One of the major drawbacks of orthogonal frequency division multiplexing (OFDM) signals is the high peak to average power ratio (PAPR) of the transmitted signal. In this paper, a new method based on hexagonal constellation is proposed to reduce PAPR and to eliminate side information for OFDM signals. In order to get better PAPR reduction performance, we propose a new PAPR reduction algorithm based on parametric minimum cross entropy (PMCE). Simulation results show that PMCE algorithm is an efficient method to achieve significant PAPR reduction.