This is actually where I learned about it. I was elected to serve on the Board of Directors for the HOA I was living in, and one of the other directors was wanting to amend the CC&Rs to prohibit the mounting of antennas. I thought that was ridiculous, so I looked into it (being in an engineer in the communications field) and discovered what he wanted to do was illegal. So I called them on it and blocked the amendment. The HOA has the right to specify where the installation can take place, but cannot outright ban the antenna. The also cannot impose prior approval requirements which essentially impose a restriction. Based on what I learned, I would suggest just putting it up and when they come yelling and screaming, point them to the rule and state you didn't need permission (per the rule) and the burden is on them (per the rule) to prove their restrictions are permissable, not the other way around.

See this link for more information: FCC Over The Air Reception Device Rule

DISCLAIMER: I am not a lawyer and any advice given in this post is for entertainment purposes only. Follow my advice at your own risk. (or consult a real lawyer).