Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Optimally diverse communication channels in disordered environments with tuned randomness


Multichannel wireless systems have become a standard solution to address our information society’s ever-increasing demand for information transfer. The capacity that such systems can achieve is ultimately limited by the channel diversity in a given propagation medium, and numerous approaches to reduce channel cross-talk by engineering software or hardware details of the signals and antenna arrays have been proposed. Here we show that optimal channel diversity can be achieved by physically shaping the propagation medium itself. Using a reconfigurable metasurface placed inside a random environment, we tune the disorder and impose perfect orthogonality of wireless channels. We report experiments in the microwave domain in which we impose equal weights of the channel matrix eigenvalues for up to 4 × 4 systems, and almost equal weights in larger systems. We also demonstrate enhanced wireless image transmission in an office room in which we augmented the 3 × 3 system’s number of effectively independent channels from two to the optimum of three.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Experimental set-up and procedure.
Fig. 2: Evolution of normalized channel matrix eigenvalues λ during iterative optimization of channel diversity.
Fig. 3: Orthogonality of optimized channel matrices for 30 realizations of disorder.
Fig. 4: Emulated wireless transfer of a full-colour image based on experimentally measured channel matrices in an office room.

Data availability

The raw data used in this work are available at


  1. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948).

    Article  MathSciNet  Google Scholar 

  2. Foschini, G. J. & Gans, M. J. On limits of wireless communications in a fading environment when using multiple antennas. Wirel. Pers. Commun. 6, 311–335 (1998).

    Article  Google Scholar 

  3. Telatar, E. Capacity of multi‐antenna Gaussian channels. Trans. Emerg. Telecommun. Technol. 10, 585–595 (1999).

    Article  MathSciNet  Google Scholar 

  4. Moustakas, A. L., Baranger, H. U., Balents, L., Sengupta, A. M. & Simon, S. H. Communication through a diffusive medium: Coherence and capacity. Science 287, 287–290 (2000).

    Article  Google Scholar 

  5. Simon, S. H., Moustakas, A. L., Stoytchev, M. & Safar, H. Communication in a disordered world. Phys. Today 54, 38–43 (September, 2001).

  6. Alamouti, S. M. A simple transmit diversity technique for wireless communications. IEEE J. Sel. Areas Commun. 16, 1451–1458 (1998).

    Article  Google Scholar 

  7. Miller, D. A. Establishing optimal wave communication channels automatically. J. Lightwave Technol. 31, 3987–3994 (2013).

    Article  Google Scholar 

  8. Yan, Y. et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing. Nat. Commun. 5, 4876 (2014).

    Article  Google Scholar 

  9. Andrews, M. R., Mitra, P. P. & deCarvalho, R. Tripling the capacity of wireless communications using electromagnetic polarization. Nature 409, 316–318 (2001).

    Article  Google Scholar 

  10. Lerosey, G., de Rosny, J., Tourin, A. & Fink, M. Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007).

    Article  Google Scholar 

  11. del Hougne, P., Rajaei, B., Daudet, L. & Lerosey, G. Intensity-only measurement of partially uncontrollable transmission matrix: demonstration with wave-field shaping in a microwave cavity. Opt. Express 24, 18631–18641 (2016).

    Article  Google Scholar 

  12. Roy, O. & Vetterli, M. The effective rank: a measure of effective dimensionality. In 15th European Signal Process. Conf. 606–610 (EURASIP, 2007).

  13. Kaina, N., Dupré, M., Fink, M. & Lerosey, G. Hybridized resonances to design tunable binary phase metasurface unit cells. Opt. Express 22, 18881–18888 (2014).

    Article  Google Scholar 

  14. Sievenpiper, D., Zhang, L., Broas, R. F., Alexopolous, N. G. & Yablonovitch, E. High-impedance electromagnetic surfaces with a forbidden frequency band. IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).

    Article  Google Scholar 

  15. Sihvola, A. Metamaterials in electromagnetics. Metamaterials 1, 2–11 (2007).

    Article  Google Scholar 

  16. Tulino, A. M. & Verdú, S. Random Matrix Theory and Wireless Communications Vol. 1 (Now Publishers, Boston-Delft, 2004).

