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Employing smart antennas in the central access point (CAP) of wireless Internet access networks is studied. A polling-based adaptive beamforming multiple access protocol (PB-ABFMA) is proposed. In PB-ABFMA, CAP requests the corresponding mobile terminal (MT) to transmit a training sequence just before the data packet transmission, so the temporal reference beamforming (TRB) can be performed by the smart antennas. CAP schedules packet transmissions based on polling mechanism and dynamic TDMA. CAP and MT transmit alternately. A mini-slot is used to keep connectivity when an MT is idle, therefore, the access delay is reduced. A simple and effective access method is proposed to guarantee rapid access of new arrival MT to the channel. Based on the "request-reply" traffic, which is the main traffic in the Internet, the theoretical analysis of channel utilization is presented. The mean turn around delay and performance of the proposed access method are evaluated by simulation. Results show that the proposed PB-ABFMA protocols effectively support the application of smart antennas and provide high channel utilization and low turn around delay.