Fifth generation (5G) wireless technology is a new wireless communication system that must meet different complementary needs: the high data rate for mobile services, low energy consumption and long-range for connected objects, low latency to ensure real-time communication for critical applications and, high spectral efficiency to improve the overall system capacity. The waveforms and associated signal processing present a real challenge in the implementation of each generation of wireless communication networks. Different research works have discussed this topic; but, these works are limited to the Filter-Bank Multi-Carrier (FBMC), Universal Filtered Multi-Carrier (UFMC), and Filtered Orthogonal Frequency-Division Multiplexing (F-OFDM) waveforms. In this work, we review the technical basics of the physical layer for the LTE system which uses, OFDM modulation for the downlink and the single carrier frequency division multiple access (SC-FDMA) technique for the uplink. Besides, this paper presents the diverse waveforms candidate for 5G systems, including, FBMC, UFMC, and F-OFDM, and compares these techniques with Constant Envelope-OFDM (CE-OFDM), which is an advantageous form regarding power consumption, especially for battery-powered devices. Simulations are carried out to compare the performance of the OFDM, CE-OFDM, F-OFDM, UFMC, and FBMC in terms of power spectral density (PSD) and Bit Error Rate (BER). It has been demonstrated that (CE-OFDM) constitutes a more efficient solution in terms of energy consumption than the other technics. By comparison with the other technics, the CE-OFDM scheme performances, in terms of BER and PSD, are controllable by the values of its parameters (M, h, and J). This advantage gives designers of the system to consider the mutual choice between spectral efficiency and the BER. Moreover, the (F-OFDM), (UFMC), and (FBMC) schemes could constitute a more efficient solution in terms of power spectral density. It can be concluded from this paper that CE-OFDM wave form gives the best performance in terms of power consumption by reducing the Peak to Average Power Ratio (PAPR) associated with the OFDM system and FBMC is an efficiency technique to reduce the inter-carrier interference (ICI).