AN LR31 PLT DEPARTING TEB RWY 1 DID NOT TURN TO THE ASSIGNED RADAR VECTOR HDG BECAUSE OF POOR RADIO CONTACT.

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ON A POSITIONING FLT DURING DAY VFR CONDITIONS FROM TEB; NJ; TO WHITE PLAINS; NY. WE DEP RWY 1 AT TEB ON THE SID AND WERE GIVEN VECTORS TO THE NE. THIS WAS A NON PAX LEG SO THE FO WAS FLYING THE ACFT AND I WAS HANDLING COMS AND NAV. WHEN INSTRUCTED TO CONTACT NY DEP WE DID SO AND EXPERIENCED DIFFICULTY IN HEARING AND UNDERSTANDING THE CTLR DUE TO WEAK AND BROKEN XMISSIONS; WE ADVISED THE CTLR OF THIS. WE WERE DIRECTED TO MAKE A R TURN TO WHAT I BELIEVED TO BE 180 DEGS WHICH I APPARENTLY MISUNDERSTOOD AND I DO NOT REMEMBER WHICH I ACKNOWLEDGED; 80 DEGS OR 180 DEGS. DURING THE TURN I DID ASK THE FO TO VERIFY HE ALSO UNDERSTOOD 180 DEGS WHICH HE ACKNOWLEDGED HE DID. DURING THE TURN WE WERE SWITCHED OVER TO THE NEXT CTLR WHO IMMEDIATELY INSTRUCTED US TO MAKE AN IMMEDIATE L TURN TO 360 DEGS BEFORE WE RE-ENTERED TEB'S AREA. WE COMPLIED WITH A HARD L TURN TO A HEADING OF 360 DEGS. THE CTLR THEN ADVISED US THAT WE HAD BEEN PREVIOUSLY ASSIGNED A HDG OF 080 DEGS AND WE HAD GONE THROUGH THAT HDG. DURING THIS BRIEF EXCURSION THROUGH OUR ASSIGNED HDG AND BACK TO A HDG OF 360 DEGS WE OBSERVED NO TFC CONFLICT AND RECEIVED NO TCAS ADVISORIES. THE FLT PROCEEDED FROM THIS POINT UNEVENTFULLY TO OUR LNDG IN WHITE PLAINS WITH NO FURTHER RADIO DIFFICULTIES. A MAINT SQUAWK ON THE NUMBER ONE RADIO HAS BEEN RPTED AND ENTERED INTO THE ACFT LOG. I FEEL CONTRIBUTING FACTORS INVOLVED IN THIS EVENT WERE BUSY RADIO TFC AT THAT TIME OF DAY; RADIO RECEPTIONS THAT WERE ALMOST UNREADABLE AND BROKEN AND NOT CLARIFYING WITH THE CTLR THE HDG ASSIGNMENT IF ANY DOUBT EXISTED. IT SHOULD BE NOTED THAT THIS ENTIRE EVENT TOOK PLACE WITHIN ABOUT FIFTEEN SECONDS DURING WHICH TIME I DID TUNE RADIO NUMBER TWO TO THE DEPARTURE FREQUENCY IN HOPES OF BETTER RECEPTION.