Methods to exploit the diversity of propagating waves are crucial to the efficient operation of wireless communication systems. Such diversity occurs along two different dimensions: space and time. Both of them pose fundamental limits on the amount of information that can be carried by electromagnetic radiation. This project attempts to present a unified view of these separate axes, based on the physical notion of space frequency spectrum of the propagating field, and to draw connections between the fields of information theory and electromagnetic theory.
More specifically, the project defines the concept of information transmission in a multiple antenna channel from physical principles, and investigates how the amount of information transported over the channel to the receiver depends on both the spatial and the frequency bandwidth of the radiating system composed by the transmitting antennas and the scattering objects present in the environment. The spatial information content is quantified in a similar fashion than its temporal counterpart, by reducing the inverse problem of field reconstruction to a communication problem in space, and determining the relevant communication modes of the channel by rigorously applying the sampling theorem on the field's vector space. This research involves extensions of the concept of information rate from time to space, and is aimed at revealing fundamental dualities and trade-offs between these two dimensions.
