Some Statistical Properties of Multicarrier Signals and Related Measures

In this paper we study some statistical properties of a multicarrier signals using the order statistics. Analytical expressions for the probability density function of different order statistics of a sampled OFDM system is presented. We then find the amount of power which is clipped from each order of the signal when the signal is passed through a clipping nonlinearity. This is used to represent the relevance of peak-to-average power ratio (PAPR) to evaluate the effect of nonlinearity on the performance of a multicarrier system. The agreements between the theoretical results and the simulated ones demonstrate the validity of the analysis. We will also study different metrics for the signal envelope variations in terms of the sensitivity of each metric to amplitude nonlinearities. In the end the performance of an OFDM system with selected mapping based on different metrics is evaluated and compared with each other

I. Introduction

Due to its robustness against time dispersion in multipath fading channels, OFDM is one of the major candidates for many emerging high speed wireless data communication systems [1]–[3]. In an OFDM system the data is transmitted over a number of parallel frequency channels, each being modulated by a baseband QAM or PSK symbol. As a result the amplitude of such a signal can have very large fluctuations. This large amplitude variations is a big disadvantage of OFDM, which tends to reduce the power efficiency of the RF power amplifier. Since the amplifier is typically rather nonlinear for high input amplitudes, it may be necessary to decrease the input amplitude to reduce the distortion.