I like the idea but the big satellite dish would be useless with out a satellite in orbit. If there are satellites then there are a whole can of worms to contend with, No reason not to have GPS or Internet, that not survival that's just living in a 3rd world country
Satellites are an narrow beam communication device not an Omnidirectional broadcast antenna,
but having control of a radio/antenna array which is basic technology anyone with some wire, resistors, some carbon and a bit of power can create a basic transmitter/receiver, that could give the occupying player an advantage maybe the ablilty to hear all broadcasts on the island but only on the frequency he is on at that time.
I think the CB/ham-radio is the best solution and maybe up-gradable antennas, hand held versions having a small broadcast range while home/base units would have larger range depending on the level of your antenna,
What about a satellite balloon you can send up high? It can gain energy from the sun, and/or the wind, and also position himself, it is possible in reality IMO. Another challenge to build (1/map), which may even get you a screenshot of the map from up there.