Você provavelmente está procurando a série de livros que é a Trigon Disunity publicada de 1985 a 1987.
O primeiro livro, Emprise - embora a capa que você provavelmente se lembra seja:
O resumo da Wikipedia sobre o livro é:
The world has been devastated by the Food and Fuel Wars turning once-powerful nations into loose groupings of isolated farming communities. Barter has replaced currency, and scientists — blamed for the world's misery — are burned at the stake. Hidden in the Idaho hills, astronomer Allen Chandliss struggles to maintain his primitive radio telescope, listening in secret for signs of the intelligent life, which may be the only hope to improve things on Earth. After seventeen years a repeating signal is received from Cassiopeia. He manages to send a message to a group of scientists in England. The race is on to decode the signal and then find the resources to respond to it...
O segundo livro da série Enigma
Set 150 years after the events of the first book, the 'aliens' turned out to be human and considered themselves to have been colonized from Earth in the distant past.
que é uma parte essencial da correspondência com sua descrição.
Como mencionado, esta é uma trilogia e um terceiro livro Empry
