OK, first of all, no HOA can prevent you from installing a TV antenna in order to receive local TV stations, period! The FCC ruling of 15 years ago:
http://www.fcc.gov/mb/facts/otard.html overrules the HOA''s ability to enforce any anti-antenna policy. if you have any question about it, print out the link that I linked to you, and show it to your HOA if you are concerned about crossing them: basically, if you are in your own home, and have sole use of your roof, then you have the right to install an antenna. if you are in a condo or townhouse, the rules are different, so look over the link that gave you.
Having said that: you are in a truly awful area for TV reception: shadowed by mountains, with no direct line-of-sight to the Mt. Wilson transmitters. Even though the transmitters are only about 30 miles from you, you will need the largest and most powerful antenna available just to see ABC, KCAL and FOX, without much hope of seeing the other LA transmitters. Under the circumstances, I am not sure that giving up a subscription service like cable TV or satellite is a good idea for you. If you really want to peruse it, I will try to advise you, but I am not optimistic about your chances of seeing a big variety of programming over-the-air.