Air carrier Captain reported loss of communication with ramp personnel during push back using wireless headsets. The Captain was unable to hear brakes set command; and ramp personnel left the push back without communication with the Captain. The Captain contacted the station to send a ramp crew out to the aircraft with an operable headset to confirm that; push back was complete; and the aircraft was safe for taxi.

Narrative

I was PIC (Pilot In Command) of ZZZ [to] ZZZ1. Prior to push-back; I could hear the ground crew trying repeatedly to get the headphones to work; but eventually we were able to communicate well enough to begin the push. When the push-back was complete; I could sort of make out 'set brakes;' and since this made sense; I set the brakes. That was the last I could hear from them. Eventually; a marshaller walked in front of the nose and tried giving 'engine start' signals. I flashed the taxi lights at him and tried to signal NO; as the FOM says we cannot use hand signals on this fleet. I sent a message; while the FO contacted ZZZ Ops to tell them that we could not use hand signals. Incredibly; the guy with the wands got upset and just WALKED AWAY! Same with the tug crew! We had no idea if it was safe or not to start the engines and taxi. They were gone! We called back to the station and asked them to send someone with an operable headset to finish the dispatch of our flight; and that we'd sit there until they did so. After a few more minutes; a different guy came out and did a very professional job of getting us started with a solid salute and release from guidance.This problem is not just at ZZZ. It is everywhere. The wireless headphones just don't work very well; and make for an unsafe situation.