Three-dimensional channel modelling using spherical statistics for multiple-input multiple-output systems

Recently, the third generation partnership standards bodies (3GPP/3GPP2) have defined a two-dimensional channel model for multiple-input multiple-output (MIMO) systems, where the propagating plane waves are assumed to arrive only from the azimuthal direction and therefore not include the elevation domain. As a result of this assumption, the derived angle-of-arrival (AoA) distribution is characterised only by the azimuth direction of these waves. The AoA distribution of multipaths is implemented with a novel three-dimensional approach. The von Mises-Fisher (VMF) probability density function is used to describe their distribution within the propagation environment in both azimuth and co-latitude. More specifically, the proposed model uses a mixture of VMF distributions. A mixture can be composed of any number of clusters and this is clutter specific. The parameters of the individual cluster of scatterers within the mixture are derived and an estimation of those parameters is achieved using the spherical K-means algorithm and also the expectation maximisation algorithm. Statistical tests are provided to measure the goodness of fit of the proposed model. The results indicate that the proposed model fits well with MIMO experimental data obtained from a measurement campaign in Germany.