This paper presents a mathematical model for communication subject to both interference and noise. The spatial distribution of the interfering nodes is accounted for by resorting to a Poisson point process in the two-dimensional plane. We consider a realistic scenario of slowly-moving, asynchronous nodes in a wireless environment subject to both log-normal shadowing and fast Rayleigh fading. Under this scenario, we determine the statistical distribution of the cumulative interference at the output of a linear receiver, located anywhere in the two-dimensional plane. Furthermore, we provide the corresponding error performance analysis, which is valid for any linear modulation scheme. The proposed model captures all the essential physical parameters that impact network interference, but is simple enough to allow a tractable analysis and provide fundamental insights. Furthermore, our work generalizes the conventional analysis of linear detection in the presence of additive white gaussian noise (AWGN) and fast fading, allowing the traditional results to be extended in a simple way to include the effect of interference.