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The objective of this survey is to provide the readers and practitioners in the industry with a broader understanding of the high peak-to-average power ratio (PAPR) problem in orthogonal frequency division multiplexing (OFDM) systems and generate a taxonomy of the available solutions to mitigate the problem. Beginning with a description of OFDM systems, the survey describes the most commonly encountered impediment of OFDM systems, the PAPR problem and consequent impact on power amplifiers leading to nonlinear distortion. The survey clearly defines the metrics based on which the performance of PAPR reduction schemes can be evaluated. A taxonomy of PAPR reduction schemes classifies them into signal distortion, multiple signaling and probabilistic, and coding techniques with further classification within each category. We also provide complexity analyses for a few PAPR reduction methods to demonstrate the differences in complexity requirements between different methods. Moreover, the paper provides insights into the transmitted power constraint by showing the possibility of satisfying the constraint without added complexity by the use of companding transforms with suitably chosen companding parameters. The rapid growth in multimedia-based applications has triggered an insatiable thirst for high data rates and hence increased demand on OFDM-based wireless systems that can support high data rates and high mobility. As the data rates and mobility supported by the OFDM system increase, the number of subcarriers also increases, which in turn leads to high PAPR. As future OFDM-based systems may push the number of subcarriers up to meet the higher data rates and mobility demands, there will be also a need to mitigate the high PAPR that arises, which will likely spur new research activities. The authors believe that this survey will serve as a valuable pedagogical resource for understanding the current research contributions in the area of PAPR reduction in OFDM systems, the - ifferent techniques that are available for designers and their trade-offs towards developing more efficient and practical solutions, especially for future research in PAPR reduction schemes for high data rate OFDM systems.