A freind has 6 or 8 layers of old carpet for a back stop ,he has it inside but a frame could be built outside.
He put poles up to hang peices of carpet over.
His poles are 8 feet off the ground and 8' long .
He uses 8'x 16' peices of used carpet ( free from a installer)
The poles are 1" rigid conduit 3" apart.
Arrow removal is not easy ,but I have never seen a arrow penatrate to the fletching.
If you miss alot you may have to replace the top layer . LOL

Johnch