Degree-of-freedom gain from polarimetric antenna elements

Extending the sampling argument for linear arrays to higher dimensional Euclidean spaces, we obtained the resolvable angular cells for planar and volumetric arrays. By applying the reasoning steps outlined in this paper, we derived the polarization degree-of-freedom (DOF) gain for various array geometry. The derivation is detailed in (Poon and Tse, 2009). For completeness, we also use multipole decomposition to derive the total degrees of freedom which is a product of polarization DOF gain and array DOF gain.