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Generalized Kramers–Kronig receiver for coherent terahertz communications

Abstract

Modern communication systems rely on efficient quadrature amplitude modulation formats that encode information on both the amplitude and phase of an electromagnetic carrier. Coherent detection of such signals typically requires complex receivers that contain a continuous-wave local oscillator as a phase reference and a mixer circuit for spectral down-conversion. In optical communications, the so-called Kramers–Kronig scheme has been demonstrated to simplify the receiver, reducing the hardware to a single photodiode1,2,3. In this approach, a local-oscillator tone is transmitted along with the signal, and the amplitude and phase of the complex signal envelope are digitally reconstructed from the photocurrent by exploiting their Kramers–Kronig-type relation4,5,6. Here, we transfer the Kramers–Kronig scheme to high-speed wireless communications at terahertz carrier frequencies. To this end, we generalize the approach to account for non-quadratic receiver characteristics and employ a Schottky-barrier diode as a nonlinear receiver element. Using 16-state quadrature amplitude modulation, we transmit a net data rate of 115 Gbit s−1 at a carrier frequency of 0.3 THz over a distance of 110 m.

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Fig. 1: Vision of a future wireless backbone network.
Fig. 2: SBD receiver characteristics.
Fig. 3: Experimental set-up.
Fig. 4: Results of the QPSK transmission experiments bridging a distance of 110 m.
Fig. 5: Results of the 16QAM transmission experiments bridging a distance of 110 m.

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Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request.

References

  1. Mecozzi, A., Antonelli, C. & Shtaif, M. Kramers–Kronig coherent receiver. Optica 3, 1220–1227 (2016).

    Article  ADS  Google Scholar 

  2. Zhong, K., Lu, C., Pak, A. & Lau, T. Digital signal processing for short-reach optical communications: a review of current technologies and future trends. J. Lightwave Technol. 36, 377–400 (2018).

    Article  ADS  Google Scholar 

  3. Chen, X. et al. Kramers–Kronig receivers for 100 km datacenter interconnects. J. Lightwave Technol. 36, 79–89 (2018).

    Article  ADS  Google Scholar 

  4. Voelcker, H. Demodulation of single-sideband signals via envelope detection. IEEE Trans. Commun. 14, 22–30 (1966).

    Article  Google Scholar 

  5. Kramers, M. H. A. La diffusion de la lumière par les atomes. Atti Cong. Intern. Fis. 2, 545–557 (1927).

    Google Scholar 

  6. Kronig, R. de L. On the theory of the dispersion of X-rays. J. Opt. Soc. Am. 12, 547–557 (1926).

    Article  ADS  Google Scholar 

  7. Nagatsuma, T., Ducournau, G. & Renaud, C. C. Advances in terahertz communications accelerated by photonics. Nat. Photon. 10, 371–379 (2016).

    Article  ADS  Google Scholar 

  8. Ma, J. et al. Security and eavesdropping in terahertz wireless links. Nature 563, 89–93 (2018).

    Article  ADS  Google Scholar 

  9. Kawanishi, T. THz and photonic seamless communications. J. Lightwave Technol. 37, 1671–1679 (2019).

    Article  ADS  Google Scholar 

  10. Koenig, S. et al. Wireless sub-THz communication system with high data rate. Nat. Photon. 7, 977–981 (2013).

    Article  ADS  Google Scholar 

  11. Puerta, R. et al. Single-carrier dual-polarization 328 Gb/s wireless transmission in a D-band millimeter wave 2 × 2 MU-MIMO radio-over-fiber system. J. Lightwave Technol. 36, 587–593 (2018).

    Article  ADS  Google Scholar 

  12. Li, X. et al. 1 Tb/s millimeter-wave signal wireless delivery at D-band. J. Lightwave Technol. 37, 196–204 (2019).

    Article  ADS  Google Scholar 

  13. Seeds, A. J., Shams, H., Fice, M. J. & Renaud, C. C. Terahertz photonics for wireless communications. J. Lightwave Technol. 33, 579–587 (2015).

    Article  ADS  Google Scholar 

  14. Yu, X. et al. 160 Gbit/s photonics wireless transmission in the 300–500 GHz band. APL Photon. 1, 081301 (2016).

    Article  ADS  Google Scholar 

  15. Kallfass, I. et al. 64 Gbit/s transmission over 850 m fixed wireless link at 240 GHz carrier frequency. J. Infrared Millim. Terahertz Waves 36, 221–233 (2015).

