Falcon is a character in the holoprogram Julian Bashir, Secret Agent, a mercenary and rival to the main character played by Julian Bashir. The two had been enemies for nine years as of 1964, since 1955. Though an individual operator, Falcon was sometimes allied with Dr. Hippocrates Noah.
In 2372, after the explosion of the runabout USS Orinoco, the transporter pattern of Miles O'Brien was temporarily stored in the program and the character of Falcon took on his physical characteristics. (DS9: "Our Man Bashir")
After the temporary emergency, O'Brien himself often returned to the program with Bashir and assumed the character of Falcon under more willing circumstances. However, he was irked at the fact that he seemed to always play the villain. (DS9: "A Simple Investigation")