Spectral Properties of Clipping Noise

Abstract

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.

Quantization Methods Based on Norms for Complex Gaussian-Like Signals in SDR Applications

“…We empirically deduce that the EVM of the quantized and clipped oversampled signal can be obtained from the EVM of the signal sampled at Nyquist rate by a shift of about -5 dB. The reason of the performance improvement achieved by the oversampled signal is due to the fact that the clipping and quantization noise spreads over the whole bandwidth [8], which corresponds to non-null subcarrier at Nyquist rate, but both null and non-null subcarrier if OSR > 1. The noise power per subcarrier is then reduced for oversampled signals.…”

“…The clipping noise based on the usual method has been largely studied in the literature and well reviewed in [8]. Thus, assuming that the real and imaginary parts of W c k are i.i.d., and denoting by f n the standard normal distribution, then by using [8]-( 9) we obtain…”

PAPR Reduction Techniques Based on Chirp Selection for Single and Multi-User Orthogonal Chirp Division Multiplexing System

“…where |xn| 2 E{|xn| 2 } is the square modulus of the normalized signal. The main drawback of clipping is to induce non-linear distortions, which can be modeled as an additional white Gaussian noise [24]. The method hereby presented aims at reducing based on the maximum likelihood criterion is hereby presented.…”

Quantization Methods Based on Norms for Complex Gaussian-Like Signals in SDR Applications

“…However, it is worth indicating that papers like [5,6] consider the complex amplitude of the signal, whereas [7][8][9] consider the amplitude of the real or imaginary part of the signal. Numerous papers and overviews deal with the errors generated by quantization [10], clipping [5][6][7][8][9], or both [11]. However, most of the papers consider the usual quantization and clipping method applied to inphase and quadrature components separately.…”

“…Note that the clipping is a well known method in OFDM as it is is applied to reduce the peak to average power ratio (PAPR) of the signal [5,6]. However, it is worth indicating that papers like [5,6] consider the complex amplitude of the signal, whereas [7][8][9] consider the amplitude of the real or imaginary part of the signal. Numerous papers and overviews deal with the errors generated by quantization [10], clipping [5][6][7][8][9], or both [11].…”