Using Set Theoretic Estimation to Address the PAPR Problem of Spectrum-Constrained Signals

In the last decades, many solutions have been proposed to cope with high Peak-to-Average Power Ratio (PAPR) of OFDM communication systems. We focus here on signals whose spectrum's amplitude respects a fix spectrum mask. We first build a framework based on Set Theoretic Estimation that offers many tools to reduce the PAPR down to the 3dB lower bound. By means of this framework, we then propose new algorithms that address the PAPR problem with a convergence time drastically lower than any of the previously used algorithms. Relying on our framework, we give insights on how the algorithms succeed in performing better, both from a signal processing and an algebraic perspective.