ACR HVT PUSHED BACK ONTO RWY FOR ENGINE START WITHOUT TWR CLRNC.

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I WAS CAPT OUT OF AUS. OUR COMPANY IS USING A NEW PARKING FAC WHICH IS EXTREMELY NOISE SENSITIVE WHICH REQUIRES A 3 ENG SHUTDOWN AND PULL IN TO PARKING AND A 1 ENG PUSHBACK. THE COMPANY ISSUED A LETTER COVERING THIS PROC. THIS PROC REQUIRES TAXIING DOWN RWY 35 TO TXWY P AND SHUTTING DOWN ALL ENG EXCEPT #3; HOOKING UP TO TUG AND BEING TOWED INTO PARKING SPOT. COMPANY LETTER ALSO SAYS THAT DURING NIGHT OPERATION (DEP) THE REVERSE ORDER WOULD BE FOLLOWED. DURING FIRST NIGHT; OUR GND PERSONNEL; TOLD ME THAT THEY HAD A MEETING WITH THE ARPT PERSONNEL AND THAT IT WAS UNDERSTOOD THAT WHEN WE CALLED FOR PUSHBACK THAT WE WOULD BE PUSHING BACK ONTO RWY 35 BECAUSE PARALLEL TXWY WAS TO NARROW FOR ACFT. FIRST NIGHT OPERATION WENT OK AS PLANNED. ON SECOND NIGHT; 9/FRI/88; THE SAME OPERATION WAS PLANNED AS THE NIGHT BEFORE HOWEVER I WAS OPERATING WITH A DIFFERENT F/O. WHEN IT BECAME TIME TO PUSHBACK I INSTRUCTED HIM TO CALL GND AND REQUEST A PUSHBACK CLRNC. DURING THE TIME WHILE HE WAS IN CONTACT WITH GND CTL; I WAS CALLED ON THE INTERPHONE BY OUR GND PERSONNEL. THEREFORE I MISSED MOST OF THE GND CTLRS INSTRUCTIONS AND ALL I HEARD WAS 'CALL READY TO TAXI.' I ASKED MY F/O WHAT GND HAD SAID AND HE SAID GND SAID; 'CLR TO PUSHBACK AND CALL READY TO TAXI.' AT THE FINISH OF PUSHBACK WE CALLED GND CTL READY FOR TAXI. AT THAT POINT GND QUESTIONED OUR POS AND SAID THAT HE DIDN'T KNOW THAT HE HAD CLRED US TO PUSH ONTO A RWY. AT THAT POINT HE CLRED US TO TAXI AND NOTHING FURTHER WAS SAID. I NOTIFIED THE COMPANY AND THE CHIEF PLT CALLED THE TWR THAT MORNING. THE CHIEF PLT CALLED ME AND SAID THAT THERE WAS A COM BREAKDOWN SOMEWHERE AND THAT THE PROB WAS BEING ADDRESSED. HE ALSO INFORMED ME THAT THE GND CTLR HAD BEEN OFF DUTY PRIOR TO THAT NIGHT(S) AND WAS NOT INFORMED AS TO OUR PUSHBACK PROC OR REQUIREMENTS. AT THIS TIME THE TWR SAID THAT THEY WERE NOT PLANNING TO TAKE ANY ACTION.