its either a fairy ring , or kikuyu yellows
either way I would aerate it and hit it with a good fungicide like banner max or chipco gt ,
if you don't want to spend the dollars on the fungicide I would aerate it the give it a hit with a good quality wetting agent
water it in and give it a big feed to help it grow out, but let it dry out between waterings you don't want it to stay wet
a lot of time you will see puff balls or toad stools growing in the perimeter if its a fairy ring