  Outage probability and capacity of a class of block-fading MIMO channels are
considered with partial channel distribution information. Specifically, the
channel or its distribution are not known but the latter is known to belong to
a class of distributions where each member is within a certain distance
(uncertainty) from a nominal distribution. Relative entropy is used as a
measure of distance between distributions. Compound outage probability defined
as min (over the transmit signal distribution) -max (over the channel
distribution class) outage probability is introduced and investigated. This
generalizes the standard outage probability to the case of partial channel
distribution information. Compound outage probability characterization (via
one-dimensional convex optimization), its properties and approximations are
given. It is shown to have two-regime behavior: when the nominal outage
probability decreases (e.g. by increasing the SNR), the compound outage first
decreases linearly down to a certain threshold (related to relative entropy
distance) and then only logarithmically (i.e. very slowly), so that no
significant further decrease is possible. The compound outage depends on the
relative entropy distance and the nominal outage only, all other details
(nominal fading and noise distributions) being irrelevant. The transmit signal
distribution optimized for the nominal channel distribution is shown to be also
optimal for the whole class of distributions. The effect of swapping the
distributions in relative entropy is investigated and an error floor effect is
established. The compound outage probability under Lp distance constraint is
also investigated. The obtained results hold for a generic channel model
(arbitrary nominal fading and noise distributions).
