On unbounded path-loss models: effects of singularity on wireless network performance

This paper addresses the following question: how reliable is it to use the unbounded path-loss model G(d) = d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-α</sup> , where α is the path-loss exponent, to model the decay of transmitted signal power in wireless networks? G(d) is a good approximation for the path-loss in wireless communications for large values of d but is not valid for small values of d due to the singularity at 0. This model is often used along with a random uniform node distribution, even though in a group of uniformly distributed nodes some may be arbitrarily close to one another. The unbounded path-loss model is compared to a more realistic bounded path-loss model, and it is shown that the effect of the singularity on the total network interference level is significant and cannot be disregarded when nodes are uniformly distributed. A phase transition phenomenon occurring in the interference behavior is analyzed in detail. Several performance metrics are also examined by using the computed interference distributions. In particular, the effects of the singularity at 0 on bit error rate, packet success probability and wireless channel capacity are analyzed.