It could be an angel of shortsightedness.
How about seeing only the tiles next to the doomguy (i.e.: all 8 of them) and nothing else at all ?
Then again, I have a feeling I already suggested that as Angel of Blindness...
Could be fun, though. You'd either use up a LOT of ammo or stumble through the levels trying to melee everything you DON'T see. Still doable, as the messages would still tell you where special levels and uniques are present and when you hear something writhing in pain because you accidentally shot it ;).