I. Introduction
Orthogonal frequency division multiplexing (OFDM) systems have been extensively applied in wireless communication systems, e.g. Worldwide Interoperability for Microwave Access (WiMAX). OFDM systems have one major disadvantage, i.e. a very high Peak-to-Average Power Ratio (PAPR) at the transmitter [1]. When the OFDM signals with high PAPR are transmitted through a nonlinear device, such as a high-power amplifier (HPA) or a digital-to-analog converter (DAC), a high peak signal generates out-of-band energy and in-band distortion. These degradations would seriously affect the performance of OFDM systems. In order to reduce the PAPR of OFDM systems, methods [2]–[11] have been studied for a few years. They fall into two categories [2].