Signal Classification Using a Peak-to-Average Power Ratio Statistic

This paper addresses signal classification based on an average power statistic for peak-to-average-power ratio (PAR) reduced signals. Specifically, it is assumed that either a QAM or a Complex Gaussian finite-length symbol is transmitted in a noisy, peak-limited channel with known peak power. The goal is determine the whether an uninformed receiver can distinguish between these signal types using an average power statistic. Several methods for transmitting through peak-power channels are examined including optimal clipping and piecewise linear scaling (PWLS) with selected mapping (SLM) PAR reduction. For the analysis, it is necessary to derive the mean power for each of the transmission methods. Accordingly, we show how the harmonic mean PAR, E[1/PAR], is related to the mean power and derive E[1/PAR] in closed form. We find that average power is a accurate discriminator for low-order QAM and Gaussian symbols. For high-order QAM, accurate discrimination is also possible when the noise level is sufficiently low or when enough signal samples are available.