What was found
(CAN) ENROUTE, AFTER DEPARTURE, ADVISED THAT THEY HAVE ENCOUNTERED LDG GEAR INOPERATIVE CAUTION LIGHT AND NOSE GEAR DOOR OPEN, AMBER DOOR INDICATION, ILLUMINATED. FLIGHT CREW COMPLETED THEIR CHECK LIST AND RETURNED TO DEPARTURE AND ACFT WAS REMOVED FROM SERVICE. AFTER EXHAUSTIVE TROUBLESHOOTING IT WAS DISCOVER THAT THE CULPRIT WAS THE NDRCL PROXIMITY SENSOR. FAULTY PROXIMITY SENSOR, NDRCL, REPLACED, GROUND CHECK ACCOMPLISHED SATISFACTORY. ACFT RETURNED TO SERVICE.