On the Antenna-Channel Interactions : A Spherical Vector Wave Expansion Approach
Abstract: The main focus of this thesis is the analysis of the interactions between antennas and channels where electromagnetic fields play a central role. Our goal has been to devise a general framework to enable a clear separation of the properties of the propagation channel from the influence of the antennas at the same time as it provides a common ground for a joint characterization of their properties. For this we have taken help of two tools: 1) a solution to Maxwell’s equations, i.e., a spherical vector wave (svw) multi-modal expansion of the electromagnetic field and 2) the scattering matrix representation of an antenna that provides a full description of all its properties as a transmitting, receiving or scattering device. These tools offer a natural characterization of the polarizational, directional, and spatial properties of multiple-input multiple-output (MIMO) antenna systems. In this thesis we first show that under some assumptions the propagation channel and the antenna are equivalent. The equivalence is in the sense that the impact of the channel cross-polarization ratio (XPR) and the antenna effective cross-polarization discrimination (XPD) on the mean effective gain (MEG) of an antenna are symmetrical. We also find bounds on the MEG in a wireless channel. Then we provide closed form expressions for the covariance of the field multi-modes as a function of the Power Angle Spectrum (PAS) and the channel XPR. A new interpretation of the MEG of antennas in terms of field multi-modes is also provided where the maximum MEG is obtained by conjugate mode matching between the antennas and the channel. We also show the (intuitive) result that the optimum decorrelation of the antenna signals is obtained by the excitation of orthogonal spherical vector wave modes. The cross-correlation coefficient between signals at two antenna branches (ports) in the presence of spatially selective interference and additive white gaussian noise is also investigated showing that spatial interference can also be readily modeled in terms of the svw mode expansion. We further devise a correlation model for co- and cross-polarized field components and introduce the concept of mode-to-mode channel mapping, the M-matrix, between the receive and transmit antenna modes. The M-matrix maps the modes excited by the transmitting antenna to the modes exciting the receive antennas and vice versa. The covariance statistics of this M-matrix are expressed as a function of the double-directional power-angular spectrum (PAS) of co- and cross-polarized components of the electromagnetic field. We finally derive physical limitations on the interactions of antennas exciting TM or TE modes (but not both) and wireless propagation channels. Rather than maximizing antenna gain in a single direction we obtain physical limitations on the antenna gain pattern, which is directly translated to more condensed parameters, i.e. the instantaneous effective gain Gi and the mean effective gain Ge if instantaneous realizations or correlation statistics of the expansion coefficients of the electromagnetic field are known, respectively. The obtained limitations are on the maximum of Gi/Q and Ge/Q, which establish a trade-off between link gain and the antenna quality factor Q.
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