Date: 201807
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Aircraft: EMB ERJ 170/175 ER/LR
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
Airspace: Class B ZZZ
ATC / advisory: Ramp ZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown
Second reporter function: Pilot Flying; First Officer
Anomaly: Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Clearance; Ground Event / Encounter Other / Unknown
Detector: Person Flight Crew
When detected: Other Pushback
Result: Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Contributing factors: Equipment / Tooling; Human Factors; Procedure
Primary problem: Equipment / Tooling

Narrative: After the passenger door was closed and the before start check list was completed I got on the intercom circuit and called for the ramp to respond. A voice answered me back and I told them to go ahead with their items necessary to complete pushback. The voice answered back and said that the area was clear; the FOD walk was complete and they were waiting brake release. I told them that the brake was released; nosewheel steering disengaged and I would advise when we had pushback clearance. Shortly after this another Ramp personnel with a remote headset on his head appeared to my left of the airplane and was pointing to his headset as if trying to establish communication. I asked the voice on my intercom circuit who am I supposed to be talking to during this push back and he responded back that he was the one to communicate with.We were on gate XX; and we heard the aircraft adjacent to us on XY call for pushback. Ramp control stated to both of us that they had one inbound aircraft and then they would get us out. I observed an aircraft coming around the taxiway towards the ramp and just as he started to make his turn into the X alley; suddenly our push crew started pushing us back. I immediately stated 'Stop the Push!' loudly; with no response back and our push crew continued to push us into the middle of the alley. Ramp control was yelling at us at the same time; and my First Officer stated that we had lost all communications with our push crew. The inbound aircraft quickly turned away from the alley to avoid a collision while I tried in vain to talk to our push crew. I then explained to ramp control that we did not clear our crew for push and in a few moments a ramp manager plugged into our aircraft and I explained what happened; and he said he would look into it.After much discussion with my First Officer; we both came to the conclusion that the push crew for XX was in fact talking to the aircraft on XY and vice a versa. Somehow the wireless headsets used during pushback had gotten crossed from one aircraft to the other; and what happened to us was the result of mistaken identity as to who was talking to who. This could have very easily resulted in injury or worse to personnel or aircraft damage or worse; had the inbound crew not taken proper and timely action; not to mention that the ramp control temporarily lost control of their ramp and we lost the control of our aircraft. I feel the procedures for the use of wireless headsets during pushback be reviewed in light of this incident. I would also like a response back after this review has been completed.


Second narrative: [Report narrative contains no additional information.]


Synopsis: EMB-175 flight crew reported the ramp crew pushed the aircraft without clearance; towards conflicting taxiing aircraft.