  We study network utility maximization (NUM) in the context of cellular single
station association (SSA) policies, which assigns each mobile user (MU) to a
single base station (BS). We measure an SSA policy in terms of the induced
\alpha-proportional fairness utility of each user's downlink rate, summed over
all users. The general SSA NUM problem involves choosing an optimal association
from MUs to BSs as well as an optimal allocation of BS resources to associated
MUs. Finding an exact solution to such centralized user association problems is
well-known to be NP-hard. Our contributions are as follows: i) we give an
explicit solution for the optimal BS allocation for a given SSA, which
establishes SSA NUM as a purely combinatiorial problem; ii) we establish the
integrality gap for the association problem to be one, and prove the relaxation
to be a non-convex optimization problem; iii) we provide both centralized and
distributed greedy algorithms for SSA, both with and without the exchange of
instantaneous rate information between users and stations. Our numerical
results illustrate performance gains of three classes of solutions: i) SSA
solutions obtained by greedy rounding of multi-station associations (a
centralized convex program), ii) our centralized and distributed greedy
algorithms with/without rate information exchanged, and iii) simple association
heuristics.
