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Outage probability and capacity of a class of block-fading MIMO channels areconsidered with partial channel distribution information. Specifically, thechannel or its distribution are not known but the latter is known to belong toa class of distributions where each member is within a certain distance(uncertainty) from a nominal distribution. Relative entropy is used as ameasure of distance between distributions. Compound outage probability definedas min (over the transmit signal distribution) -max (over the channeldistribution class) outage probability is introduced and investigated. Thisgeneralizes the standard outage probability to the case of partial channeldistribution information. Compound outage probability characterization (viaone-dimensional convex optimization), its properties and approximations aregiven. It is shown to have two-regime behavior: when the nominal outageprobability decreases (e.g. by increasing the SNR), the compound outage firstdecreases linearly down to a certain threshold (related to relative entropydistance) and then only logarithmically (i.e. very slowly), so that nosignificant further decrease is possible. The compound outage depends on therelative entropy distance and the nominal outage only, all other details(nominal fading and noise distributions) being irrelevant. The transmit signaldistribution optimized for the nominal channel distribution is shown to be alsooptimal for the whole class of distributions. The effect of swapping thedistributions in relative entropy is investigated and an error floor effect isestablished. The compound outage probability under Lp distance constraint isalso investigated. The obtained results hold for a generic channel model(arbitrary nominal fading and noise distributions).

Compound Outage Probability and Capacity of a Class of Fading MIMO Channels with Channel Distribution Uncertainty