Contents 1. Introduction
Orthogonal Frequency Division Multiplexing (OFDM) is a technique to send information over several orthogonal carriers in a parallel fashion. This system has been adopted in many standards thanks to its robustness against frequency selective channels and its optimal use of the bandwidth. However, the OFDM signal presents large amplitude variations compared to a single carrier signal, because it is the sum of many narrowband signals in the time domain with different amplitudes. Based on this fact, in-band and out-of-band distortions occur during the introduction of the signal into a non linear device, as the High Power Amplifier (HPA). To study these high amplitude fluctuations, the Peak-to-average Power Ratio (PAPR) has been defined. The PAPR is as a random variable, as the symbols arrive randomly at the modulation input. There are two ways to study this measure, one is based on the static approach that expresses the maximum of the PAPR as equal to the number of carriers [1], the other one analyzes the Complementary Cumulative Distribution Function (CCDF) of the PAPR [2], [3], [4]. In these studies, the PAPR has been defined over one OFDM symbol, and the derivation of its distribution is based on the observation of this single OFDM symbol. In our work in [5], a general distribution for the Generalized Waveforms for Multi-Carrier (GWMC) signal, based on the observation of several GWMC symbols, has been derived. In this paper, we first describe the GWMC system considered in our derivations in Section 2. In Section 3, we derive an upper bound of the PAPR for the GWMC signal. We show how the observation duration changes the PAPR behavior in Section 4.1. The infinite observation case is also presented and analyzed in Section 4.2. Finally, Section 5 concludes the paper.
