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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 cancellation, 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 cancellation are considered and compared via their outage probabilities. The partial cancellation 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.