Power line communications is the use of power lines for the dual purpose of power transmission and data transmission. It is an emerging field of communication for the home area network of smart grid. Power line noise, namely background noise and impulsive noise, significantly affects the performance of power line communication systems. In this paper, we derive the condition for optimum detection of quadrature phase shift keying signals over Nakagami-m distributed additive background noise in power line communication system. The probability density function and the cumulative distribution function of the decision variables for the real part and imaginary part of the background noise are derived. We use the copula approach to model the dependence among the decision variables. The analytical average symbol error rate and average bit error rate of the PLC system is numerically computed. Simulations suggest that the proposed receiver performs significantly better than the existing suboptimal receiver. © 2015 IEEE.