Analytical outage probability for max-based schedulers in delay-constrained applications

The calculation of exact outage probabilities in delay-constrained multiuser-systems has been an unsolved problem. This paper introduces an analytical method to calculate the probability of an outage for max-based schedulers, which take a scheduling decision by choosing the user with an associated maximum metric. While this analysis is, therefore, suited for purely opportunistic scheduling, it is also suited for proportional fair scheduling, the arguably most important scheme in today´s wireless systems. The approach presented in this paper does not restrict key system properties in any way: it can be applied to an arbitrary number of users with arbitrary channel statistics and arbitrary delay constraints. In order to prove the practicability, the outage probability is calculated for opportunistic and proportional fair scheduling scenarios, and it is shown to perfectly match the results of extensive numerical simulations. Furthermore, the most important practical implementation issues are discussed, and a new and highly useful interpretation of the maximum order statistic of i.n.i.d. (independent non-identically distributed) random variables is introduced.