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Being an evolution of IEEE 802.16e, IEEE 802.16j mobile multi-hop relay (MMR) is proposed to gain coverage extension and throughput enhancement. This research conducts theoretical analysis and performance evaluation on the on-demand bandwidth allocation in IEEE 802.16j MMR networks. Theoretical analysis shows that such systems using conventional bandwidth allocation will seriously suffer from low bandwidth utilization. We then develop a new, spectrum efficiency based adaptive resource allocation algorithm. Simulation results verified that, compared with conventional on-demand bandwidth allocation method, the proposed method is more bandwidth efficient and exhibits better fairness in such networks. In terms of throughput, packet loss rate and delay, the performance of SEBARA algorithm is further evaluated in an OPNET-based 802.16j MMR simulation platform. Both theoretical analysis and simulation indicate the novel method provides an attractive solution for bandwidth allocation in 802.16j MMR networks.