  17. Kuhl, U., Stöckmann, H. & Weaver, R. Classical wave experiments on chaotic scattering. ‎J. Phys. A 38, 10433 (2005).

    Article  MathSciNet  Google Scholar 

  18. Hemmady, S., Zheng, X., Antonsen, T. M. Jr, Ott, E. & Anlage, S. M. Universal statistics of the scattering coefficient of chaotic microwave cavities. Phys. Rev. E 71, 056215 (2005).

    Article  Google Scholar 

  19. Dupré, M., del Hougne, P., Fink, M., Lemoult, F. & Lerosey, G. Wave-field shaping in cavities: Waves trapped in a box with controllable boundaries. Phys. Rev. Lett. 115, 017701 (2015).

    Article  MathSciNet  Google Scholar 

  20. Kaina, N., Dupré, M., Lerosey, G. & Fink, M. Shaping complex microwave fields in reverberating media with binary tunable metasurfaces. Sci. Rep. 4, 6693 (2014).

    Article  Google Scholar 

  21. Ambichl, P. et al. Super-and anti-principal-modes in multimode waveguides. Phys. Rev. X 7, 041053 (2017).

    Google Scholar 

  22. Böhm, J., Brandstötter, A., Ambichl, P., Rotter, S. & Kuhl, U. In situ realization of particlelike scattering states in a microwave cavity. Phys. Rev. A. 97, 021801 (2018).

    Article  Google Scholar 

  23. Fromenteze, T., Decroze, C. & Carsenat, D. Waveform coding for passive multiplexing: Application to microwave imaging. IEEE Trans. Antennas Propag. 63, 593–600 (2015).

    Article  Google Scholar 

  24. Fromenteze, T., Kpré, E. L., Carsenat, D., Decroze, C. & Sakamoto, T. Single-shot compressive multiple-inputs multiple-outputs radar imaging using a two-port passive device. IEEE Access 4, 1050–1060 (2016).

    Article  Google Scholar 

  25. Miller, D. A. Device requirements for optical interconnects to silicon chips. Proc. IEEE 97, 1166–1185 (2009).

    Article  Google Scholar 

  26. Chang, M. F., Roychowdhury, V. P., Zhang, L., Shin, H. & Qian, Y. RF/wireless interconnect for inter-and intra-chip communications. Proc. IEEE 89, 456–466 (2001).

    Article  Google Scholar 

  27. Phang, S. et al. Near-field MIMO communication links. IEEE Trans. Circuits Syst. I, Reg. Papers 65 , 3027–3036 (2018).

  28. Vellekoop, I. M. & Mosk, A. P. Phase control algorithms for focusing light through turbid media. Opt. Commun. 281, 3071–3080 (2008).

    Article  Google Scholar 

  29. Popoff, S., Lerosey, G., Fink, M., Boccara, A. C. & Gigan, S. Image transmission through an opaque material. Nat. Commun. 1, 81 (2010).

    Article  Google Scholar 

Download references


P.d.H. thanks A. Aubry and U. Kuhl for fruitful discussions. P.d.H. acknowledges funding from the French “Ministère de la Défense, Direction Générale de l’Armement”.

Author information

Authors and Affiliations



G.L. initiated the project. P.d.H. conceived and conducted the project, and wrote the manuscript. All authors discussed the project.

Corresponding authors

Correspondence to Philipp del Hougne or Geoffroy Lerosey.

Ethics declarations

Competing interests

P.d.H. declares no competing interests. G.L. and M.F. have founded and are, respectively, chief scientist and scientific advisor of Greenerwave, a company that seeks to commercialize metasurfaces, inter alia, for applications in wireless communication.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Discussion 1–5 and Supplementary Figures 1–7

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

del Hougne, P., Fink, M. & Lerosey, G. Optimally diverse communication channels in disordered environments with tuned randomness. Nat Electron 2, 36–41 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing