Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 85; Flight Crew Total 1900; Flight Crew Type 400
Communication Breakdown; Time Pressure; Confusion; Workload
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action; Flight Crew Returned To Clearance; Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory
Human Factors
After our descent via the STAR; we were following vectors into ZZZ; we departed ZZZZZ Intersection perhaps on a heading of 290 or 300; at one point we basically paralleled the airway 20 miles at 3000 ft southwest from the ZZZ VOR.At that point after following various vectors; and listening the controller yell at another aircraft using the words 'turn immediately'; a heading of 360 was given to us; which I remember complaining to my First Officer; telling him  'that heading will put us more to the north and away from ZZZ'; also on the path of departing traffic from a nearby airport; my first officer tried to confirmed the heading but due to other radio clutter and other transitions was not able to confirm it; by then we heard the words 'Aircraft X turn Immediately to 180' our TCASII gave us a Traffic advisory followed by an Resolution advisory which I follow descending from  3000 to 2300 approximately. At that point I saw a Saab 340 going above us less than one mile; we reported the traffic in sight; no abrupt maneuvers were necessary; we were clear to climb back to 3000; never made it to a heading of 360; the TCASII went off before then. Following this incident several more TA on the TCASII were noted before landing in ZZZ. Later; after landing and during the flight debrief; it was noted that perhaps the intended heading given by the ATC controller was 260; the confusion between 260 and 360 was the contributing factor causing the incident. To this day we are not 100% sure; only that is the more logical heading. Radio clutter made more difficult to confirm the instructions. We were handed over to the next controller and landed at ZZZ; we were never advised of a possible violation by any of the controllers. After this event; we did some training on ADM and CRM; to help us prevent any events like this from happening again; personally we will confirm and altitudes and heading change by both pilots.
Due to a radio clutter issue the flight crew misunderstood an assigned heading clearance in a high density terminal environment. The erroneous heading resulted in an airborne conflict which generated a TA and RA event. The aircraft was then assigned an immediate heading to exit the traffic threat area and landed uneventfully.