This thesis presents a state-of-the-art review and brings new contributions to the waveform design for 5G systems in the presence of analog nonlinearities. A system model for the typical analog impairments at each stage of the transmitter and the receiver with a channel is first presented. The highlighted nonlinearities are power amplifier (PA), phase noise, and DC offset.In this thesis, the further development of the orthogonal frequency division multiplexing (OFDM) is considered since the evolutionary approach from the 4G to the 5G is assumed to be more mature for technology demonstrations. In particular, the constant envelope OFDM (CEOFDM) where phase modulation creates a constant envelope is studied, and the results indicate that CE-OFD...