To my knowledge, there is no mechanic for Perception (or other) checks to wake up while a character is asleep. I skimmed the PHB sections on rest and abilities this morning before I left for work. Didn't look in the DMG. Had to choose between gaming and a shower and, sorry, a shower wins every time.
I suspect there's no mechanic at all for rousing from sleep (3.x had something like -10 to your Listen check to hear a sound while sleeping). For now, until I can get home and dig a bit more, I leave it to you individually to decide whether your character is a light or heavy sleeper, and whether your character heard Raza call for Brinn just now.