On the capture probability for a large number of stations

The probability of capture under a model based on the ratio of the largest received power to the sum of interference powers is examined in the limit of a large number of transmitting stations, It is shown in great generality that the limit depends only on the capture ratio threshold and the roll-off exponent of the distribution of power received from a typical station, This exponent is insensitive to many typical channel effects such as Rician or Rayleigh fading and log-normal shadowing. The model is suitable for large systems with noncoherently combined interference.