Small-scale variations of cross-polar discrimination in polarized MIMO systems

Cross-polarized MIMO systems are an attractive way to reduce equipment size while maintaining low inter-antenna correlation. The amount of leakage from one polarization to another is usually represented by the cross-polarization discrimination (XPD), making it a fundamental parameter of cross-polarized antenna systems. Starting from the definition of Rayleigh and Rice fading channels, we show that the small-scale variations of the XPD follow an F-distribution and a doubly non-central F-distribution respectively in Rayleigh and Ricean fading channels. This distribution is compared with the log-normal distribution that is usually reported in literature for the variations of the XPD. Consequences of this distribution are investigated, and it is shown that the variations of the XPD and the Ricean K-factors are linked by a non-trivial relationship. Measurements have been carried out in an indoor environment at 3.6 GHz to validate the theoretical F-model. The theoretical model and the experimental data are compared visually, by means of the mean square error and by means of the Kolmogorov-Smirnov test. The theoretical F-model shows excellent agreement with the measured XPD variations.