Precoding for PAPR Reduction of OFDM Signals With Minimum Error Probability

The precoding technique is an effective and flexible way for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. However, different precoding schemes will increase error probabilities of the system. With the knowledge of the channel information and the receiver filter, we derive a necessary condition on the chosen precoding matrices for minimizing error probability of the OFDM system in the additive white Gaussian noise (AWGN) channel. A systematic procedure in designing such an optimal precoding matrix is provided. With a proper selection, the optimal precoding matrix can meet the requirements of PAPR reduction and achieve the minimum error probability in white Gaussian noise. Our simulation results show that the chosen precoding matrix notably outperforms other general precoding matrices in both AWGN and multipath fading channels. We also proved that the precoding matrix with all the singular values equal to 1 is one of the optimal solutions.