WIAS Preprint No. 2659, (2019)

SINR percolation for Cox point processes with random powers


  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Tóbiás, András

2010 Mathematics Subject Classification

  • 82B43 60G55 60K35


  • Signal-to-interference ratio, Cox point process, Poisson point process, continuum percolation, SINR percolation, Gilbert graph, Boolean model, stabilization, random power, degree bound




Signal-to-interference plus noise ratio (SINR) percolation is an infinite-range dependent variant of continuum percolation modeling connections in a telecommunication network. Unlike in earlier works, in the present paper the transmitted signal powers of the devices of the network are assumed random, i.i.d. and possibly unbounded. Additionally, we assume that the devices form a stationary Cox point process, i.e., a Poisson point process with stationary random intensity measure, in two or higher dimensions. We present the following main results. First, under suitable moment conditions on the signal powers and the intensity measure, there is percolation in the SINR graph given that the device density is high and interferences are sufficiently reduced, but not vanishing. Second, if the interference cancellation factor γ and the SINR threshold τ satisfy γ ≥ 1/(2τ), then there is no percolation for any intensity parameter. Third, in the case of a Poisson point process with constant powers, for any intensity parameter that is supercritical for the underlying Gilbert graph, the SINR graph also percolates with some small but positive interference cancellation factor.

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