Captain reported missing signage for Taxiway P at AUS airport contributed to a taxiway deviation.

Narrative

Upon landing and receiving taxi instructions; after I repeated the instructions to exit 18L at Mike; taxi to the ramp via Bravo and Papa; the Captain noted that had not heard the inbound radio call. We performed a quick mic check and discovered no side tone was passing into the Captains headset. I raised my voice significantly and repeated the taxi instructions. We exited at taxiway Mike and entered taxiway Bravo. We noted a service vehicle; which ATC had informed us would be present. We noted the sign; as we turned North on Bravo; We both noted there had been no sign for Papa. The Captain stopped the aircraft and I called Ground to inform them we had made a mistake and missed the turn at Papa. I sought permission to complete a 180 degree turn on Bravo. There were no other aircraft on or near Bravo. Our request was approved and we completed the turn at again looked for a Papa taxiway sign; there was none. We entered the ramp without incident. I should have been less focused on trouble shooting the audio issue for the Captains headset and noted that Papa was present as the only entrance to the ramp; as per the taxi diagram.