The FB5 distribution and its application in wireless communications

Recently, the third generation partnership standards bodies (3GPP/3GPP2) have defined a channel model for multiple input multiple output (MIMO) systems. This model is a 2-dimensional (2D) model where the propagating plane waves are assumed to arrive only from the azimuthal direction and does not include the elevation domain. As a result of this assumption the derived angle of arrival (AoA) distribution is characterized only by the azimuth direction of these waves. In this paper the AoA distribution of multipaths is modeled in a novel 3-dimensional (3D) approach. The Von Mises Fisher (VMF) and Fisher Bingham (FB5) probability density functions (PDF) are used to describe their distribution within the propagation environment in azimuth and co-latitude. More specifically two separate models are proposed. The first model uses a mixture of VMF distributions and the second one uses a mixture of FB5 and VMF distributions. The parameters of the individual cluster of scatterers within the mixture are derived and an estimation of those parameters is achieved using the expectation maximization (EM) algorithm. The two models are compared. The results indicate that both mixture models perform really well. However the FB5 mixture model is proposed because it is more flexible. Both models are validated with the use of MIMO experimental data obtained from a measurement campaign in Germany.