)p=0[ap(α,β)B(12,p+β+12)(SNR2)p+β2ap(β,α)B(12,p+α+12)(SNR2)p+α2],
A(α,β)=14Γ(α)Γ(β)sin[(αβ)π],
ap(x,y)=(xy)p+yΓ(p+y2)Γ(px+y+1)p!.
E[RTT]=2×Twire+(Lf/R+TCRC)(M¯+1)Nf,
M¯=m=0MmPfm(1Pf)1PfM+1=Pf(1Pf)1PfM+1m=1MmPfm1=Pf(1Pf)1PfM+1Pf(1PfM+11Pf)=Pf(1Pf)1PfM+1(M+1)PfM(1Pf)+(1PfM+1)(1Pf)2=Pf1Pf(M+1)PfM+11PfM+1.
Bo={(1,j,k)|2j[Wmax/2],1k6},To={(1,j,0)|2j[Wmax/2]},Ss={(i,j,0)|2ij[Wmax/2]},Ca={(i,j,0)|2j<iWmax,j[Wmax/2]}.
P(1,j,k)(1,j,k+1)=PTO(1),P(1,j,k)(1,j,0)=1PTO(1),P(1,j,6)(1,j,0)=1,P(1,j,0)(1,j,1)=PTO(1),P(1,j,0)(2,j,0)=1PTO(1).
P(i,j)(1,max([i/2],2))=PTO(i),P(i,j)(max([i/2],2),max([i/2],2))=PTD(i),P(i,j)(2i,j)=1PTD(i)PTO(i).
P(i,j)(1,max([i/2],2))=PTO(i),P(i,j)(max([i/2],2),max([i/2],2))=PTD(i),P(i,j)(i+1,j)=1PTD(i)PTO(i),P(Wmax,[Wmax2])(Wmax,[Wmax2])=1PTD(Wmax)PTO(Wmax).
PTORe=i=3wPw(i);PTDRe=Pw(1)+Pw(2),w10,PTORe=i=2wPw(i);PTDRe=Pw(1),4w10,PTORe=1Pw(0);PTDRe=0,w4.
PTOSA=i=1w3Pw(i)(1(1P1(1))i)+i=w2wPw(i),PTDSA=i=1w3Pw(i)(1P1(1))i+i=w2wPw(i).
{P=P×Qi=1Npi=1,
{aii=qii1,1iN,aij=qij,1iN1,1jNandij,aNj=1,1jN.
{tn=E[RTT],n(To,Ss,Ca),tn=2kT,nBo,1k6,
Λ=W×xT×x.
JΛ,E=ΛE[energy].
E[energy]=(M¯+1)LTCPPs/2=(Pf1Pf(M+1)PfM+11PfM+1+1)LTCPPs/2.