Near vs. Far Field: Interference Aggregation in TV Whitespaces

We investigate the behavior of aggregate interference generated by cognitive radios. We find that a phase change occurs in the behavior of aggregate interference as the density of the white-space devices is increased for a fixed protection radius. For a deterministic grid model, the mean of the interference behaves differently depending on whether the problem is one of ``near field'' or ``far field''. For a more realistic Poisson-placement model, we show that the shape of the distribution of interference changes from a heavy-tailed distribution to something that is approximately Gaussian. Investigating models with random fading of signal at each transmitter, we show that fading can alter the boundary of near and far fields. These phase-changes suggest that in designing rules for whitespace devices, the FCC rules may have to be sensitive to whether the situation is one of near or far field. For Poisson placement of nodes, our results also suggest that central limit theorem-style arguments might help in obtaining a conceptually and computationally improved understanding of interference aggregation.