-Power line communication (PLC) technology is used in various areas of a smart grid. The extensive use of PLC technology has proved its key role in smart grids throughout the world. Despite PLC's advantages, it suffers from a difficulty in modeling and analysis of its power line channel. Many researchers have experimented and proposed channel models for their own defined environments; as a result, a unified model for the power line has not been presented. To overcome this problem partially, we used a Nakagami-m distribution like background noise and analyzed the performance of the binary transmission system in our previous work. In this paper, we compare the analytical and simulated BER (bit error rate) performances of QPSK (quadrature phase shift keying) transmission system with Gray encoding. We verify that the analyzed and simulated performances are well matched for different values of m.