A DHC-8 CAPT CONFUSED; 'PROCEED DIRECT TO THE RWY' WITH A CLRNC FOR THE VISUAL APCH AND BEGAN AN UNAUTH DSCNT.

Narrative

INBOUND TO SBP ARPT; WE WERE TOLD TO 'EXPECT VISUAL APCH TO RWY 29; MAINTAIN 5000 FT.' ZLA SECTOR 2 WAS ISSUING INSTRUCTIONS TO OUR FLT. WE RPTED ARPT IN SIGHT. LAX ADVISED US WE WERE '#3 FOR THE VISUAL; PROCEED DIRECT TO THE RWY.' WE SEARCHED FOR THE GA ACFT WE WERE TO FOLLOW. NO CONTACT MADE WITH TFC. OUR FLT NOW 7 MI FROM APCH END OF LNDG RWY. WE REQUESTED LOWER ALT. LAX STATED 'PROCEED DIRECT TO THE RWY.' AT THIS POINT; PF (RPTR) MISUNDERSTOOD THIS TO BE CLRNC FOR VISUAL APCH. FO DID NOT CHALLENGE THE DSCNT I INITIATED TOWARD TFC PATTERN ALT. DSNDING 400 FT BELOW ASSIGNED ALT; LAX QUERIED US AS TO OUR ALT. WE STATED OUR MISUNDERSTANDING OF VISUAL APCH CLRNC. LAX INSTRUCTED US TO MAINTAIN 4000 FT. REMAINER OF FLT UNEVENTFUL. MY WORKLOAD IN A NEW ACFT CONTRIBUTED TO THIS SIT. THIS WAS MY 5TH TRIP AFTER IOE COMPLETION AND FIRST INTO THIS ARPT. UPON LNDG; I SPOKE WITH LAX SECTOR 2 CTLR ON THE PHONE. HE INDICATED NO CONFLICTS WERE CREATED AND HIS CLRNC TO MAINTAIN 4000 FT RESOLVED ANY DEV PROBS. HE STATED HIS WORKLOAD WAS ALSO VERY HIGH AS 2 TWRS WERE TALKING TO HIM AT THE SAME TIME ALONG WITH HIS SEQUENCING DUTIES OF US INTO THE ARPT.