Spectral Properties of Clipping Noise

One serious disadvantage of any multicarrier-modulation technique such as orthogonal frequency division multiplexing (OFDM) is its high peak-to-average-power ratio (PAPR) which might lead to signal clipping in several scenarios. To maximize the transmit data rate, it is important to take this non-linear distortion into account. The most common approach is based on the Bussgang theorem, which splits the distortion in a correlated part, represented by a linear damping factor, and uncorrelated additive noise. However, there are two aspects that are not correctly considered by the Bussgang theorem. Firstly, clipping noise shows a frequency-dependent power spectrum which depends on the clipping probability. Secondly, some of the clipping noise power is located outside of the transmission bandwidth, so that it does not influence the transmission quality. In this work, the Bussgang theorem is reviewed in detail and the exact power spectral density of the uncorrelated clipping noise is approximated to determine the signal-to-noise power ratio on every subcarrier separately. Although it is shown that the frequency dependence within the transmission bandwidth is relatively small, at least 36% of the uncorrelated noise power, depending on the clipping level, lays outside of the transmission band. Monte Carlo simulations validate that a simple expression for the power spectral density allows to calculate the symbol error probability of an OFDM transmission system that suffers from clipping. Furthermore, the newly found result can be used to optimize bit allocation tables in bit loading algorithms or to calculate the channel capacity.