Building on the ubiquity of electric power infrastructure, power line communications (PLC) has been successfully used in diverse application scenarios, including the smart grid and in-home broadband communications systems as well as industrial and home automation. However, the power line channel exhibits deleterious properties, one of which is its hostile noise environment. This article aims for providing a review of noise modeling and mitigation techniques in PLC. Specifically, a comprehensive review of representative noise models developed over the past fifty years is presented, including both the empirical models based on measurement campaigns and simplified mathematical models. Following this, we provide an extensive survey of the suite of noise mitigation schemes, categorizing them into mitigation at the transmitter as well as parametric and nonparametric techniques employed at the receiver. Furthermore, since the accuracy of channel estimation in PLC is affected by noise, we review the literature of joint noise mitigation and channel estimation solutions. Finally, a number of directions are outlined for future research on both noise modeling and mitigation in PLC. Index Terms-Power-line communications, background noise, impulsive noise, narrow-band interference, noise modeling and mitigation techniques. I. INTRODUCTION A. Power-Line Communications Power-line communications (PLC) has been considered as a means of data transmission since the late 19th century [1, Ch. 1]. Early applications include narrow-band voice and data communications over both medium-and high-voltage power lines for telemetry, telecontrol and teleprotection purposes, as the predecessors of to contemporary smart grid communications [2]-[6]. However, communications over power-lines have not received wider attention until the late 1990s [7], when both the telecommunications services and the electricity industry T. Bai, M. Elkashlan and A. Nallanathan are with the School of Electronic Engineering and Computer Science,
