LGT MISSED A DESCENT CLRNC AND CTLR LATER HAD TO HAVE ACFT EXPEDITE DESCENT FOR SEPARATION.

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F/O ON THE FLT; I WAS FLYING THE ACFT. CENTER CLRED US TO DESCENDED FROM FL390 TO FL290 (NO RESTRICTIONS). WHILE CAPT WAS MAKING A PAX ANNOUNCEMENT; I LEVELED OFF AT FL290. SHORTLY AFTER; A XMISSION BY CENTER WAS TOTALLY BLOCKED BY OTHER ACFT. NONE OF IT WAS LEGIBLE. THINKING THAT IT MIGHT BE FOR US; I STATED OVER THE RADIO: 'YOU WERE BLOCKED.' (SILENCE.) OTHER ACFT ON THE FREQ: 'YOU WERE STEPPED ON.' (DEAD SILENCE.) 2-3 MINS LATER CENTER CALLED US ASKING WHAT ALT WE WERE DSNDING THROUGH. CAPT ANSWERED: 'WE ARE LEVEL AT FL290.' CENTER: 'DESCENDED TO FL240; EXPEDITE THROUGH 270.' NOTHING ELSE WAS SAID; WE COMPLIED. AFTER ENTERING OPS AT DETROIT ARPT; AGENT ADVISED ATC WAS ON THE PHONE AND WANTED TO TALK TO CAPT ABOUT POSSIBLE TFC CONFLICT OVER DRYER VOR; AND WANTED OUR VERSION OF THE FACTS. ATC CALLED US LATER THAT NIGHT AND SAID THAT AFTER LISTENING TO THE TAPES; THEY WOULD NOT PURSUE THE MATTER ANY FURTHER. CONCLUSION: ATC WAS BLOCKED BY OTHER ACFT XMITTING AT THE SAME TIME; WAS ADVISED TWICE OF THE FACT; BUT NEVER REPEATED THE CLRNC. THINKING THAT IT MIGHT BE FOR US; I SHOULD HAVE INSISTED THAT ATC REPEAT LAST XMISSION OR STATE: 'DISREGARD.' THE FACT THAT 2 ACFT ADVISED OF XMISSION BLOCKAGE WAS NOT ENOUGH. SUPPLEMENTAL INFO FROM ACN 82165: APPARENTLY THE CTLR ISSUED A CLRNC FOR US TO CROSS DRYER AT FL240. NEVER HAVING RECEIVED THE CLRNC; AND NEVER HAVING READ BACK ANY CLRNC; WE REMAINED AT FL290. THE BLOCKED XMISSION MAY HAVE BEEN DIRECTED AT US; BUT THE CTLR NEVER REPEATED HIMSELF EVEN AFTER 2 ACFT RPTED THE XMISSION BLOCKED. ALSO; AFTER BEING TOLD TO EXPEDITE THROUGH FL270; WE WERE NEVER TOLD OF ANY TFC CONFLICT WHILE IN THE AIR.