Amplitude and Sign Adjustment for Peak-to-Average-Power Reduction

In this letter, we propose a method to reduce the peak-to-mean-envelope-power ratio (PMEPR) of multicarrier signals by modifying the constellation. For$M$-ary phase-shift keying constellations, we minimize the maximum of the multicarrier signal over the sign and amplitude of each subcarrier. In order to find an efficient solution to the aforementioned nonconvex optimization problem, we present a suboptimal solution by first optimizing over the signs, and then optimizing over the amplitudes given the signs. We prove that the minimization of the maximum of a continuous multicarrier signal over the amplitude of each subcarrier can be written as a convex optimization problem with linear matrix inequality constraints. We also generalize the idea to other constellations such as 16-quadrature amplitude modulation. Simulation results show that by an average power increase of 0.21 dB, and not sending information over the sign of each subcarrier, PMEPR can be decreased by 5.1 dB for a system with 128 subcarriers.