  In cellular wireless networks, user association refers to the problem of
assigning mobile users to base station cells -- a critical, but challenging,
problem in many emerging small cell and heterogeneous networks. This paper
considers a general class of utility maximization problems for joint
optimization of mobile user associations and bandwidth and power allocations.
The formulation can incorporate a large class of network topologies,
interference models, SNR-to-rate mappings and network constraints. In addition,
the model can applied in carrier aggregation scenarios where mobiles can be
served by multiple cells simultaneously. While the problem is non-convex, our
main contribution shows that the optimization admits a separable dual
decomposition. This property enables fast computation of upper bounds on the
utility as well as an efficient, distributed implementation for approximate
local optimization via augmented Lagrangian techniques. Simulations are
presented in heterogeneous networks with mixtures of macro and picocells. We
demonstrate significant value of the proposed methods in scenarios with
variable backhaul capacity in the femtocell links and in cases where the user
density is sufficiently low that lightly-used cells can reduce power.
