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The performance of the orthogonal frequency-division-multiplexing (OFDM) system over the strictly peak power and band-limited channel is analyzed in terms of the required input back-off, bit-error rate (BER), and channel capacity on the assumption that the power amplifier is perfectly linearized. The peak-power limitation is implemented by linearly scaling the band-limited OFDM signal such that the maximum peak power of each OFDM symbol is always below the saturation level of the amplifier. The theoretical performance analysis requires the knowledge of the distribution of the peak power normalized by the symbol-wise (local) average power, referred to as symbol-wise peak-to-average power ratio (PAR) in the paper, and we also develop a method to numerically calculate its statistical distribution. The analysis of BER performance suggests that the linear scaling causes practically negligible degradation. Furthermore, the benefit of additional application of simple PAR reduction schemes, such as symbol selection and deliberate clipping and filtering, is also examined.