The information that can be transmitted through a wireless channel, with
multiple-antenna equipped transmitter and receiver, is crucially influenced by
the channel behavior as well as by the structure of the input signal. We
characterize in closed form the probability density function (pdf) of the
output of MIMO block-fading channels, for an arbitrary SNR value. Our results
provide compact expressions for such output statistics, paving the way to a
more detailed analytical information-theoretic exploration of communications in
presence of block fading. The analysis is carried out assuming two different
structures for the input signal: the i.i.d. Gaussian distribution and a product
form that has been proved to be optimal for non-coherent communication, i.e.,
in absence of any channel state information. When the channel is fed by an
i.i.d. Gaussian input, we assume the Gramian of the channel matrix to be
unitarily invariant and derive the output statistics in both the noise-limited
and the interference-limited scenario, considering different fading
distributions. When the product-form input is adopted, we provide the
expressions of the output pdf as the relationship between the overall number of
antennas and the fading coherence length varies. We also highlight the relation
between our newly derived expressions and the results already available in the
literature, and, for some cases, we numerically compute the mutual information,
based on the proposed expression of the output statistics.Comment: 16 pages, 5 figure
