Yet Cohen himself admits that he can't remember the exact source of the song. In his 1994 BBC interview, he suggests that it was actually based on several love triangles, in which he sometimes played the role of the betrayer and sometimes played the role of the betrayed. If we try to pin down the biographical roots of the song, one of many twists is that the "famous blue raincoat," which here belongs to the betrayer, actually belonged to Cohen himself.
The interesting thing about the song being written in the form of a letter is that we don't know whether the singer is reciting the words from a letter that he has composed, or if he's reading a letter that he has received. The signature at the end of the song oversimplifies things. We suggest that what makes "Famous Blue Raincoat" such a fascinating song is that Cohen's singing makes it nearly impossible to tell whether he's supposed to be the man who has written the letter or the man who has received it. The speaker is ambiguous, lost somewhere between the written lyrics and the man singing the song.