You'd need to look into the "Receiver Sensitivity" - so in example for the AP3805 on page#6 you'd need a min. signal of -85dBm for 24Mbps from the client to the AP.
http://learn.extremenetworks.com/rs/extreme/images/AP3805-DS.pdf
Every client works that way but unfortunately only few WLAN adapter vendors publish this values.
Could be that one client need -80dBm for 24Mbps and another one only -85dBm.
So you'd need to meassure the signal in the roam to see what min. basic rate would be feasible in your installation - that is normaly part of an site survey.
Might be that the door has such a high absorption that a stable WLAN connection isn't working in the room so you'd need to place one directly in the room to get a good coverage.
-Ron