Closed-form and analytical BER expression for OFDM system with μ-law companding operation

Abstract

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 the μ-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 (Eb/No) 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, Eb/N0 and μ is also given. Based on this figure, we can find the appropriate μ law for different BER and Eb/N0 condition. And then the PAPR performance can also be predicted.