A Necessary Condition for Waveforms With Better PAPR Than OFDM

This paper establishes a necessary condition that must be satisfied by the modulation waveforms of any generalized waveforms for multicarrier (GWMC) system with better peak-to-average power ratio (PAPR) than conventional orthogonal frequency division multiplexing (OFDM). GWMC systems include in particular all classical multicarrier modulation systems. As a consequence, we show that OFDM has the best PAPR performance over all GWMC systems that do not satisfy this necessary condition. We also identify an infinite family of GWMC systems with the same PAPR performance as OFDM. To illustrate our results, we present the simulations of the PAPR behavior for different GWMC systems, including some with better PAPR performance than OFDM.