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Spectral efficiency and quantum limit of BPSK transmission in a WDM system in presence of multiple interferers

Abstract

In this paper, the spectral efficiency and quantum limit for transmission of a BPSK signal in a WDM system are computed after analyzing the error probability in the presence of component crosstalk. The analysis of bit error rate (BER) is derived from the non-Gaussian probability density function for finite (N) interferers obtained using a new mathematical formulation employing Maclaurin series expansion of the Nth power of zero-order Bessel function. The model is verified with the experimental data taken from the literature. The effects of number of interfering channels, SNR and data rate on BER are studied. Results show how spectral efficiency and quantum limit deviate from ideal values due to the presence of interferers. The spectral efficiency decreases with the appearance of interferers, thus escalating the transmission cost per bit. From the study of quantum limit, it is seen that the minimum number of photons per bit required for BPSK transmission is to be increased to maintain a fixed BER as the number of interferers increases.

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References

  1. 1.

    Jara, N., Vallejos, R., Rubino, G.: Blocking evaluation and wavelength dimensioning of dynamic WDM networks without wavelength conversion. IEEE/OSA J. Opt. Commun. Netw. 9(8), 625–634 (2017). https://doi.org/10.1364/JOCN.9.000625

    Article  Google Scholar 

  2. 2.

    Sarkar, S., Das, N.R.: Study of component crosstalk and obtaining optimum detection threshold for minimum bit-error-rate in a WDM receiver. J. Lightwave Tech. 27, 4366–4373 (2009)

    Article  Google Scholar 

  3. 3.

    Goldstein, E.L., Eskildsen, L., Elrefaie, A.F.: Performance implications of component crosstalk in transparent lightwave networks. IEEE Photon. Technol. Lett. 6(5), 657–660 (1994). https://doi.org/10.1109/68.285571

    Article  Google Scholar 

  4. 4.

    Winzer, P.J.: High-spectral-efficiency optical modulation formats. J. Lightwave Technol. 30(24), 3824–3835 (2012)

    Article  Google Scholar 

  5. 5.

    Millar, D.S., Koike-Akino, T., Arık, S.Ö., Kojima, K., Parsons, K., Yoshida, T., Sugihara, T.: High-dimensional modulation for coherent optical communications systems. Opt. Express 22(7), 8798–8812 (2014)

    Article  Google Scholar 

  6. 6.

    Dalakas, V., Kamalakis, T.: Comparative study of modulation and coding schemes for coherent indoor optical wireless systems. Opt. Quant. Electron. 48, 374 (2016)

    Article  Google Scholar 

  7. 7.

    Mukherjee, P., Sarkar, S., Das, N.R.: An approach for realistic estimation of BER due to signal-component crosstalk in a WDM receiver. Optik 146, 1–7 (2017)

    Article  Google Scholar 

  8. 8.

    Ho, K.P.: Analysis of homodyne crosstalk in optical networks using Gram-Charlier Series. J. Lightwave Technol. 17(2), 149–154 (1999)

    Article  Google Scholar 

  9. 9.

    Kamalakis, T., Sphicopoulos, T.: Asymptotic behavior of in-band crosstalk noise in WDM networks. IEEE Photon. Technol. Lett. 15(3), 476–478 (2003)

    Article  Google Scholar 

  10. 10.

    Ho, K.P.: Effects of homodyne crosstalk on dual-polarization QPSK signals. J. Lightwave Technol. 29(1), 124–131 (2011). https://doi.org/10.1109/JLT.2010.2095830

    Article  Google Scholar 

  11. 11.

    Camatel, S., Ferrero, V.: Homodyne coherent detection of ASK and PSK signals performed by a subcarrier optical phase-locked loop. IEEE Photon. Technol. Lett. 18(1), 142–144 (2006)

    Article  Google Scholar 

  12. 12.

    Camatel, S., Ferrero, V.: 2.5-Gb/s BPSK ultradense WDM homodyne coherent detection using a subcarrier-based optical phase-locked loop. IEEE Photon. Technol. Lett. 18(18), 1919–1921 (2006)

    Article  Google Scholar 

  13. 13.

    Ho, K.-P.: Phase-modulated optical communication systems. Springer, New York (2005)

    Google Scholar 

  14. 14.

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

    Article  Google Scholar 

  15. 15.

    Yan, L.-S., Liu, X., Shieh, W.: Toward the Shannon limit of spectral efficiency. Photon. J. IEEE 3(2), 325–330 (2011)

    Article  Google Scholar 

  16. 16.

    Essiambre, R.-J., Tkach, R.W.: Capacity trends and limits of optical communication networks. Proc. IEEE 100(5), 1035–1055 (2012)

    Article  Google Scholar 

  17. 17.

