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Opportunistic spectrum access creates the opening of under-utilized portions of the licensed spectrum for reuse, provided that the transmissions of secondary radios do not cause harmful interference to primary users. Such a system would require secondary users to be cognitive-they must accurately detect and rapidly react to varying spectrum usage. Therefore, it is important to characterize the effect of cognitive network interference due to such secondary spectrum reuse. In this paper, we propose a new statistical model for aggregate interference of a cognitive network, which accounts for the sensing procedure, secondary spatial reuse protocol, and environment-dependent conditions such as path loss, shadowing, and channel fading. We first derive the characteristic function and cumulants of the cognitive network interference at a primary user. Using the theory of truncated-stable distributions, we then develop the statistical model for the cognitive network interference. We further extend this model to include the effect of power control and demonstrate the use of our model in evaluating the system performance of cognitive networks. Numerical results show the effectiveness of our model for capturing the statistical behavior of the cognitive network interference. This work provides essential understanding of interference for successful deployment of future cognitive networks.