PL approximation of DBPSK in DF-based cooperative FSO network with pointing error

Original Paper
  • 2 Downloads

Abstract

In this paper, we utilize piecewise linear (PL) approximation to analyze the performance of cooperative free space optical (FSO) network employing differentially modulated binary phase shift keying (DBPSK) data with multiple decode-and-forward (DF) relays. The maximum-likelihood (ML) decoding rule at the destination is approximated by PL approximation which considers the possibility of erroneous relaying and performs very similar to the ML decoder with reduced decoding complexity. The atmospheric fading optical links are modeled by Gamma–Gamma distribution subject to both types of detection techniques, i.e., heterodyne detection and intensity modulation/direct detection (IM/DD) with pointing error. We analytically formulate the probability of error for the multiple-DF relay-based FSO network. However, the novel unified expression of average bit error rate (BER) of PL decoder with single relay and single source to destination pair is derived. Further, we also derive the asymptotic approximate BER of DF-FSO network with multiple relays at high signal-to-noise ratio (SNR) of source to relay links considering heterodyne detection with negligible pointing error. In addition, the unified closed-form expressions of outage probability with single and multiple DF relays are derived in terms of Meijer G function. The expression of outage probability is examined at high SNR in order to obtain analytical diversity order. The impact of different power distribution techniques on outage probability is determined by utilizing power distribution parameters. The derived analytical results are validated through simulation.

Keywords

Differential modulation Gamma–Gamma (GG) fading Free space optics (FSO) Decode and forward (DF) relaying Pointing error Piecewise linear (PL) approximation 

