On the Properties of Cubic Metric for OFDM Signals

As a metric for amplitude fluctuation of orthogonal frequency division multiplexing (OFDM) signal, cubic metric (CM) has received an increasing attention because it is more closely related to the distortion induced by nonlinear devices than the well-known peak-to-average power ratio (PAPR). In this letter, the properties of CM of OFDM signal is investigated. First, asymptotic distribution of CM is derived. Second, it is verified that 1.7 times oversampling rate is good enough to capture the CM of continuous OFDM signals in terms of mean square error, which is also practically meaningful because the fast Fourier transform size is typically 1.7 times larger than the nominal bandwidth in the long-term evolution (LTE) cellular communication systems.

I. Introduction

Orthogonal frequency division multiplexing (OFDM) signals suffer from high amplitude fluctuation which causes performance degradation due to nonlinear devices. A well-known metric for amplitude fluctuation of OFDM signal is peak-to-average power ratio (PAPR). Many research efforts have been carried out to find efficient PAPR reduction techniques [1]. Also, the distribution of the PAPR of continuous OFDM signals was derived [2] [3] and it is widely accepted that four times oversampling is good enough to capture the PAPR of continuous OFDM signals [4]. However, there are research results showing that PAPR may not be the best metric to measure the magnitude of the envelope fluctuations. For example, Bento et al. [5] pointed out the dependency of PAPR and the number of subcarriers.