I have built my house in Minecraft PE, and I have a ton of fences and sticks, but I need to know how big of a perimeter I need to let me sleep at night?
You cannot sleep if there are hostile or mobs that are neutral but are now aggressive within 8 blocks of your bed. Neutral but can be aggressive include wolves, enderman, and zombie pigman. Do keep in mind that there might be mobs hidden underground. Also be sure to light the area up as mobs can still spawn in your base if not properly lit.
I've played PE a lot and have a rough idea of the radius of monster spawning. I think that in PE, monsters can't spawn in a radius of about 15-20 blocks and the zone of monsters not able to spawn is about... 60 blocks after the normal no monster spawning radius. Note that this information may not be very accurate and uses rough estimates by the looks from where I am.