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This paper presents a number of distributed resource allocation schemes for fixed relay stations in a network based on orthogonal frequency-division multiple access (OFDMA). Results show that the spectrum efficiency and user fairness can be enhanced by cognitive radio techniques at the relay nodes. Iterative waterfilling and iterative multilevel waterfilling are exploited in the power allocation, and results show that optimal power allocation is achieved for the applications under study. These iterative methods are then combined with a power reallocation algorithm to further enhance spectrum utilization. A novel iterative barrier-constrained waterfilling algorithm is proposed to address the data rate limitations imposed by poor base-station-to-relay channels. The proposed technique offers fast convergence, and complexity is reduced by a distributed implementation across the network. Finally, a novel distributed subcarrier and power allocation algorithm is proposed. Simulation results indicate that, although multiuser fairness is imperfect, capacity gains of up to 20% can be achieved compared with the traditional equal power allocation method. When multiuser fairness constraints are applied, a near-perfect fairness index is achieved; however, the peak capacity is reduced by approximately 10%.