Information transfer through disordered media by diffuse waves

S. E. Skipetrov
Phys. Rev. E 67, 036621 – Published 26 March 2003
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Abstract

We consider the information content h of a scalar multiple-scattered, diffuse wave field ψ(r) and the information capacity C of a communication channel that employs diffuse waves to transfer the information through a disordered medium. Both h and C are shown to be directly related to the mesoscopic correlations between the values of ψ(r) at different positions r in space, arising due to the coherent nature of the wave. For the particular case of a communication channel between two identical linear arrays of n1 equally spaced transmitters or receivers (receiver spacing a), we show that the average capacity Cn and obtain explicit analytic expressions for C/n in the limit of n and kl, where k=2π/λ, λ is the wavelength, and l is the mean free path. Modification of the above results in the case of finite but large n and kl is discussed as well. If the signal to noise ratio S/N exceeds some critical value (S/N)c, C/n is a nonmonotonic function of a, exhibiting maxima at ka=mπ (m=1,2,). For smaller S/N, ka=mπ correspond to local minima, while the absolute maximum of C/n is reached at some ka(S/N)1/2<π. We define the maximum average information capacity Cmax as C maximized over the receiver spacing a and the optimal normalized receiver spacing (ka)opt as the spacing maximizing C. Both Cmax/n and (ka)opt scale as (S/N)1/2 for S/N<(S/N)c, while (ka)opt=mπ and Cmax/nlog(S/N) for S/N>(S/N)c.

  • Received 18 October 2002

DOI:https://doi.org/10.1103/PhysRevE.67.036621

©2003 American Physical Society

Authors & Affiliations

S. E. Skipetrov*

  • Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS, 38042 Grenoble, France

  • *Email address: Sergey.Skipetrov@grenoble.cnrs.fr

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Vol. 67, Iss. 3 — March 2003

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