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At the antenna connector you may receive (or transmit) only one wave polarization. (linaer or circular). The 90° far polarizzation is generally unwanted.
Cross-polarizzation (Xpol) is the 90° far, unwanted polarizzation.
Co-polar (Copol) is the wanted polarization.
I.e. if a standard antenna TX a vertical pol. , in far field region, when you RX a Vertical one, you RX the Copol, while if you try to receive Horrizontal, you'll receive the Xpol.
Many definitions exists for Xpol. For my knowledge, the most widely adopted is the Ludwing's one.
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