    Fan, X., Bai, P., Liang, X., Zhang, J., Liu, B.: Detection algorithm of BPSK signal of parameter-adjusted bistable stochastic resonance model based on scale change. IEEE Access 8, 97643–97657 (2020). https://doi.org/10.1109/ACCESS.2020.2997705

    Article  Google Scholar 

  18. 18.

    Rabiei, A.M., Beaulieu, N.: An analytical expression for the BER of an individually optimal single cochannel interferer BPSK receiver. IEEE Trans. Commun. 55(1), 60–63 (2007)

    Article  Google Scholar 

  19. 19.

    Rabiei, A.M., Beaulieu, N.C.: A simple, intuitive expression for the BER of a jointly optimal single cochannel interferer BPSK receiver. IEEE Commun. Lett. 9(3), 201–203 (2005)

    Article  Google Scholar 

  20. 20.

    Saberali, S.M., Amindavar, H., Moghaddamjoo, A.R.: BER calculation and investigation of optimal single user detector for a BPSK signal contaminated by cochannel interferer. IEEE Commun. Lett. 12(10), 705–707 (2008)

    Article  Google Scholar 

  21. 21.

    Chung, K.: An analytical expression for the BER of optimal single user detection of a BPSK signal contaminated by multiple CCIs. EURASIP J. Wirel. Commun. Netw. 190, 2012 (2012)

    Google Scholar 

  22. 22.

    Darshi, S., Bhattacharjee, R.: BER analysis of asynchronised wireless network in presence of non-identically distributed interferers. Wirel. PersCommun. 82, 2583–2600 (2015)

    Article  Google Scholar 

  23. 23.

    Baricz, A.: Powers of modified Bessel functions of the first kind. Appl. Math. Lett. 23(6), 722–724 (2010)

    MathSciNet  Article  Google Scholar 

  24. 24.

    Abramowitz, A., Stegun, I.: Handbook of mathematical functions, 9th edn. Dover, New York (1972)

    MATH  Google Scholar 

  25. 25.

    Papoulis, A.: Probability, random variable, and stochastic processes. McGraw-Hill, New York (1984)

    MATH  Google Scholar 

  26. 26.

    Proakis, J.G.: Digital communications. McGraw-Hill, New York (2000)

    MATH  Google Scholar 

  27. 27.

    Aldis, J.P., Burr, A.G.: The channel capacity of discrete time phase modulation in AWGN. IEEE Trans. Inf. Theory 39, 184–185 (1993)

    Article  Google Scholar 

  28. 28.

    Kramer, G., Ashikhmin, A., van Wijngaarden, A.J., Wei, X.: "Spectral efficiency of coded phase-shift keying for fiber-optic communication. J. Lightwave Technol. 21(10), 2438–2445 (2003). https://doi.org/10.1109/JLT.2003.817704

    Article  Google Scholar 

  29. 29.

    Verdu, S.: Spectral efficiency in the wideband regime. IEEE Trans. Inf. Theory 48(6), 1319–1343 (2002). https://doi.org/10.1109/TIT.2002.1003824

    MathSciNet  Article  MATH  Google Scholar 

  30. 30.

    Antonelli, C., Mecozzi, A., Shtaif, M., Winzer, P.J.: Quantum Limits on the Energy Consumption of Optical Transmission Systems. J. Lightwave Technol. 32(10), 1853–1860 (2014)

    Article  Google Scholar 

  31. 31.

    Jarzyna, M.: Classical capacity per unit cost for quantum channels. Phys. Rev. A 96, 032340 (2017)

    Article  Google Scholar 

  32. 32.

    Glance, B.: Performance of homodyne detection of binary PSK optical signals. J. Lightwave Technol. 4(2), 228–235 (1986). https://doi.org/10.1109/JLT.1986.1074700

    Article  Google Scholar 

  33. 33.

    Stevens, M.L., Caplan, D.O., Robinson, B.S., Boroson, D.M., Kachelmyer, A.L.: Optical homodyne PSK demonstration of 15 photons per bit at 156 Mbps with rate-1/2 turbo coding. Opt. Express 16, 10412–10420 (2008)

    Article  Google Scholar 

  34. 34.

    Kakarla, R., Schröder, J., Andrekson, P.A.: One photon-per-bit receiver using near-noiseless phase-sensitive amplification. Light Sci. Appl. 9, 153 (2020). https://doi.org/10.1038/s41377-020-00389-2

    Article  Google Scholar 

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Correspondence to Nikhil R. Das.

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Mukherjee, P., Sarkar, S. & Das, N.R. Spectral efficiency and quantum limit of BPSK transmission in a WDM system in presence of multiple interferers. Photon Netw Commun 42, 134–141 (2021). https://doi.org/10.1007/s11107-021-00945-9

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Keywords

  • Wavelength division multiplexing
  • BPSK
  • Component crosstalk
  • Spectral efficiency and quantum limits
  • Optical network
  • SNR
  • BER