Light Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Airport; Environment - Non Weather Related
During cruise; at our assigned altitude of FL200; Denver ARTCC asked us what type of approach we wanted to execute for landing at AEJ. We requested an RNAV (GPS) approach to Runway 33. ATC cleared us to KANON direct to destination airport. We received a frequency change to 119.85 Denver ARTCC. After establishing communications on the new frequency; we received a clearance to descend to 16;400 feet. I then established visual contact of the arrival airport.  While descending through FL180; ATC informed us that radar contact was lost on our flight. While descending through 17;900 feet; we started having difficulty hearing transmissions from ATC on our radio. We asked for an approach clearance in the blind.  Denver ARTCC replied; 'You're on a visual approach; why do you need an approach clearance.'I interrupted their reply as to having a visual approach clearance. I set up the automation of the aircraft to commence the approach. During the descent; communications with ATC was very poor. Therefore; we received broken messages with another aircraft on the frequency. We then heard a broken and weak communications between Denver ARTCC and aircraft to relay to us we were 1;000 feet below assigned altitude. I stopped the descent at 15;400 feet and started a climb back to 16;400 feet. At 15;800 feet; we heard another poor transmission between Denver ARTCC and the aircraft; to relay to us that we were cleared for an approach to AEJ. I re-established the aircraft on the RNAV (GPS) approach to runway 33. After landing; we canceled our IFR flight plan by telephone.
[Report narrative contained no additional information.]
Turbojet flight crew reported encountering communications difficulties with Center while approaching a mountainous terrain airport.