In this paper, we present our study on the Peak-to-Average Power Ratio (PAPR) of precoding-based Orthogonal Frequency Division Multiplexing (OFDM) systems. We analyze the probability density functions of various types of precoded OFDM signals. Then we show that the precoders can change the statistical properties of OFDM signals and hence the distribution of PAPR. We further compare the PAPR reduction performance of the precoded OFDM systems and show that these systems can have PAPR up to 4.5 dB lower than the conventional OFDM system. ©2007 IEEE.