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This paper analyzes the optimal D2D user allocation over multi-bands in the heterogeneous networks. The heterogeneous networks contain one or several cellular systems and D2D communication shares uplink resource with them. By allocating D2D users on different bands, it can reduce the interference between D2D and cellular systems and improve D2D transmission capacity at the same time. Through utilizing stochastic geometry, the problem is formed as sum D2D transmission capacity on each band with constraints that guarantee outage probilities of both cellular and D2D transmission. The primal problem is first proved to be convex and then solved by constructing Lagrange function and KKT conditions.
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