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-resourceblock (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.
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