Certified by.....................................................

This thesis presents a mathematical model for communication subject to both interfer-ence and noise. We introduce a realistic framework where the interferers are spatially scattered according to a Poisson field, and are operating asynchronously in a wireless environment; subject to path loss, shadowing, and multipath fading. We consider both cases of slow and fast-varying interferer positions. 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. We characterize the error probability and capacity of the link, when subject to both network interference and thermal noise. We derive the power spectral density (PSD) of the cumulative interference at any loca-tion in the plane. We put forth the concept of spectral outage probability (SOP), a new characterization of the cumulative interference generated by communicating nodes in a wireless network. Lastly, we quantify the cumulative interference distribution, error probability, channel capacity, PSD, and SOP as a function of various important system parameters, such as the signal-to-noise ratio (SNR), interference-to-noise ratio (INR)