Using the Douglas-Rachford Algorithm to Optimally Reduce the PAPR

Peak-to-Average Power Ratio (PAPR) is a major challenge to overcome when dealing with multi-carrier systems such as OFDM communication systems. We focus here on signals whose spectrum's amplitude respects a fix spectrum mask, as the ones used in Transform Domain Communication Systems. When previous literature only focused on the Projection Onto Convex Sets (POCS) algorithm to reduce the PAPR, we propose here to enhance it and to use the Douglas-Rachford algorithm. The convergence time is then drastically lower. Theory concerning the convergence property and experimental results are brought.