Closed Form Asymptotic Expression of a Random-Access Interference Measure

A model describing the cumulative effect of the independent access of K users to a shared resource, which is formed by N elements, is proposed, based on which an integer interference measure ζ is defined. While traditional cases can be reconducted to reference well-known results, for which ζ is either Gaussian or Poissonian, the proposed model provides a more general framework that offers the tool for understanding the nature of ζ. In particular, an asymptotic closed form expression ( K → ∞, N → ∞, K/N\\→ ∞β∈(0,∞)) for ζ distribution is provided for systems presenting constructive versus destructive interference, and as such is applicable to characterizing statistical properties of interference in a wide range of random multiple access channels.