Outage probability under channel distribution uncertainty

Outage probability of a class of block-fading (MIMO) channels is considered under channel distribution uncertainty, when 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 from a nominal distribution. Relative entropy is used as a measure of distance between distributions. Compound outage probability defined as min (over the input distribution) -max (over the channel distribution class) outage probability is introduced and investigated, which 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 a two-regime behavior: when the nominal outage probability decreases, the compound outage first decreases linearly down to a certain threshold and then only logarithmically (i.e. very slowly), so that no significant further decrease is possible. The input 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 obtained results hold for a generic channel model (arbitrary nominal fading and noise distributions).