In this paper, we propose the use of Spectrally Efficient Frequency Division Multiplexing (SEFDM) with additional techniques such as Frequency Domain Cyclic Prefix (FDCP) and Modified Non-Linear (MNL) acceleration for efficient handling of the impact of delay and Doppler shift in mobile communication channels. Our approach exhibits superior performance and spectral efficiency in comparison to traditional communication systems, while maintaining low computational cost. We study a model of the SEFDM communication system and investigate the impact of MNL acceleration with soft and hard decision Inverse System on the performance of SEFDM detection in the AWGN channel. We also analyze the effectiveness of FDCP in compensating for the impact of Doppler shift, and report BER detection figures using Regularized Sphere Decoding in various simulation scenarios. Our simulations demonstrate that it is possible to achieve acceptable performance in Doppler channels while maintaining the superiority of SEFDM over OFDM in terms of spectral efficiency. The results suggest that our proposed approach can tackle the effects of delay and Doppler shift in mobile communication networks, guaranteeing dependable and high-quality communication even in extremely challenging environments.