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Opportunistic scheduling provides the capability of resource management in wireless networks by taking advantage of multiuser diversity and by allowing delay variation in delivering data packets. It generally aims to maximize system throughput or guarantee fairness and quality of service (QoS) requirements. In this paper, we develop an extended proportional fair (PF) scheduling policy that can statistically guarantee three kinds of QoS. The scheduling policy is derived by solving the optimization problems in an ideal system according to QoS constraints. We prove that the practical version of the scheduling policy is optimal in opportunistic scheduling systems. As each scheduling policy has some parameters, we also consider practical parameter adaptation algorithms that require low implementation complexity and show their convergences mathematically. Through simulations, we confirm that our proposed schedulers show good fairness performance in addition to guaranteeing each user's QoS requirements.