People might be downvoting this because of it's tone, but it's correct. If you're putting up radio shows, DJ sets or anything that uses other people's music you need to clear each track in it. Owning a piece of music doesn't entitle you to broadcast it, it merely entitles you to listen to it.
Well, you'd still owe a fee as the broadcaster. Unless I'm very muh mistaken, you can't just buy a bunch of CDs and then have public performance rights; it's just that as long as you pay the GEMA fees, rightholders can't decline to license the work to you.
That's why I said "entitled". Yes, you don't have the license unless you pay GEMA (after the fact, btw), but the license must be granted to you at a fixed fee.