Spherical Vector Wave Expansion of Gaussian Electromagnetic Fields for Antenna-Channel Interaction Analysis

In this paper, we introduce an approach to analyze the interaction between antennas and the propagation channel. We study both the antennas and the propagation channel by means of the spherical vector wave mode expansion of the electromagnetic field. Then we use the expansion coefficients to study some properties of general antennas in those fields by means of the antenna scattering matrix. The focus is on the spatio-polar characterization of antennas, channels and their interactions. We provide closed form expressions for the covariance of the field multimodes as function of the power angle spectrum (PAS) and the channel cross-polarization ratio (XPR). A new interpretation of the mean effective gains (MEG) of antennas is also provided. The maximum MEG is obtained by conjugate mode matching between the antennas and the channel; we also prove the (intuitive) results that the optimum decorrelation of the antenna signals is obtained by the excitation of orthogonal spherical vector modes.