  The Kronecker channel model of wireless communication is analyzed using
statistical mechanics methods. In the model, spatial proximities among
transmission/reception antennas are taken into account as certain correlation
matrices, which generally yield non-trivial dependence among symbols to be
estimated. This prevents accurate assessment of the communication performance
by naively using a previously developed analytical scheme based on a matrix
integration formula. In order to resolve this difficulty, we develop a
formalism that can formally handle the correlations in Kronecker models based
on the known scheme. Unfortunately, direct application of the developed scheme
is, in general, practically difficult. However, the formalism is still useful,
indicating that the effect of the correlations generally increase after the
fourth order with respect to correlation strength. Therefore, the known
analytical scheme offers a good approximation in performance evaluation when
the correlation strength is sufficiently small. For a class of specific
correlation, we show that the performance analysis can be mapped to the problem
of one-dimensional spin systems in random fields, which can be investigated
without approximation by the belief propagation algorithm.
