Then you're doing it wrong I guess. Even if you're on airplane mode, the radiation is still there. Just leave the phone at least 1 meter away from you then you should be fine.
Because the main culprit for radiation is actually the battery. Although wi-fi is the only one that might affect human sleep.
Well if so, I can't really help out. Because instead of putting phone to sleep, I put them away.
Name: Nexus 4 Mako
ROM: BrainMaster JWR
Kernel & Tweaks: Franco/Trinity
Devices I once had(Or still have):
LG Nexus 4(present), Samsung Nexus S(present), LG Optimus 4X HD P880(sold), HTC Sensation XE Pyramid(sold), Samsung Galaxy Wonder i8150(spare)
Devices I have minor experience about:
Samsung Galaxy Y, Samsung Galaxy i9100, Samsung Galaxy i9100G, Samsung Galaxy SIII Mini i8190N, HP iPaQ500(retired and yes its an antique)