A new three-dimensional (3-D) geometry-based reference model for cross-polarization discrimination (XPD) in narrow-band fixed-to-fixed (F-to-F) or fixed-to-mobile (F-to-M) wireless channels is proposed. The proposed model is based on the superposition of polarization components on conservation-of-polarization planes (CoP-planes). This novel approach is used to derive the XPD at each distance without the aid of measurement data or its approximation. To the best of our knowledge this is the first purely theoretical geometry-based XPD reference model. Using our reference model, we obtain a relationship between XPD and channel modeling factors such as the distance between the transmitter and the receiver, the azimuth/elevation angles of arrival and departure (A/E-AoA and A/E-AoD), multipath delays, and the distribution of scatterers. Our analytical XPD model is in close agreement with previously reported results from other authors that are based on empirical measurement data, and it also overcomes the shortcoming of over approximation/oversimplification of the measurement data.
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