An analytical solution of the peak to average power ratio problem in orthogonal frequency division multiplexing modulation

This paper deals with the peak-to-average-power-ratio (PAPR) issue, which typically affects the digital transmission on power line communication (PLC) systems. In these systems, the power line is exploited as a communication multicarriers channel, where the sub-channels are made mutually independent by using orthogonal frequencies (orthogonal frequency division multiplexing or OFDM). Each component carries a string of bits associated with both amplitude and phase, which then represents the routed information. On the other hand, depending on the phases of the sub-carriers, the OFDM signal which has to be transmitted could present high instantaneous peaks. These peaks could saturate the transmitting amplifiers, modifying the shape of the OFDM symbol and then affecting its information content. Furthermore, such spikes give rise to electromagnetic compatibility issues for the electric devices. In this paper, the selected mapping (SLM) method is applied to mitigate the PAPR phenomenon. This method consists in shifting the phases of the components in order to minimize the amplitude of the peaks. The determination of the optimal set of phase shifts is a very complex problem, so that the SLM approaches proposed in the literature all resort to iterative algorithms to solve it. On the other hand, as this calculation has to be performed online, both the computational cost and the effect on the bit error rate (BER) cannot be established a priori. In this paper, an analytical approach is presented and its performance is evaluated for the case study of a PLC system implemented in a train locomotive.