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Generalized Kramers–Kronig receiver for coherent terahertz communications


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.


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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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Authors and Affiliations



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 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).

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