Yep, you can have only one.
The rule applies not so much to purple cards, as it does to all cards with the 'radio tower' icon on it. All purple cards have that icon, but so do the landmarks. These cards are unique per player.
rulebook, page 7 wrote:
Players may not construct more than one of each type of card with the [icon] in their town. A player may construct as many unique [icon] cards as they choose, but may never construct a second of the same [icon] card.