The HOA has the burden to prove that an exception to the FCC OTARD rule should be made. You are not obligated to obtain their approval or even notify them of an antenna installation that falls under the protection of the OTARD rules.
Simply read and understand the OTARD rules, then stay within their scope so you have their full protection. If the need arises, invite the HOA to read them themselves.
Often the HOA will try to ignore the difference between a satellite receiving antenna (which the FCC specifies size limits for) and terrestrial TV antennas (which are not limited in size under the OTARD rules).
If they want to play tough, I've always thought it would be fun to offer that I'll forgo an antenna installation IF... they provide a full lineup of TV programing fully equal in quality to that which is available to me over the air... AND, the service would have to include 24-7-365 on-call service in the event an impairment or failure in service occurred... all at no cost to me, in perpetuity, and I would be free to recruit any and all HOA members to use the same service.
