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Scheduling can obtain multi-user diversity if channel state information (CSI) is known, such as for low-mobility users and can exploit frequency diversity if CSI is not available at the transmitter, such as for high-mobility users. In this paper, we investigate resource allocation exploiting frequency and multiuser diversity for LTE downlink systems with users of different mobilities. To facilitate resource allocation, we first develop a user classification algorithm to identify high- and low-mobility users. Based on user mobility classification, we then propose a scheduling algorithm to simultaneously obtain multi-user diversity for those low-mobility users and frequency diversity for those high-mobility users. It is demonstrated by computer simulation that the performance of the proposed scheduling algorithm provides 6% and 23% gain of overall cell throughput, and 5.6% and 18% gain of 10th percentile throughput over proportional fairness based frequency-selective and frequency-diversity scheduling algorithms, respectively. Furthermore, the proposed scheduling algorithm has the same order of computational complexity as the frequency-selective scheduling algorithm.