  This paper considers the 3D spatial fading correlation (SFC) resulting from
an angle-of-arrival (AoA) distribution that can be modelled by a mixture of
Fisher-Bingham distributions on the sphere. By deriving a closed-form
expression for the spherical harmonic transform for the component
Fisher-Bingham distributions, with arbitrary parameter values, we obtain a
closed-form expression of the 3D-SFC for the mixture case. The 3D-SFC
expression is general and can be used in arbitrary multi-antenna array
geometries and is demonstrated for the cases of a 2D uniform circular array in
the horizontal plane and a 3D regular dodecahedral array. In computational
aspects, we use recursions to compute the spherical harmonic coefficients and
give pragmatic guidelines on the truncation size in the series representations
to yield machine precision accuracy results. The results are further
corroborated through numerical experiments to demonstrate that the closed-form
expressions yield the same results as significantly more computationally
expensive numerical integration methods.
