Abstract-Peak-to-average power-ratio reduction for OFDM systems is investigated in a probabilistic framework. A new constellation extension technique is developed whereby the data for each subcarrier are represented either by points in the original constellation or by extended points. In this paper, the analysis ofDiscrete Hartley Transform (DHT)precoded OFDM systemusing M-QAM (where M=16, 32, 64, 256) is performed. An optimal representation of the OFDM signal is achieved by using a de-randomization algorithm where the conditional probability involved is handled by using the Chernoff bound and the evaluation of the many hyperbolic cosine functions involved is replaced by a tight upper bound. The simulation results are based on DHT precoded OFDM system with DFT precoded OFDM system, Walsh Hadamard Transform (WHT) precoded OFDM system, Selected Mapping (SLM) based OFDM system and OFDM conventional. Simulation results show that the PAPR of DHT precoded OFDM system is lower than WHT precoded OFDM system, SLM-OFDM system and OFDM conventional and the work is even compared with De-randomization for number of rotation(R).