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

TL;DR

This paper introduces a new framework for analyzing the outage probability and capacity of MIMO channels with uncertain channel distributions, using relative entropy to model distribution ambiguity and deriving properties of the compound outage probability.

Contribution

It generalizes outage probability to account for distribution uncertainty, providing a convex optimization characterization and revealing a two-regime behavior in outage reduction.

Findings

Compound outage probability decreases linearly then logarithmically with SNR.

Optimal transmit signal distribution for nominal channel is also optimal for the distribution class.

Results hold for generic channel models with arbitrary fading and noise distributions.

Abstract

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).