Minimum Spanning Circle Method for Using Spare Subcarriers in PAPR Reduction of OFDM Systems

In orthogonal frequency division multiplexing (OFDM) systems, spare subcarriers are available due to low signal-to-noise ratio (SNR) in some subcarriers or fragments after resource scheduling. Utilizing these spare subcarriers to carry scrambling codes, the peak-to-average-power ratio (PAPR) of the system can be largely reduced without sacrificing bandwidth, with no in-band distortion or out-of-band radiation, but only with a little increase of signal transmission power. In this letter, we derive that the PAPR reduction problem using one spare subcarrier is equivalent to the well-known minimum spanning circle problem. Based on this concept, an approach called minimum spanning circle method (MSCM) is proposed to find the optimal scrambling codes. As validated in simulations, our method is effective, efficient, and simple to realize.