New Aspects of Electromagnetic Information Theory for Wireless and Antenna Systems

Abstract

This paper investigates information-theoretic characterization, via Shannon's information capacity and number of degrees of freedom, of wave radiation (antenna) and wireless propagation systems. Specifically, the paper derives, from the fundamental physical point of view of Maxwell's equations describing electromagnetic fields, the Shannon information capacity of spacetime wireless channels formed by electromagnetic sources and receivers in a known background medium. The theory is developed first for the case of sources working at a fixed frequency (timeharmonic case) and is expanded later to the more general case of temporally bandlimited systems (time-domain fields). In the bandlimited case we consider separately the two cases of time-limited and essentially bandlimited systems and of purely bandlimited systems. The developments take into account the physical radiated power constraint in addition to a constraint in the source L 2 norm which acts to avoid antenna superdirectivity. Based on such radiated power and current L 2 norm constraints we derive the Shannon information capacity of canonical wireless and antenna systems in free space, for a given additive Gaussian noise level, as well as an associated number of degrees of freedom resulting from such capacity calculations. The derived results also illustrate, from a new information-theoretic point of view, the transition from near to far fields.Index Terms-Antenna, degrees of freedom, electromagnetic information, information capacity, wave information, wireless.

On the Singular Spectrum of the Radiation Operator for Multiple and Extended Observation Domains

“…Accordingly, since the kernel function of the radiation operator behaves like an entire function of exponential type [16] (when the source and the observation domains do not overlap), the singular values exhibit an abrupt exponential decay beyond a critical index which in general depends on the size of the scatterers, the working frequency, and the observation domain. This has been shown explicitly for some particular configurations for which multipole expansion coincides with the radiation operator spectrum [8,17]. In these cases, the singular values exhibit an almost step-like behavior [18] (i.e., the radiation operator is almost rank deficient) and the NDF can be quite naturally estimated as the number of singular values preceding the knee.…”

“…This point of view is of fundamental importance in space-time wireless systems and in particular to multipleinput multiple-output (MIMO) communication systems. The link between the electromagnetic NDF and Shannon's information theory has been recently discussed in [8]. The NDF is also linked to the concepts of the -entropy and -capacity which characterize the topological information theory introduced by Kolmogorov and Tihomirov [9].…”

“…However, it must be remarked that previous constraints, being in some sense global, do not assure that the bulk of the unknown source is recovered nor that the conveyed information is maximized. This happens when the source projects significantly over high order singular functions, when the noise is colored, or when some kind of constraints is exploited [8]. In these cases identifying the NDF is more involved and the knowledge of the singular value behavior, even though still important, provides only a partial picture of the problem.…”

An Electromagnetic Analysis of Noise-Based Intrinsically Secure Communication in Wireless Systems

“…Let us consider the continuous communication channel model drawn in Figure 1 [11,12,16,17]. For the sake of simplicity, a scalar case will be considered.…”

“…Broadly speaking, any antenna uses the available degrees of freedom of the electromagnetic field mainly following two possible goals: to concentrate (and possibly maximize) energy on the receiving antenna or to maximize the amount of information available on the receiving antenna [11,[15][16][17]. In this paper, it will be shown that, in the noise-based unconditionally secure communication systems, the degrees of freedom of the electromagnetic field are used in a third way.…”