FLC OF AN AIRBUS A320 DSNDED BELOW ASSIGNED APCH ALT DUE TO REPLYING TO WRONG CALL SIGN. ATC CTLR SAID NOTHING WHEN THE CAPT READ BACK THE CLRNC.

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DURING ARR AT MONTEGO BAY; JAMAICA; COMS WITH SANGSTER APCH CTL WERE VERY DIFFICULT DUE TO THE HVY ACCENT OF THE JAMAICAN CTLR. WHILE AT 7000 FT MSL ON THE 12 DME ARC OF THE VOR DME APCH TO RWY 7; WE MISTAKENLY ACCEPTED AN APCH CLRNC APPARENTLY MEANT FOR ANOTHER ACFT AND BEGAN OUR DSCNT TOWARD THE PUBLISHED MINIMUM ALT ON THE ARC (3000 FT MSL). THE PNF READ BACK THE CLRNC AND RECEIVED NO RESPONSE FROM SANGSTER APCH. A RESPONSE WAS NEITHER EXPECTED NOR REQUIRED BY ICAO POLICY. LATER DURING THE APCH; SANGSTER APCH CTL ASKED OUR POS AND ALT. WHEN WE REPLIED THAT WE WERE DSNDING THROUGH 5500 FT MSL TOWARD 3000 FT MSL SANGSTER APCH CTL TOLD US THAT THE APCH CLRNC THAT WAS ISSUED ABOUT 2 MINS EARLIER WAS MEANT FOR ANOTHER ACFT AND THAT OUR LAST CLRNC WAS ONLY TO 7000 FT. THEN; SANGSTER APCH CLRED US FOR THE APCH AND WE LANDED UNEVENTFULLY. AS FAR AS I KNOW; MINIMUM SEPARATION FROM OTHER ACFT WAS NOT COMPROMISED. MORE FLUENCY IN ENGLISH AS WELL AS THE INSTALLATION OF A RADAR WOULD GREATLY HELP SANGSTER APCH CTL AVOID SIMILAR INCIDENTS.