Improving spatial degrees of freedom using superdirectivity

Abstract

In this thesis, the effect of mutual coupling on the capacity of electromagnetic channels is analyzed, where transceivers are confined in given regions. The thesis consists of three different works, which deal with different electromagnetic channels. For the first part of this thesis, the capacity of continuous-space electromagnetic channels, where transceivers are confined in given lossy regions, is analyzed. Compared to the existing literature, the contribution of our work is summarized as follows. First, we assume the regions confining the transceivers are filled with dielectric, which is either lossy or lossless and show how the capacity is affected by the physical loss of the source region. Also, we consider the actual power consumption of the source, whereas only the current strength or the radiation power has been considered in many existing works. In addition, we use the fluctuation-dissipation theorem to model the noise, whereas the previous works have used either the i.i.d. field fluctuation or the interference-like noise. All these differences make the degrees-of-freedom (DoF) in our work different from those in the previous works, in some cases significantly higher. We also derive the Q factor analytically under our assumptions and consider how the capacity is affected by the Q factor. Finally, we compare our work with the existing literature and analyze the maximum gain of spherical dielectric antennas in practical applications. For the second part of this thesis, the mutual coupling among vector antenna (VA) elements is derived based on the electromagnetic theory, where a uniform circular array (UCA) with VAs is utilized as the transmit antenna array. By exploiting our result on the mutual coupling, we also analyze the electromagnetic channel from the transmitter to a receiver that measures the electric field surrounding the transmitter. As a result, we show the number of spatial degrees of freedom can be increased by exploiting the mutual coupling. For the last part of this thesis, we show interference can be removed if mutual coupling is properly utilized, where a two-user Gaussian multiple access channel (MAC) is assumed. Specifically, we analyze the capacity region of the channel, where each transmitter has its own antenna and the receiver can measure the electric field in a given lossless spherical volume with additive noise. The additive noise at the sphere is assumed to satisfy the statistical property followed from the fluctuation-dissipation theorem. As a result, it turns out the interference can be almost perfectly removed regardless of the physical size of the receiver and the angular position of the transmitters, i.e., the angle defined by lines between each transmitter and the center of the sphere, when the distance between each transmitter and the receiver is sufficiently far apart.