Closed-Form and Analytical BER Expression for OFDM System with μ-Law Companding Operation

The μ-law companding function has been applied widely in orthogonal frequency division multiplexing（OFDM） to reduce the peak-to-average power ratio（PAPR）. However, nonlinear distortion caused by the μ-law companding function is considered a key impairment in OFDM communication systems.Few studies have addressed theoretical nonlinear distortion caused by μ-law companding function for OFDM systems. In this paper,we derive a closed-form expression of signal distortion as well as the closed-form bit error rate（BER） of OFDM system caused by theμ-law companding function. Based on the theoretical signal distortion and BER expression,the theoretical BER value and signal distortion value can also be calculated, which can guide us to choose appropriate μ value for different BER condition and bit-to-noise（E;/N;） condition efficiently. Then the PAPR performance can also be predicted. The results show good agreement on the Monte-Carlo simulation results and the obtained theoretical BER results. Furthermore, based on theoretical signal distortion and theoretical BER expression, the figure of the relationship among BER value,E;/N;and μ is also given. Based on this figure,we can find the appropriate μ law for different BER and E;/N;condition. And then the PAPR performance can also be predicted.