    Article  Google Scholar 

  16. Ma, J., Shrestha, R., Moeller, L. & Mittleman, D. M. Invited article: channel performance for indoor and outdoor terahertz wireless links. APL Photon. 3, 051601 (2018).

    Article  ADS  Google Scholar 

  17. Schneider, G. J., Murakowski, J. A., Schuetz, C. A., Shi, S. & Prather, D. W. Radiofrequency signal-generation system with over seven octaves of continuous tuning. Nat. Photon. 7, 118–122 (2013).

    Article  ADS  Google Scholar 

  18. Carpintero, G. et al. Wireless data transmission at terahertz carrier waves generated from a hybrid InP-polymer dual tunable DBR laser photonic integrated circuit. Sci. Rep. 8, 3018 (2018).

    Article  ADS  Google Scholar 

  19. Nagatsuma, T. & Carpintero, G. Recent progress and future prospect of photonics-enabled terahertz communications research. IEICE Trans. Electron. E98.C, 1060–1070 (2015).

    Article  ADS  Google Scholar 

  20. Harter, T. et al. 110 m THz wireless transmission at 100 Gbit/s using a Kramers–Kronig Schottky barrier diode receiver. In Proc. 2018 European Conference on Optical Communication 1–3 (IEEE, 2018).

  21. Rappaport, T. S. et al. Millimeter wave mobile communications for 5G cellular: it will work! IEEE Access 1, 335–349 (2013).

    Article  Google Scholar 

  22. Andrews, J. G. et al. What will 5G be? IEEE J. Sel. Areas Commun. 32, 1065–1082 (2014).

    Article  Google Scholar 

  23. Minimum Requirements Related to Technical Performance for IMT-2020 Radio Interface(s) Report No. M.2410-0 (ITU-R, 2017).

  24. Latva-aho, M. & Leppänen, K. (eds) Key Drivers and Research Challenges for 6G Ubiquitous Wireless Intelligence (6G Flagship, Univ. Oulu, 2019).

  25. Lowery, A. J., Wang, T. & Corcoran, B. Clipping-enhanced Kramers–Kronig receivers. In Proc. 2019 Optical Fiber Communications Conference and Exhibition M1H.2 (OSA, 2019).

  26. Ito, H., Furuta, T., Muramoto, Y., Ito, T. & Ishibashi, T. Photonic millimetre- and sub-millimetre-wave generation using J-band rectangular-waveguide-output uni-travelling-carrier photodiode module. Electron. Lett. 42, 1424–1425 (2006).

    Article  ADS  Google Scholar 

  27. Shoji, Y., Hamaguchi, K. & Ogawa, H. Millimeter-wave remote self-heterodyne system for extremely stable and low-cost broad-band signal transmission. IEEE Trans. Microw. Theory Tech. 50, 1458–1468 (2002).

    Article  ADS  Google Scholar 

  28. Hermelo, M. F. et al. Spectral efficient 64-QAM-OFDM terahertz communication link. Opt. Express 25, 19360–19370 (2017).

    Article  ADS  Google Scholar 

  29. Schmogrow, R. et al. Error vector magnitude as a performance measure for advanced modulation formats. IEEE Photon. Technol. Lett. 24, 61–63 (2012).

    Article  ADS  Google Scholar 

  30. Schmogrow, R. et al. Corrections to ‘error vector magnitude as a performance measure for advanced modulation formats’. IEEE Photon. Technol. Lett. 24, 2198 (2012).

  31. Smith, B. P., Farhood, A., Hunt, A., Kschischang, F. R. & Lodge, J. Staircase codes: FEC for 100 Gb/s OTN. J. Lightwave Technol. 30, 110–117 (2012).

    Article  ADS  Google Scholar 

  32. Li, Z. et al. Digital linearization of direct-detection transceivers for spectrally efficient 100 Gb/s/λ WDM metro networking. J. Lightwave Technol. 36, 27–36 (2018).

    Article  ADS  Google Scholar 

  33. Cai, Y. et al. FPGA investigation on error-floor performance of a concatenated staircase and Hamming code for 400G-ZR forward error correction. J. Lightwave Technol. 37, 188–195 (2019).

    Article  ADS  Google Scholar 

  34. Essiambre, R.-J. et al. Capacity limits of optical fiber networks. J. Lightwave Technol. 28, 662–701 (2010).

    Article  ADS  Google Scholar 

  35. IEEE Standard for High Data Rate Wireless Multi-Media Networks—Amendment 2: 100Gb/s Wireless Switched Point-to-Point Physical Layer Standard No. 802.15.3d-2017 (IEEE, 2017).

