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A novel random phase updating algorithm for peak-to-average power ratio (PAPR) reduction of the OFDM signal is addressed. The phase of each subcarrier is updated by a random increment until the PAPR goes below a certain threshold level. The influence of different distributions for the phase increments and the variance of distributions on the mean and variance of PAPR, as well as the number of iterations to reach the threshold, are investigated. Further, the random phase updating algorithm has been extended by dynamically reducing the threshold level. After successful updating of the phase shifts, the threshold level is reduced and the variance of the phase increments is changed. Results of the simulations of the algorithms are provided. It is shown that the random phase updating algorithm with dynamic threshold gives the best results and can reduce the mean power variance of an 8-carrier OFDM signal with BPSK modulation, by a factor of 7 dB. In order to reduce the complexity, the random phase updating algorithm is investigated with quantization and grouping of the phase shifts. Results show that for a 16-carrier OFDM system, 2-level quantization of phase shifts in 8 groups of 2 carriers gives no significant increase in the power variance while reducing complexity.