Don't get confused about chair vs. antenna. The FEDs have laid down the law that supersedes HOA rules about antennas, but they haven't done anything similar about deck chairs. You are allowed to receive signals over the air regardless of what your HOA rules say. Time and time again challenges to this rule by HOAs fail. The core idea is that you have rights to receive these signals and it takes an antenna to receive them. The HOA must bend to reasonable needs (such as an antenna) so that you can receive the signals.
All that said, the HOA may still be able to dictate type of chairs on your deck/patio. But you do have rights to receive the signals. And it does take an antenna to receive those signals. The HOA must bend if you press the issue.
Also note that you don't even need their permission. Just put up what you need and leave it to them to try to force you to take it down. That's where the FED law trumps the HOA rules the best. If you try to go the permission route, they'll stall and stall, deny, etc. But if you just put up what you need, the most they'll be able to do is get you to move it to another location. More simply, it's much like a game of poker. You call their bluff (that they can somehow deny you access to the signals) and they can't play any card that will result in your NOT having access to the signals. They can ask you to relocate the antenna, but they can't ask you to relocate it such that you lose access to the signals. On the other hand, asking an HOA for permission will almost only get you denials (but they have no legal right to deny you, per the FED law). Basically, Nike offers the best advice on this topic: "Just do it". Then, it forces them to try to force you to remove/move it. The best they'll be able to do is to get you to put it in a different spot (but it will have to be a spot that still gets you the signals). Most simply: in every scenario, you win, except the one where you believe that the HOA has some right that supersedes this particular Federal law (they don't).
Lastly, at only 20 miles away, you probably don't need a massive antenna. Use the tool at:
http://www.antennaweb.org/aw/welcome.aspx to get a feel for the size of antenna(s) you may need. That will be much better than trying to guess. And you may want to try a quality set of "rabbit ears". They may do the trick. The nice thing about Digital TV signals is either you get the video at full quality or you don't; there is not partial quality in digital TV. If you can get all the channels you seek with rabbit ears, the picture quality should be as good as if you put up the most massive antenna you can buy.
If you do buy an outside antenna to go on your deck/patio, you don't need to actually mount it to test it- just put it on a chair(s) or table and see if it can pull in a quality signal. If so, then you can mount it. If not, return it and try another. Again, at 20 miles, you shouldn't have a big problem barring major nearby obstacles and/or lots of hills/mountains between you and the towers.
One last tip about outdoor antenna selection: besides using the tool referenced above, a very easy way to find the right size/type is drive around the neighborhood looking for installed antennas. Note their size/type. Then look for something similar.
