My BCM4318 works just fine on BT4b without any problem. In fact it works fast efficiently without any sort of patching or recompiling anything, "out of the box" you might say.
root@dell:~# aireplay-ng -9 mon0
08:28:09  Trying broadcast probe requests...
08:28:09  Injection is working!
08:28:11  Found 1 AP 

08:28:11  Trying directed probe requests...
08:28:11  00:21:27:XX:XX:XX - channel: 11 - 'TP-LINK'
08:28:13  Ping (min/avg/max): 1.167ms/52.256ms/157.530ms Power: -60.07
08:28:13  30/30: 100%
All sorts of attacks work with injection speed of 500 pps.

You might note it's mon0 in lieu of wlan0 if you started your wlan with airmon-ng.