Assessing peak-to-average power ratios for communications applications

High peak-to-average ratio (PAR) is a significant drawback for orthogonal frequency division multiplexing (OFDM). Accordingly, many authors have proposed different PAR reduction methods that rely on different trade-offs. It is important to quantify the effectiveness of an individual PAR reduction method. The PAR at a certain probability level (10^-4, 10^-5, etc) has proven to be a popular but inconsistent metric. We propose to use the expected PAR, E[PAR], as a metric to compare the different PAR reduction methods, in this paper we derive a closed form expression for the E[PAR] for the selected mapping (SLM) approach. We also evaluate SLM in terms of its computational cost as characterized by the expected number of different phase mappings to be tried.