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This paper proposes an enhanced opportunistic beamforming scheme with power allocation search algorithms over finite feedback channels for a broadcast channel. Instead of continually varying the power allocation for multiple beams based on instantaneous channel state information (CSI) feedback, the proposed scheme determines power allocation in advance solely based on channel statistics and the number of mobile stations (MSs). This scheme maintains power allocation throughout multiple training and data transmission periods as long as channel statistics and the number of MSs are unchanged. As a result, the proposed scheme reduces the complexity for searching power allocation, and becomes robust over finite feedback channels. Computer simulations show that the proposed power allocation search algorithms efficiently find the near optimal power allocation with low complexity. The simulations also show that, although the proposed scheme predetermines power allocation solely based on channel statistics and the number of MSs, it outperforms the opportunistic beamforming scheme using instantaneous CSI feedback with finite feedback rates.