Joint user association and resource allocation in small cells with limited backhaul capacity

User association and resource allocation for downlink orthogonal frequency division multiplexing (OFDM) should be jointly optimized in small cells networks with limited backhaul in order to maximize the network utility. In general, the joint user association and per-band resource allocation problem is known as an integer NP-hard problem requiring exponential order of computational complexity to find the global optimal point. To obtain a solution with feasible computational complexity, most previous works solve this problem by relaxing the integer problem of the per-band resource allocation to a real-valued problem by assuming that channel gain is averaged out over all the frequency bands and that base stations allocate a real-valued proportion of the bandwidth. We propose two sub-optimal algorithms to solve the original integer problem with polynomial order of computational complexity in pursuit of maximizing the network utility with limited backhaul constraints. The network utility and geometric mean of receiving rates for the two proposed schemes are evaluated via numerical simulations. The computational complexity of the two schemes are also represented, respectively, showing the trade-off between the network utility and complexity.