I. Introduction
Orthogonal Frequency Division Multiplexing (OFDM) is the mainstream of high-speed wireless communication because of some features such as high resistance to multi-path fading and high spectral efficiency. However, since OFDM is one of the multi-carrier modulation, an OFDM signal can have a very high peak-to-average power ratio (PAPR). High PAPR brings about signal distortion at a non-linear high power amplifier, which causes inter-symbol interference and out-of-band radiation. As a result, the deterioration of bit error rate (BER) occurs. In order to eliminate signal distortion, the amplifier at the transmitter must operate at the linear region, but it leads to degradation of the power efficiency. This problem leads to decreasing the uptime of battery-driven mobile terminals. PAPR reduction schemes are studied widely [1] [2], which are roughly divided into two groups, those causing signal distortion and those not. Clipping and Filtering (CAF) [3] is a simple solution to reduce the high PAPR, which clips high peaks exceeding a certain threshold before passing through the non-linear power amplifier. Nevertheless, BER degrades on account of deliberate signal distortion. As solutions without signal distortion, there are selective mapping (SLM) [4] and partial transmitted sequence (PTS) [5]. These solutions bring no deterioration of BER because they do not give deliberate signal distortion. In SLM and PTS, many OFDM signals are generated as candidates of the transmitted signal, and then the one with the minimum PAPR is transmitted. In PTS, a set of frequency-domain signals for OFDM is partitioned into disjoint groups called clusters and then inverse fast Fourier transform (IFFT) is performed for each cluster to generate its time-domain signal separately. A candidate is generated by summing the time-domain signals which are obtained from each cluster. At this time, each cluster is weighted by a phase rotating factor individually. By changing the phase rotating factor given to each cluster, numerous candidates are generated.