Capacity of the Continuous-Space Electromagnetic Channel

Abstract

Constructing the capacity bound of a multiple-input multiple-output wireless system is often performed by assuming specified antenna configurations and a propagation environment and determining the signaling strategy which maximizes throughput. This paper extends this approach to further determine the optimal antenna characteristics which maximize the capacity for the propagation scenario, with the resulting capacity bound representing the ultimate maximum achievable value if optimal antenna design and signaling are used. In this approach, the spatially-continuous transmit currents and receive fields are represented using eigenfunctions of appropriate operators. It is shown that, except under certain conditions where array supergain solutions emerge, the capacity remains bounded for finite transmit power. The approach also shows how to limit supergain effects using practical constraints. Model problems and numerical computations are provided for different power constraints at the transmitter and noise characteristics at the receiver.Index Terms-Information theory, multipath channels, multipleinput multiple-output (MIMO) systems.

New Aspects of Electromagnetic Information Theory for Wireless and Antenna Systems

“…This is in contrast to all past work we are aware of where the main emphasis has been to either constrain the source norm [24], [25], [37] or, more recently, to constrain the radiated power only, while indirectly limiting the source norm by means of different approaches like the restriction of the transmission currents to specific subspaces [31], the use of channel models that include the effect of the losses and thermal noise [28], or the truncation of the number of terms in the expansions of the field [32], [33]. In fact, our adoption of this methodology complements recently reported approaches in [28] and [31] to estimate wireless electromagnetic capacity while penalizing antenna superdirectivity, and our treatment also provides a different and independent reformulation of some of the results in [28], [31] where, like those papers, we show that the radiated power alone is generally insufficient as a constraint for electromagnetic capacity calculations and that, instead, it must be complemented in practice by other physically motivated constraints (such as the norm constraint). Our treatment complements the analysis in those papers by considering the two most typically adopted constraints simultaneously, and also goes beyond the scope of that past work by extending the results to broadband fields.…”

“…In recent years, the need for both fundamental theory and computational methodology for estimating both NDF and Shannon's information capacity [19], [20] of a variety of wave radiation and propagation systems, including random media channels, has been growing steadily, mostly due to its fundamental importance in space-time wireless channels including multiple-input multiple-output (MIMO) systems [21]- [23]. The present paper builds from recent work with this motivation, being of particular relevance the investigations carried out by: Hanlen et al [24], [25] who investigated general communication channels within a general abstract operator theory in Hilbert spaces and, within the scalar framework, the information capacity in the formally tractable case of sources and fields in spherical regions under the standard source norm constraint; Hui et al [26] who similarly provided general expressions for the information capacity of Gaussian wireless links from a spatial region to another; Hanlen and Fu [27] who proposed numerical techniques for estimating the NDF of general wave propagation systems including media formed by collections of scatterers embedded to a given background medium (e.g., free space); Jensen and Wallace [28] (see also their related past work in [29] and [30]) who studied the information capacity of Gaussian wireless links between two volumes under a constraint in the radiated power and who also proposed an approach to limit antenna superdirectivity while making the optimal power allocations for the different wave propagative modes connecting the volumes; Morris et al [31] who also studied the effect of the superdirectivity on the information capacity of MIMO systems under a radiated power constraint; Gustafsson and Nordebo [32], [33] who studied the spectral efficiency of an antenna inside a sphere, as measured by the information capacity, by means of a model of MIMO channels combining information theory, antenna theory, and broadband matching theory; Migliore [34] who considered the capacity and NDF of a group of antennas and scatterers inside a sphere by means of the multipole expansion and equivalent electrical networks and who also proposed a way to take into account the temporal resources by means of a sampling theory in space and time [35]; Chakraborty and Franceschetti [36] who also considered the capacity of space-time communication channels by means of a generalized sampling theorem applied 0018-926X/$25.00 © 2008 IEEE to space and time; Poon et al [37] who considered NDF and information capacity of indoor wave propagation systems based on combined analytical and empirical, measurement-based models, while also illustrating, among other aspects, the role of cooperative versus noncooperative users in the envi...…”

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.…”

On Some Optimal Mimo Antenna Coefficients in Multipath Channels

“…These prior studies have shown relevant findings concerning the effects of mutual coupling on MIMO system performance. Moreover, a few papers describe the optimal antenna coefficients for MIMO systems [13][14][15].…”