  A joint resource allocation (RA), user association (UA), and power control
(PC) problem is addressed for proportional fairness maximization in a
cooperative multiuser downlink small cell network with limited backhaul
capacity, based on orthogonal frequency division multiplexing. Previous studies
have relaxed the per-resource-block (RB) RA and UA problem to a continuous
optimisation problem based on long-term signal-to-noise-ratio, because the
original problem is known as a combinatorial NP-hard problem. We tackle the
original per-RB RA and UA problem to obtain a near-optimal solution with
feasible complexity. We show that the conventional dual problem approach for RA
cannot find the solution satisfying the conventional KKT conditions. Inspired
by the dual problem approach, however, we derive the first order optimality
conditions for the considered RA, UA, and PC problem, and propose a sequential
optimization method for finding the solution. The overall proposed scheme can
be implemented with feasible complexity even with a large number of system
parameters. Numerical results show that the proposed scheme achieves the
proportional fairness close to its outer bound with unlimited backhaul capacity
in the low backhaul capacity regime and to that of a carefully-designed genetic
algorithm with excessive generations but without backhaul constraint in the
high backhaul capacity regime.
