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In this paper, we introduce a new framework to compute the Average Symbol Error Probability (ASEP) of an intended wireless communication system subject to network interference and noise. The interfering nodes are assumed to be randomly distributed in the 2D Euclidean plane according to a homogeneous Poisson point process. Our framework is applicable to performance prediction and optimization of, e.g., emerging heterogeneous cellular and cognitive radio networks. More specifically, we move from and generalize the semi-analytical framework recently introduced by Pinto and Win , and develop a new mathematical model which offers a simple single-integral expression of the ASEP under very general channel and interference conditions. The framework is exact, avoids Monte Carlo methods for its computation, and is applicable to asynchronous and synchronous scenarios. Our numerical examples show that both setups have almost the same performance, and that the ASEP in the presence of synchronous interference is a very tight upper-bound of the ASEP in the presence of asynchronous interference. This is a relevant result, as we show in this paper that in the former case all parameters of interest can be computed in closed-form. Our analytical derivation is substantiated through extensive Monte Carlo simulations.