3 COMPANY ACFT WITH SIMILAR FLT NUMBERS WERE ON THE ARR INTO DTW AT THE SAME TIME. THE RPTING CREW WRONGLY DSNDED AFTER THEY HAD RECEIVED AND READ BACK A CLRNC THAT THEY THOUGHT WAS FOR THEIR AIRPLANE. THE FREQ CONGESTION AND CALL SIGN CONFUSION DURING THE INCIDENT HAS THIS DC9-40 CREW STILL WONDERING IF THE CTLR STATED THE WRONG NUMBER OR IF THEY HAD MISHEARD THE CLRNC.

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AT 21 NM; OUTBOUND FROM LFD VOR ON THE 127 DEG RADIAL ON THE MIZAR 2 ARR INTO DETROIT; CONFUSION OVER CALL SIGNS OCCURRED ON ATC CTR FREQ. NUMEROUS ACFT WERE BEING SEQUENCED FOR ARR; INCLUDING OUR CALL SIGN (ACR XABB) AND SIMILAR SOUNDING CALL SIGNS; COMPANY XACB AND COMPANY XADB. CTR ISSUED WHAT WE THOUGHT TO BE AN INSTRUCTION FOR COMPANY ACR XABB (US) TO DSND TO 12000 FT AND TURN TO A 30 DEG HDG. I ACKNOWLEDGED THE CALL; REPEATING THE INSTRUCTIONS. THE CAPT INITIATED THE DSCNT. WE BOTH REMARKED THAT A TURN TO 30 DEGS WAS NOT LOGICAL AT THAT POINT IN OUR RTE. I ASKED THE CTLR IF HE HAD GIVEN US A TURN TO 30 DEGS. HE STATED; 'NO YOU SHOULD BE ON COURSE.' I THEN ASKED IF HE HAD GIVEN US A DSCNT TO 12000 FT. HE RESPONDED; 'NO.' THE CAPT IMMEDIATELY RETURNED TO FL210. LOWEST ALT DURING THE EVENT WAS 20400 FT INDICATED ALT. NO CONFLICT EXISTED; AND THE CTLR APPARENTLY WAS NEVER AWARE THAT WE HAD BEEN OFF THE PREVIOUS ALT. THE CALL SIGNS XABB; XACB; AND XADB DO NOT LOOK PARTICULARLY SIMILAR ON PAPER; HOWEVER; WHEN STATED AS 'FOUR DIGIT SINGULAR NUMBERS PRONOUNCED IN FULL' ON A CROWDED FREQ; WITH STATIC AND ENVIRONMENTAL NOISE PRESENT; THE POTENTIAL FOR MISTAKEN XMISSIONS IS HIGH. WHEN SUCH SIMILAR CALL SIGNS ARE SCHEDULED INTO A CROWDED APCH CORRIDOR SIMULTANEOUSLY; THE POTENTIAL FOR CLRNC DEVS IS MAGNIFIED. SUPPLEMENTAL INFO FROM ACN 351103: THE HDG WAS NOT LOGICAL AT THIS POS ON THE ARR. NORMALLY IF ATC NEEDS SEPARATION AT THIS POINT THEY WILL SLOW THE ACFT AND VECTOR R OF COURSE. THIS ERROR WAS REALIZED; THERE WAS NO TFC ON TCASII; AND ATC MADE NO FURTHER COMMENT. I STILL AM NOT SURE WHETHER WE ANSWERED SOMEONE ELSE'S RADIO CALL AND ATC DID NOT CORRECT IT WITH THE READBACK OR IF ATC MISTAKENLY USED OUR CALL SIGN WHEN HE INTENDED THE CALL FOR ANOTHER ACFT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: DURING THE PREVIOUS MONTH AND A HALF; EVERY SINGLE TIME THAT THIS FLC WENT INTO DTW; THEY WERE MET WITH THIS SAME PROB. THIS RPTR AND FO WERE 'LABORIOUSLY' LISTENING; WHEN THIS INCIDENT OCCURRED. FREQ CONGESTION WAS SO GREAT THAT RPTR CAPT FEELS CERTAIN THE CTLR DID NOT HEAR THEIR READBACK OR SEE THEIR ACFT BEGIN A DSCNT.