Orthogonal Frequency Division Multiplexing (OFDM) is chosen as a multiplexing technique and broadly used in today's radiocommunication environments to overcome spectrum insufficiency. In current OFDM applications, the IDFT/DFT algorithms are used for modulation and demodulation, efficiently implemented using the IFFT/FTT. The IFFT and FFT are some of the main components of OFDM systems, requiring intensive computation, especially for a high number of sub-channels. Reducing the computational burden of the IFFT/FFT would offer an advantage in reducing the total OFDM system complexity. In this proposed system, the idea of implementing the very fast Fourier transform (VFFT) in OFDM (later, it is called G-OFDM) is based on a trade-off between performance and complexity. The implementation complexity of G-OFDM is lower than OFDM. However, there is a performance cost. G-OFDM has been studied both analytically and in simulation over the AWGN channel. In particular, performance is marred by the non-uniformity of SNR among sub-carriers. In this study, it was proposed two G-OFDM variants called G1-OFDM and G2-OFDM. G1-OFM is the least complex among all G-OFDM scenarios but gives the worst performance, while G2-OFDM gives the best performance but is the most complex. The results show that the performance of G-OFDM and its variants can be improved through the application of different values of n-quantization levels. In other words, using n-quantization levels, we can decrease the processing loss of the G system.