Communication Through a Diffusive Medium: Coherence and Capacity

Abstract

Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave propagation in diffusive media is combined with information theory to show how interference affects the information transmission rate between antenna arrays. Nontrivial dependencies of the information capacity on the nature of the antenna arrays are found, such as the dimensionality of the arrays and their direction with respect to the local scattering medium. This approach provides a physical picture for understanding the importance of scattering in the transfer of information through wireless communications.The ongoing communications revolution has motivated researchers to look for novel ways to transmit information (1, 2). One recent development (3, 4) is the suggestion that, contrary to long-held beliefs, random scattering of microwave or radio signals may enhance the amount of information that can be transmitted on a particular channel. Prompted by this suggestion, we introduce a realistic physical model for a scattering environment and analytically evaluate the amount of information that can be transmitted between two antenna arrays for a number of example cases. On the one hand, this lays a new foundation for complex microwave signal modeling, an important task in a world with ever-increasing demand for wireless communication, and, on the other, introduces a new arena for physicists to test ideas concerning disordered media.From information theory (5), the capacity of a channel between a transmitter and a receiver, that is, the maximum rate of information transfer at a given frequency, can be described in terms of the average power of the signal S and the noise N at the receiver: C = log 2 (1+S/N ). More generally (2), the communication channel connecting several transmitters and receivers is described by a matrix G iα giving the amplitude of the received signal α due to transmitter i. The information carried by the channel can be characterized using several quantities, such as the capacity or mutual information, which are typically functionals of the matrix G, which must be known in order to predict these quantities. Often G cannot be predicted for actual systems, such as wireless communication networks or optical fibers, because of the complicated scattering and interference of waves that is involved. It is crucial, therefore, to develop physical models for the signal propagation, as it is only through such models that one can understand the real effects of scattering and interference on the amount of information that can be communicated.In many cases, only partial information is available for prediction; in these situations, one only has a statistical description of G. Instead of making assumptions about G directly, the usual procedure in information theory, we introduce statistical models for the physical environment from which we derive the properties of G. The adv...

Controlling waves in space and time for imaging and focusing in complex media

“…This is a major topic of interest in wireless communications -both in electromagnetism and in underwater acoustics -because it compensates for the distortions induced by a complex communication channel, maximizes the energy transfer, spatially multiplexes information and provides a means of physically coding information 81,104-106 . Indeed, as was shown by Moustakas and colleagues 107 , the information capacity of a medium can be significantly improved by scattering. Researchers recently proposed the use of time reversal for developing new sensors, by applying the quantum concept of fidelity to classical waves 108 .…”

Eigenvalue density of correlated complex random Wishart matrices

“…Important examples of this case occur in data analysis problems [11], where random samples have temporal and spatial correlations, and particularly in wireless communication and information theory [5,6]. The purpose of this paper is to derive the eigenvalue density of correlated complex Wishart matrices exactly.…”

“…The properties of these so-called Wishart Matrices, which are viewed as "fundamental to multivariate statistical analysis" [4], also find important applications in fields from information theory and communication [5][6][7], to mesoscopics [8], to high energy physics [9], to econo-physics [10].…”

“…However, twenty years before their first work on the subject, Wishart [3] examined random matrices of the form MM † as a tool for studying multivariate data. The properties of these so-called Wishart Matrices, which are viewed as "fundamental to multivariate statistical analysis" [4], also find important applications in fields from information theory and communication [5][6][7], to mesoscopics [8], to high energy physics [9], to econo-physics [10].In many cases one is interested in Wishart matrices where the elements of M are not completely independent random variables, but have correlations along rows and/or columns. Important examples of this case occur in data analysis problems [11], where random samples have temporal and spatial correlations, and particularly in wireless communication and information theory [5,6].…”

Continuous-wave spatial quantum correlations of light induced by multiple scattering

“…5(c)]. This phenomenon that is of a purely quantum origin could open new possibilities to increase the information capacity in communication applications since the amount of transmitted information can be increased in a strongly scattering environment [33]. The classical limit of the information capacity is given by the signal-to-noise ratio of the detected light utilizing a light source with Poissonian photon statistics.…”