Hans Freudenthal wrote a book "Lincos: Design of a Language for Cosmic Intercourse, Part 1" in which he shows how to build up communication with aliens over nothing but a radio channel that can transmit pulses. He starts with mathematics and logic, and builds up to other concepts such as time, space, and social interaction. Part 2 would have taken it further but never appeared.

However, as far as I know it has never been used to establish communication with aliens.