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To fully utilize radio resources by intelligently filling in as much radio spectrum gaps as possible, the concept of cognitive radio network has been well accepted. A challenge inherent in this technology is how to build a mechanism that can allocate resource by learning and adapting to a specific radio transmission environment. In this paper, we propose a cognitive resource management scheme that is specifically designed for allocating radio resource in a cognitive radio ad hoc network (CRAHN) environment. The proposal applies cognitive processes in a cross-layer design, which acquires knowledge from the physical layer, the medium access control (MAC) layer, and application layer. It intelligently allocates resources according to traffic demands, traffic priorities, link capabilities, and link qualities.