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In wireless communications, 3GPP LTE is one of the solutions to meet the greater transmission data rate demand. One issue inherent to this technology is the PAPR (Peak-to-Average Power Ratio) of OFDM (Orthogonal Frequency Division Multiplexing) modulation. This high PAPR affects of the efficiency of power amplifiers. One approach to mitigate this effect is the Crest Factor Reduction (CFR) technique. In this work we simulate the impact of Hard Limited Clipping Crest Factor Reduction technique on BER (Bit Error Rate) in OFDM based Systems. In general, the results showed CFR has more effect on higher digital modulation schemes, as expected. More importantly, we show the worst-case degradation due to CFR on QPSK, 16QAM, and 64QAM signals in a linear system. For example, hard clipping of 9dB results in a 2dB increase in signal to noise energy at a 1% BER for 64-QAM modulation.