  A statistical model of interference in wireless networks is considered, which
is based on the traditional propagation channel model and a Poisson model of
random spatial distribution of nodes in 1-D, 2-D and 3-D spaces with both
uniform and non-uniform densities. The power of nearest interferer is used as a
major performance indicator, instead of a traditionally-used total interference
power, since at the low outage region, they have the same statistics so that
the former is an accurate approximation of the latter. This simplifies the
problem significantly and allows one to develop a unified framework for the
outage probability analysis, including the impacts of complete/partial
interference cancelation, of different types of fading and of linear filtering,
either alone or in combination with each other. When a given number of nearest
interferers are completely canceled, the outage probability is shown to scale
down exponentially in this number. Three different models of partial
cancelation are considered and compared via their outage probabilities. The
partial cancelation level required to eliminate the impact of an interferer is
quantified. The effect of a broad class of fading processes (including all
popular fading models) is included in the analysis in a straightforward way,
which can be positive or negative depending on a particular model and
propagation/system parameters. The positive effect of linear filtering (e.g. by
directional antennas) is quantified via a new statistical selectivity
parameter. The analysis results in formulation of a tradeoff relationship
between the network density and the outage probability, which is a result of
the interplay between random geometry of node locations, the propagation path
loss and the distortion effects at the victim receiver.