  36. Hesler, J., Hui, K. & Crowe, T. Ultrafast millimeter wave and THz envelope detectors for wireless communications. In Proc. 2012 International Topical Meeting on Microwave Photonics 93–94 (IEEE, 2012).

  37. Hesler, J. L. & Crowe, T. W. NEP and responsivity of THz zero-bias Schottky diode detectors. In Proc. Joint 32nd International Conference on Infrared and Millimeter Waves and 15th International Conference on Terahertz Electronics 844–845 (IEEE, 2007).

  38. Tessmann, A. et al. High-gain submillimeter-wave mHEMT amplifier MMICs. In Proc. 2010 MTT-S International Microwave Symposium 53–56 (IEEE, 2010).

  39. Toll, J. S. Causality and the dispersion relation: logical foundations. Phys. Rev. 104, 1760–1770 (1956).

    Article  ADS  MathSciNet  Google Scholar 

  40. Füllner, C. et al. Complexity analysis of the Kramers–Kronig receiver. J. Lightwave Technol. 37, 4295–4307 (2019).

    Article  ADS  Google Scholar 

  41. Li, Z. et al. Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers–Kronig receivers. In Proc. 2017 European Conference on Optical Communication W2D.3 (IEEE, 2017).

  42. Savory, S. J. Digital coherent optical receivers: algorithms and subsystems. IEEE J. Sel. Top. Quantum Electron. 16, 1164–1179 (2010).

    Article  ADS  Google Scholar 

  43. Farrow, C. W. A continuously variable digital delay element. In Proc. 1988 International Symposium on Circuits and Systems 2641–2645 (IEEE, 1988).

  44. Godard, D. N. Self-recovering equalization and carrier tracking in two-dimensional data communication system. IEEE Trans. Commun. 28, 1867–1875 (1980).

    Article  Google Scholar 

  45. Pfau, T. & Hoffmann, S. Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations. J. Lightwave Technol. 27, 989–999 (2009).

    Article  ADS  Google Scholar 

  46. Randel, S. et al. All-electronic flexibly programmable 864 Gb/s single-carrier PDM-64-QAM. In Proc. 2014 Optical Fiber Communication Conference Th5C.8 (OSA, 2014).

  47. Faruk, S. & Savory, S. J. Digital signal processing for coherent transceivers employing multilevel formats. J. Lightwave Technol. 35, 1125–1141 (2017).

    Article  ADS  Google Scholar 

  48. Bo, T. & Kim, H. Kramers–Kronig receiver operable without digital upsampling. Opt. Express 26, 13810–13818 (2018).

    Article  ADS  Google Scholar 

  49. Mecozzi, A., Antonelli, C. & Shtaif, M. Kramers–Kronig receivers. Adv. Opt. Photon. 11, 480–517 (2019).

    Article  Google Scholar 

  50. Freude, W. et al. Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM and BER. In Proc. 14th International Conference on Transparent Optical Networks 1–4 (IEEE, 2012).

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Acknowledgements

This work was supported by the European Research Council (ERC consolidator grant ‘TeraSHAPE’, no. 773248), the Alfried Krupp von Bohlen und Halbach Foundation, the Helmholtz International Research School of Teratronics (HIRST) and the Karlsruhe School of Optics and Photonics (KSOP). The work relies on instrumentation funded by the European Regional Development Fund (ERDF, grant EFRE/FEIH_776267), the Deutsche Forschungsgemeinschaft (DFG; grants DFG/INST 121384/166-1 and DFG/INST 121384/167-1) and the Hector Stiftung (Hector Foundation).

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Contributions

T.H., C.F. and C.K. developed the idea; J.L.H. developed and supplied the SBD; the experiments were performed by T.H. and C.F. with the support of J.N.K., S.U., J.L.S., M.B. and E.B.; algorithms for data generation and signal processing were implemented by T.H., C.F. and S.R.; the project was supervised by A.-S.M., W.F., S.R. and C.K.; the paper was written by T.H., C.F., W.F., S.R. and C.K.; all authors revised the paper.

Corresponding author

Correspondence to C. Koos.

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Competing interests

J.L.H. is chief technology officer of Virginia Diodes Inc., a company manufacturing and selling high-speed SBDs for terahertz signal processing. All other authors have no competing interests.

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Supplementary Information

Supplementary Sections 1–10, Figs. 1–13 and Table 1.

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Harter, T., Füllner, C., Kemal, J.N. et al. Generalized Kramers–Kronig receiver for coherent terahertz communications. Nat. Photonics 14, 601–606 (2020). https://doi.org/10.1038/s41566-020-0675-0

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