Distribution of envelope power using selected mapping in OFDM systems with nonlinearity

Selected mapping (SLM) techniques have been used to reduce the high peak-to-average power ratio (PAR) in Orthogonal Frequency Division Multiplexing (OFDM) systems. The capacity of PAR reduction can be increased by improving the PAR statistics at the cost of complexity of the OFDM transmitter. However, it is difficult to clarify the performance degradation in the presence of nonlinearities, such as a power amplifier (PA), with the PAR metric because the statistical distribution of PAR focuses only on the highest peak, even though PAR reduction can help to reduce the required PA backoff. The nonlinear distortion is related to the amount of signal greater than the saturated threshold value; therefore, it is desirable to know the envelope power distribution. In this paper, we derive a closed form expression for the envelope power distribution in SLM/OFDM systems with nonlinearity, and verify the derived expression with simulation results.