Intrinsic cross-polarization ratio (IXR) for antenna arrays and improving polarimetry via polarization diversity

I extend the concept of the intrinsic cross-polarization ratio (IXR) to an array of an arbitrary number of antenna elements. IXR is a figure-of-merit for the polarimetric performance of dual-polarized antenna elements, but it is easily generalized to more than two antennas by considering the effective dual-polarized response of polarimetrically beam-formed array. I also show that for a sparse array (i.e. arrays in which mutual-coupling can be ignored) of identical dual-polarized elements all with the same alignment, it is not possible to make the array IXR better than the IXR of dual-polarized element through beam-forming. However, such arrays can be improved by physically rotating the dual-polarized elements such that their alignments are not all the same. An array in which not all the dual-polarized elements do not all have the same alignment is a form of polarization diversity. I argue that polarization diversity is way to improve the polarimetric performance of arrays.