References

  1. 1.
    Andrews, L., Phillips, R., Hopen, C.: Laser Beam Scintillation With Applications. SPIE, New York (2001)CrossRefMATHGoogle Scholar
  2. 2.
    Kedar, D., Arnon, S.: Urban optical wireless communication networks: the main challenges and possible solutions. IEEE Commun. Mag. 42(5), s2–s7 (2004)CrossRefGoogle Scholar
  3. 3.
    Kaushal, H., Kaddoum, G.: Optical communication in space: challenges and mitigation techniques. IEEE Commun. Surv. Tutor. 19(1), 57–96 (2017)CrossRefGoogle Scholar
  4. 4.
    Nosratinia, A., Hunter, T.E., Hedayat, A.: Cooperative communication in wireless networks. IEEE Commun. Mag. 42(10), 74–80 (2004)CrossRefGoogle Scholar
  5. 5.
    Laneman, J.N., Tse, D.N.C., Wornell, G.W.: Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Trans. Inf. Theory 50(12), 3062–3080 (2004)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Sendonaris, A., Erkip, E., Aazhang, B.: User cooperation diversity—Part I: system description. IEEE Trans. Commun. 51(11), 1927–1938 (2003)CrossRefGoogle Scholar
  7. 7.
    Safari, M., Uysal, M.: Relay-assisted free-space optical communication. IEEE Trans. Wirel. Commun. 7(12), 5441–5449 (2008)CrossRefGoogle Scholar
  8. 8.
    Abou-Rjeily, C., Haddad, S.: Cooperative diversity for free-space optical communications: transceiver design and performance analysis. IEEE Trans. Commun. 59(3), 658–663 (2011)CrossRefGoogle Scholar
  9. 9.
    Bhatnagar, M.R.: Average BER analysis of differential modulation in DF cooperative communication system over Gamma–Gamma fading FSO links. IEEE Commun. Lett. 16(8), 1228–1231 (2012)CrossRefGoogle Scholar
  10. 10.
    Zhao, Q., Li, H.: Differential modulation for cooperative wireless system. IEEE Trans. Signal Process. 55(5), 2273–2283 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Trinh, H.V., Thang, T.C., Pham, A.T.: Two-way all-optical AF relaying FSO systems over Malaga (\({\mathscr {M}}\)) channels with pointing errors. In: Proceedings of IEEE International Conference on Communications (ICC). Kuala Lumpur, Malaysia, pp. 1–7, May 2016Google Scholar
  12. 12.
    Ju, M., Kim, I.-M.: ML performance analysis of the decode-and-forward protocol in cooperative diversity networks. IEEE Trans. Wirel. Commun. 8(7), 3855–3867 (2009)CrossRefGoogle Scholar
  13. 13.
    Sharma, P.K., Bansal, A., Garg, P., Tsiftsis, T., Barrios, R.: Relayed FSO communication with aperture averaging receivers and misalignment errors. IET Commun. 11(1), 45–52 (2017)CrossRefGoogle Scholar
  14. 14.
    Bhatnagar, M.R.: Decode-and-Forward based differential modulation for cooperative communication system with unitary and non-unitary constellations. IEEE Trans. Veh. Technol. 61(1), 152–165 (2012)CrossRefGoogle Scholar
  15. 15.
    Bansal, A., Bhatnagar, M.R., Hjrungnes, A., Han, Z.: Low-complexity decoding in DF MIMO relaying system. IEEE Trans. Veh. Technol. 62(3), 1123–1137 (2013)CrossRefGoogle Scholar
  16. 16.
    Bansal, A., Bhatnagar, Manav R., Hjrungnes, Are: Decoding and performance bound of demodulate-and-forward based distributed alamouti STBC. IEEE Trans. Wirel. Commun. 12(2), 702–713 (2013)CrossRefGoogle Scholar
  17. 17.
    Sandalidis, H.G., Tsiftsis, T.A., Karagiannidis, G.K.: Optical wireless communications with heterodyne detection over turbulence channels with pointing errors. IEEE/OSA J. Lightw. Technol. 27(20), 4440–4445 (2009)CrossRefGoogle Scholar
  18. 18.
    Bansal, A., Sharma, P.K., Bhatnagar, M.R.: DF cooperation over Gamma–Gamma fading FSO links with an erroneous relay. In: Proceedings of IEEE International Conference on Commnications (ICC), London, UK, pp. 1–6, June 2015Google Scholar
  19. 19.
    Ansari, I.S., Yilmaz, F., Alouini, M.S.: Performance analysis of free-space optical links over M\(\acute{a}\)laga (\(\mathscr {M} \)) turbulence channels with pointing errors. IEEE Trans. Wirel. Commun. 15(1), 91–102 (2016)CrossRefGoogle Scholar
  20. 20.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products, 6th edn. Academic Press, San Diego (2000)MATHGoogle Scholar
  21. 21.
    Brychkov, Yu A., Marichev, O.I.: Integrals and Series: More Special Functions, vol. 3. Gordon and Breach Science Publishers, London (1990)MATHGoogle Scholar
  22. 22.
    Gappmair, W.: Further results on the capacity of free-space optical channels in turbulent atmosphere. IET Commun. 5(9), 1262–1267 (2011)CrossRefGoogle Scholar
  23. 23.
    Ansari, I.S., Yilmaz, F., Alouini, M.S.: Performance analysis of FSO links over unified Gamma–Gamma turbulence channels. In: Vehicular Technology Conference (VTC Spring’ 2015), Glasgow, Scotland, pp. 1–5, May 2015Google Scholar
  24. 24.
    Trees, H.L.V.: Detection, Estimation, and Modulation Theory: Part I. Detection, Estimation, and Linear Modulation Theory. Wiley, New York (2001)CrossRefMATHGoogle Scholar
  25. 25.
    Biyari, K.H., Lindsey, W.C.: Statistical distributions of hermitian quadratic forms in complex Gaussian variables. IEEE Trans. Inf. Theory 39(3), 1076–1082 (1993)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover Publications, New York (1972)MATHGoogle Scholar
  27. 27.
    Wolfram Research, I.: Mathematica Edition: Version 8.0. Wolfram Research, Inc. (2010)Google Scholar
  28. 28.
    Chatzidiamantis, N.D., Karagiannidis, G.K.: On the distribution of the sum of Gamma–Gamma variates and applications in RF and optical wireless communications. IEEE Trans. Commun. 59(5), 1298–1308 (2011)CrossRefGoogle Scholar
  29. 29.
    Proakis, J.G., Salehi, M.: Digital Communications, 5th edn. McGraw-Hill, New York (2008)Google Scholar
  30. 30.
    Papoulis, A., Pillai, S.U.: Probability, Random Variables and Stochastic Processes, 4th edn. McGraw Hill, New York (1991)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of ECEIGDTUWNew DelhiIndia
  2. 2.Division of ECENetaji Subhas Institute of TechnologyDwarka, New DelhiIndia

Personalised recommendations