Low-medium-altitude platforms (LMAPs) are being actively researched and developed as a key solution to improve the performance and services of emergency communications. In order to provide higher capacity, throughput and quality of service guarantee to territorial users in emergency scenarios, a LMAP-based WiMAX system, AirWiMAX, is presented in this paper. Firstly, a hierarchical AirWiMAX topology is presented. Secondly, a joint radio resource allocation is carried out simultaneously at the time, frequency and power domain for the AirWiMAX downlink. This problem is modelled as a cooperative game in which a fairness criterion is enforced. Simulation results show that compared to the other two typical resource allocation algorithms, that is, the max-rate algorithm and the max-min fairness algorithm, the proposed algorithm achieves a good trade-off between the overall system throughput and the fairness.