A TRACON Controller reported an aircraft turned to the wrong heading and flew below the Minimum Vectoring Altitude. The course deviation placed the aircraft in an area of poor radio coverage where ATC could not communicate with them.

Narrative

I was working the arrival rush ILS approaches to Runway XXL. I had numerous aircraft being vectored for the ILS. ZZZ1 [Center] gave me 4 aircraft inbound from the west. This is not unusual for evening arrivals. I had to break Aircraft X off the approach for compression on final. I canceled the approach clearance and issued a left turn heading 010 maintain six thousand. The aircraft looked like they were making a right turn. The pilot asked what heading I gave him. I told him that it looked like he was in a right turn and issued a heading of 190. I had Aircraft Y at seven thousand on the right downwind. I then issued a heading of 250 to Aircraft X to allow for final spacing then a turn of 280 degrees. I turned Aircraft Y to 070 heading and had them join the LOC. I then issued a 010 heading to Aircraft X. They were east of the 062 MVA. Aircraft X did not respond I attempted to establish communications with Aircraft X. Both approach frequencies; guard frequency; and also broadcasted in the blind for Aircraft X to ident if he could hear me. I also broadcasted climb immediately in the blind for Aircraft X. The Tower Supervisor suggested I have Aircraft Y relay for me. I had Aircraft Y [reach] out to Aircraft X. Aircraft Y could communicate with Aircraft X I instructed Aircraft X to climb and maintain 080 and fly northbound away from higher terrain. Once Aircraft X reached 080 they could communicate with me. I vectored them back to the localizer and cleared them for the approach. We have a known communication limitation to the south west of ZZZ. It usually does not affect aircraft within 30 miles of the airport. In this incident I believe there may be an issue with our communication equipment.