Contents I. Introduction
As a promising technique, orthogonal frequency division multiplexing (OFDM) has been widely applied in modern wireless communications due to its high spectral efficiency and low susceptibility to the multipath propagation [1]. However, a major drawback of OFDM-based transmission systems is its high instantaneous peak-to-average power ratio (PAPR), which leads to undesired in-band distortion and out-of-band radiation if the linear range of the high power amplifier (HPA) is not sufficient [2], [3]. In an OFDM system with subcarriers, the complex baseband representation of OFDM signal is given by $$x(t)={1\over\sqrt{N}}\sum_{k=0}^{N-1}X_{k}\cdot e^{j{2\pi kt\over T}},\quad 0\leq t\leq T,\eqno{\hbox{(1)}}$$where and the vector denotes the frequency-domain OFDM symbols and is the symbol duration. Based on the central limit theorem, when is large, can be approximated as a complex Gaussian process; thus, it is possible that the maximum amplitude of OFDM signal may well exceed its average amplitude. To overcome this issue, various methods have been developed [4], among which, nonlinear companding transform (NCT) is an efficient solution in reducing the PAPR of OFDM signal. The concept of NCT was first introduced in [5], which used the -law companding and could significantly outperform the traditional clipping. Earlier NCT methods have primarily focused on designing the nonlinearity of the transfer curve [6], [7]. Later, the work of [8] first indicated the importance of exploiting the statistical characteristics of the OFDM signal. Up to now, several such NCT methods have been proposed, e.g. the exponential companding (EC) in [9], the uniform companding (UC) in [10], the piecewise companding (PC) in [11], and the trapezium or trapezoidal companding (TC) in [12] and [13], etc.
