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Power line noise is known to affect the performance of broadband power-line communications significantly. This paper presents a frequency-domain approach to characterize and model the statistical variation of power-line noise. The model considers both the background noise and the impulsive noise. The background noise model is based on statistical analysis of the results from two long-term measurements of noise spectrum conducted at two separate sites of a laboratory and a residential apartment. On the other hand, the impulsive noise model is obtained by direct measurements from the noise sources (i.e., various electrical household appliances). The amount of impulse noise reaching a power-line communications (PLC) receiver can then be determined with consideration of the channel transfer characteristics between the noise sources and the PLC receiver. Using these noise models, the performance of two major classes of digital modulation schemes, namely single-carrier modulation and multicarrier modulation, are analyzed and compared. It is found that the multicarrier scheme performs better than the single-carrier scheme when subjected to the observed power-line noise with non-Gaussian statistics.