UNAUTHORIZED RWY ENTRY BY ACR. PLTDEV.

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LNDG 4R AT EWR WE ROLLED OUT TO TAXIWAY K AND TURNED L. TWR INSTRUCTIONS WERE TO TURN L ON TAXIWAY PAPA. AS WE TAXIED ON K WE WERE UNABLE TO SEE LIGHTED TAXIWAY P OR SIGN INDICATING TAXIWAY P. AS WE APCHED 4L TWR CLRED US DOWN 22R TO GATE. IMMEDIATE ACTION SHOULD BE TAKEN TO IMPROVE VHF FAA RADIOS. PWR TRANSMISSIONS WERE WEAK AND FADED. IMMEDIATE ACTION SHOULD BE TAKEN TO PROPERLY LIGHT ALL TAXIWAYS AND INSTALL STANDARD LIGHTED TAXI AND RWY SIGNS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: CALLBACK MADE AS PART OF RWY INCURSION STUDY. RPTR CONFIRMED TYPE ACFT. CONFIRMED TAXIWAYS INVOLVED. RPTR THINKS THAT TWR GAVE L TURN ON TAXIWAY P LATE AND THEY MAY HAVE BEEN ALREADY PAST THAT TAXIWAY. DOES NOT RECALL SEEING ANY TAXIWAY P SIGNS. ACFT ON FINAL FOR RWY 4L WAS EITHER GIVEN A GAR OR SIDE STEP TO 4R. THERE WAS NO CRITICAL CONFLICT AND TWR CTLR TOLD THEM TO TAXI ON RWY 22R TO TAXIWAY G AND CLRED TO GATE. CLRNC TO TURN L ON P WAS XMITTED TO ACFT X WHILE THEY WERE ROLLING OUT ON 4R. CLRNC ACKNOWLEDGED BY FO. FAA RADIO QUALITY DID NOT AFFECT THEIR CLRNC RECEPTION; BUT OTHER ACFT WERE HAVING TROUBLE UNDERSTANDING TWR. RPTR SAYS HE DOES NOT COMMUNICATE WELL WITH FEMALE COPLTS AND THINKS A MALE COPLT MIGHT HAVE SPOKEN UP SOONER TO PREVENT RWY ENTRY. WANTS FAA TO GIVE ARPTS THE FUNDS TO INSTALL GOOD RED AND GREEN LIGHTING SYS FOR RWY ENTRY OR XING.