  Shannon's mutual information of a random multiple antenna and multipath
channel is studied in the general case where the channel impulse response is an
ergodic and stationary process which is assumed to be available at the
receiver. From this viewpoint, the channel is represented by an ergodic
self-adjoint block-Jacobi operator, which is close in many aspects to a block
version of a random Schr\"odinger operator. The mutual information is then
related to the so-called density of states of this operator. In this paper, it
is shown that under the weakest assumptions on the channel, the mutual
information can be expressed in terms of a matrix-valued stochastic process
coupled with the channel process. This allows numerical approximations of the
mutual information in this general setting. Moreover, assuming further that the
channel impulse response is a Markov process, a representation for the mutual
information offset in the large Signal to Noise Ratio regime is obtained in
terms of another related Markov process. This generalizes previous results from
Levy~\emph{et.al.}. It is also illustrated how the mutual information
expressions that are closely related to those predicted by the random matrix
theory can be recovered in the large dimensional regime.
