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In this paper, a goal programming model is proposed for general downlink channel assignment. Unlike many channel assignment schemes with quality of service (QoS) requirements constraints, QoS requirements are formulated as mathematical functions in the objective functions of our schemes. This approach allows greater flexibility for QoS formulation. With this formulation, when there is insufficient amount of resource, the proposed schemes can provide the compromise solutions more conveniently without explicit admission controls. As a result, resource can be allocated more efficiently according to this model. Based on this model, the channel swapping algorithm and the best-first-assign algorithm are proposed. Simulation results show that with the proposed algorithm, less channel resource is required to meet the client demand.