RPTED LOSS OF SEPARATION WHEN FO OF ACR DC9 TAKES CLRNC FOR OTHER ACFT WITH SIMILAR CALL SIGN AND THE READBACK WITH CALL SIGN IS MISSED BY THE CTLR.

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ACFT #1 AND ACFT #2 ON PARALLEL NBOUND HEADING FOR SEQUENCING OVER ARR FIX TO THE E. ACFT #1 AT FL190 N AND W OF ACFT #2 AT 17000 FT. CALL SIGNS ARE SIMILAR AND PLTS ARE AWARE OF EACH OTHER. ACFT #2 ISSUED R TURN TO E HEADING AND DSCNT TO 14000 FT. CLRNC TAKEN BY ACFT #1. INCORRECT CALL SIGN MISSED IN READBACK. ACFT #1 TURNED TOWARDS AND DSNDED THROUGH ACFT #2; WHO NEVER ALTERED HEADING OR ALT. THE INSTALLATION OF DATA LINK TO DISPLAY THE ALT SET IN ACFT AUTOPLT ON CTLR DATA BLOCK COULD ELIMINATE THIS AND MOST OTHER READBACK/HEARBACK ERRORS. SUPPLEMENTAL INFO FROM ACN 392664: AT THAT TIME THE LEAD FLT ATTENDANT OPENED THE DOOR TO ASK QUESTION. WHILE I WAS MOMENTARILY ANSWERING FLT ATTENDANT; THE FO RECEIVED AN ATC CLRNC. WHEN I TURNED MY ATTN BACK TO FLYING THE FO ADVISED ME WE WERE CLRED TO 14000 FT AND TURN TO 090 DEGS AND INTERCEPT THE CRL 246 DEG; MIZAR ARR. WHILE HE WAS OFF ATC REQUESTED MY ALT. I RESPONDED; 16900 FT. ATC ADVISED US TO CLB TO FL180 AND TURN TO 360 DEGS. THE SAME TIME WE OBSERVED TFC AT 1 O'CLOCK POS; 3 MI AND 200 FT ABOVE US. THE FO ADVISED ME THAT ATC'S ORIGINAL CLRNC WAS PARTIALLY BLOCKED DUE TO THE VERY CONGESTED FREQ. HE HEARD ACR XA. WHEN HE RESPONDED TO ATC TO DSND TO 14000 FT AND TURN HE INCLUDED OUR CALL SIGN ACR XXXA. ATC RESPONDED; ROGER; RESUME NORMAL SPD. FO; RESPONDED ROGER; NORMAL SPD ACR XXXA. SUPPLEMENTAL INFO FROM ACN 392451: I HEARD A PARTIALLY COVERED CALL SIGN ENDING IN XA. OUR CALL SIGN WAS XXXA. THE RADIO CALLS WENT SOMETHING LIKE THIS: ATC: ACR ??XA TURN R TO 090 DEGS DSND AND MAINTAIN 14000 FT; INTERCEPT THE CRL 246 DEG RADIAL INBOUND; EXPECT MIZAR AT 12 AND 250. ME: I PAUSED A FEW SECONDS THEN REPLIED: UNDERSTAND R TO 090 DEGS; INTERCEPT THE ARR; DSND TO 14000 FT; WE'RE ALREADY AT 250 KTS; ACR XXXA. ATC: ROGER; RESUME NORMAL AIRSPD; EXPECT MIZAR AT 12 AND 250. ME: NORMAL AIRSPD ACR XXXA. ATC: EXPECT MIZAR AT 12 AND 250. ME: ROGER. FACTORS: CAPT DISTRACTED WITH OTHER DUTIES (NO BACKUP FOR ME). RADIO CONGESTION PARTIALLY COVERING A CALL SIGN. SIMILAR CALL SIGNS; THERE WAS ACR YYXA IN THE AREA. ME ACCEPTING THE CLRNC WITHOUT POSITIVELY INSISTING THAT ATC CONFIRM THE CALL WAS FOR US. ATC WAS VERY BUSY AND MOST LIKELY DID NOT CATCH MY CALL SIGN DURING THE READBACKS.