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The scheduling scheme of exploiting multiuser diversity gain increases network capacity drastically; however, feedback information overhead linearly increases as the number of users increases. Thus, the allocation of an optimum amount of system resources in feedback signaling is quite an important problem. We analyze the exact capacity of the contention-based multiuser diversity scheduler, which considers the quantitative feedback overhead. The optimum feedback threshold is derived based on the analyzed capacity model. Moreover, the method of searching the optimum resource to be allocated in feedback signaling is proposed.