A couple books I'd put in this category:
1. Roadside Picnic, by the Strugatsky brothers, loose basis of Tarkovsky's Stalker movie.
2. XX by Rian Hughes -- hugely under-rated book. Starts with a signal from outer space and goes quite far, and also has a book-within-a-book. Nearly 1000 pages but found it very engaging.
Currently trying to read Stanlislaw Lem's His Master's Voice which has a similar theme of a possible signal from an alien intelligence.
I absolutely love Lem, and I just read Roadside Picnic this year.
I had not heard of XX before - will have to check it out, thanks.