The FCC says you can have almost any antenna necessary to pick up OTA signals and your HOA can't say a damn thing about it!
http://www.fcc.gov/mb/facts/otard.html
Q: What types of restrictions are prohibited?
A: The rule prohibits restrictions that impair a person's ability to install, maintain, or use an antenna covered by the rule. The rule applies to state or local laws or regulations, including zoning, land-use or building regulations, private covenants, homeowners' association rules, condominium or cooperative association restrictions, lease restrictions, or similar restrictions on property within the exclusive use or control of the antenna user where the user has an ownership or leasehold interest in the property. A restriction impairs if it: unreasonably delays or prevents use of; (2) unreasonably increases the cost of; or (3) precludes a person from receiving or transmitting an acceptable quality signal from an antenna covered under the rule. The rule does not prohibit legitimate safety restrictions or restrictions designed to preserve designated or eligible historic or prehistoric properties, provided the restriction is no more burdensome than necessary to accomplish the safety or preservation purpose.
Q: Who do I call if my town, community association or landlord is enforcing an invalid restriction?
A: Call the Federal Communications Commission at (888) CALLFCC (888-225-5322), which is a toll-free number, or 202-418-7096, which is not toll-free. Some assistance may also be available from the direct broadcast satellite company, multichannel multipoint distribution service, television broadcast station, or fixed wireless company whose service is desired.