In this paper, we consider a down-link transmission of multicell virtualized wireless networks (VWNs) where users of different service providers (slices) within a specific region are served by a set of base stations (BSs) through orthogonal frequency division multiple access (OFDMA). In particular, we develop a joint BS assignment, sub-carrier and power allocation algorithm to maximize the network throughput, while satisfying the minimum required rate of each slice. Under the assumption that each user at each transmission instance can connect to no more than one BS, we introduce the user-association factor (UAF) to represent the joint sub-carrier and BS assignment as the optimization variable vector in the mathematical problem formulation. Sub-carrier reuse is allowed in different cells, but not within one cell. As the proposed optimization problem is inherently non-convex and NP-hard, by applying the successive convex approximation (SCA) and complementary geometric programming (CGP), we develop an efficient two-step iterative approach with low computational complexity to solve the proposed problem. For a given power-allocation, Step 1 derives the optimum userassociation and subsequently, for an obtained user-association,Step 2 find the optimum power-allocation. Simulation results demonstrate that the proposed iterative algorithm outperforms the traditional approach in which each user is assigned to the BS with the largest average value of signal strength, and then, joint sub-carrier and power allocation is obtained for the assigned users of each cell. Especially, for the cell-edge users, simulation results reveal a coverage improvement up to 57% and 71% for uniform and non-uniform users distribution, respectively leading to more reliable transmission and higher spectrum efficiency for VWN.Index Terms-Complementary geometric programming, successive convex approximation, joint user association and resource allocation, virtualized wireless networks.

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