The Fisher–Bingham Spatial Correlation Model for Multielement Antenna Systems

In this paper, we study the effect of the elevation of incoming multipaths at a multielement antenna receiver by using a novel 3-D approach. It is shown that under a more general 3-D angle-of-arrival (AoA) model, namely, the Fisher–Bingham five-parameter (FB5) distribution, the spatial fading correlation (SFC) that is experienced between the adjacent antenna array elements decreases as the elevation increases. The FB5 distribution does not have a known series expansion, and therefore, the defining SFC integral can only numerically be evaluated. The proposed SFC function is further extended to capture the effect of multiple clusters of scatterers in the propagation channel. We, therefore, propose a mixture SFC function that is scaled according to the probability that each cluster contributes to the channel. The parameters of the individual components that constitute the mixture are estimated by using a soft expectation maximization (soft-EM) algorithm. The results indicate that the proposed model fits well with the data obtained from a multiple-input–multiple-output (MIMO) measurement campaign in the city of Ilmenau, Germany.