Citation X (C750)
Communication Breakdown; Confusion
Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew FLC complied w / Automation / Advisory
Procedure
While descending...we were talking to Approach. They descended us to 3;000 on a downwind leg 5 miles from ZZZ. They gave us a heading of 340 to pick up the visual. The frequency was very congested. After being on the 340 heading past the airport approximately 6 miles; ATC told us to turn heading 160 to the airport and this is where I thought I heard him say cleared for visual. I proceeded to configure the aircraft for landing and started my descent for the visual approach since we had the airport in sight. I proceeded to intercept the RNAV final and was following the VGP info; when ATC told us to check altitude and that we were assigned 3;000 feet. The non-flying pilot stated that we had the airport in sight and wanted to cancel IFR. ATC told us to squawk 1200 and switch to Unicom.I believe the congested frequency had to do with the confusion of our clearance. I should have asked for vectors to the RNAV approach.
I called ATC to notify them we now had the field in sight; but it took a few moments to get through due to the frequency congestion. ATC issued a 'Low Altitude Alert' and stated that our cleared altitude was 3;000 feet. I responded with; 'Field in sight' at which time ATC stated; 'Cleared for the visual approach.' Altitude deviation was approximately 300 feet.
After ATC issued a turn toward the airport; a C750 flight crew descended from assigned altitude thinking they were cleared for a visual approach.