Spectrum sensing is vital for secondary unlicensed nodes to coexist and avoid interference with the primary licensed users in cognitive wireless networks. In this paper, we develop models for bounding interference levels from secondary network to the primary nodes within a spectrum sensing framework. Instead of classical stochastic approaches where Poisson point processes are used to model transmitters, we consider a more practical model which takes into account the medium access control regulations and where the secondary Poisson process is judiciously thinned in two phases to avoid interference with the secondary as well as the primary nodes. The resulting process will be a modified version of the Matérn point process. For this model, we obtain bounds for the complementary cumulative distribution function of interference and present simulation results which show the developed analytical bounds are quite tight. Moreover, we use these bounds to find the operation regions of the secondary network such that the interference constraint is satisfied on receiving primary nodes. We then obtain theoretical results on the primary and secondary throughputs and find the throughput limits under the interference constraint.