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This paper studies the impact of phased array antennas directivity onto the throughput performance of WPANs adopting the IEEE 802.15.3 MAC standard in the 60 GHz band. High gain directional transmission is desirable in the 60 GHz band to overcome the high signal attenuation typical of these frequencies and improve the wireless channel reliability in order to achieve data rates up to 5 Gbps. In our antenna system model, directional transmission at both transmitter and receiver side is accomplished through a simplified scheme of direction of arrival estimation and beamsteering. We have implemented the antenna system and the antenna control protocol within 802.15.3 MAC in ns2. Our simulation analysis shows that the accuracy of the antenna pointing direction must increase with the antenna directivity otherwise significant throughput degradation is experienced.