This paper establishes a solid mathematical model for Over the Air (OTA) test and characterization of 5G millimeter wave User Equipment (UE) in Compact Antenna Test Ranges (CATR). Special attention is paid to receiver characteristics and polarization mismatch problem which is encountered in spherical coverage tests. The received power of a UE with dual-polarized antenna system is derived and output SNR is calculated using Maximal Ratio Combining (MRC) principle. And finally, some of the misconceptions in 3rd Generation Partnership Project (3GPP) standards publications is addressed