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Gauss-Poisson processes (GPPs) are a class of clustered point processes, which include the Poisson point process as a special case and have a simpler structure than the general Poisson cluster point processes. A key property of the GPP is that it is completely defined by its first- and second-order statistics. In this paper, we first show the properties of the GPP and provide an approach to fit the GPP to a given point set. A fitting example is presented. We then propose the GPP as a model for wireless networks that exhibit clustering behavior and derive the signal-to-interference-ratio distributions for different system models: 1) the basic model where the desired transmitter is independent of the GPP and all nodes in the GPP are interferers; 2) the non-cooperative model where the desired transmitter is one of the nodes in the GPP; and 3) the cooperative model, where the nodes in a GPP cluster transmit cooperatively …