This paper puts forth a mathematical model for narrowband (NB) communication subject to ultra wideband (UWB) network interference and additive white Gaussian noise (AWGN). We introduce a framework where the UWB interferers are spatially scattered according to a Poisson field, and are operating asynchronously in a wireless environment subject to path loss, shadowing, and fast fading. Under this scenario, we determine the statistical distribution of the aggregate network interference at the output of a linear NB receiver, located anywhere in the two-dimensional plane. Then, we provide an exact expression for the error probability of the NB link, which is valid for any linear modulation scheme (e.g., M-ary phase shift keying or M-ary quadrature amplitude modulation). Our work generalizes the conventional analysis of coherent NB detection in the presence of AWGN and fast fading, allowing the traditional results to be extended to include the effect of UWB network interference