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The use of smart antennas in extending coverage range and capacity of wireless LANs dictates the employment of novel media access control (MAC) schemes, with which the access point (AP) provides access to users by learning their spatial signatures. This paper puts forward an exact approach to analyze the performance of the schemes in terms of required time so that the AP becomes aware of user locations and grants access to the system. The numerical results show that the scheme which distinguishes the users residing in or out of broadcasting coverage range of the AP can provide rapider media access. In addition, the simulation results verify the theoretical approach.