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The WiMax mesh networks based on IEEE 802.16 standard (2004) was developed with the goal of providing for easy, fast and cost-effective network set-up, deployment and extension. The standard defines scheduling scheme in mesh mode, but don't specify spatial resource management in the protocol. In this paper, we design a general algorithm for SSs to achieve concurrent transmission in both uplink and downlink streams. Constructing and adjustment of routing tree is also given in the paper. Simulation results show that overall end-to-end throughput is greatly improved when using our proposed algorithm for concurrency, and that the algorithm performs best when the routing tree is adjusted.