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In this paper, a model for the static channel assignment in multi-radio multi-channel wireless mesh networks is proposed. We describe an interference model in wireless communication environment. The degree of detail in the model determines the accuracy of channel assignment. In many wireless mesh networks studies, the simplistic protocol interference model is adopted, but the model is usually not realistic and practical. Therefore, we construct a physical interference model and put forward a pure integer quadratic programming (PIQP) model to solve the channel assignment problem and maximize the capacity of wireless mesh networks. The feasibility and effectivity of the channel assignment solution are suggested by the results of simulation.