This paper deals with an optimized software implementation of a narrowband power line modem. The modem is a node in Automatic Meter Reading (AMR) system compliant to IEC 61334-5-1 profile and operates in the CENELEC-A band. Because of the hostile communication environments of power line channel, a new design approach is carried out for an S-FSK demodulator capable of providing lower Bit Error Rate (BER) than standard specifications. The best compromise between efficiency and architecture complexity is investigated in this paper. Some implementation results are presented to show that a communication throughput of 9.6 kbps is reachable with the designed S-FSK modem.