Information transfer through disordered media by diffuse waves

Abstract

We consider the information content h of a scalar multiple-scattered, diffuse wave field psi(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 psi(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 n>>1 equally spaced transmitters or receivers (receiver spacing a), we show that the average capacity <C> proportional, variant n and obtain explicit analytic expressions for <C>/n in the limit of n--> infinity and kl--> infinity, where k=2pi/lambda, lambda 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=mpi (m=1,2, em leader ). For smaller S/N, ka=mpi correspond to local minima, while the absolute maximum of <C>/n is reached at some ka approximately (S/N)(1/2)<pi. We define the maximum average information capacity <C>(max) as <C> maximized over the receiver spacing a and the optimal normalized receiver spacing (ka)(opt) as the spacing maximizing <C>. Both <C>(max)/n and (ka)(opt) scale as (S/N)(1/2) for S/N<(S/N)(c), while (ka)(opt)=mpi and <C>(max)/n approximately log(S/N) for S/N>(S/N)(c).