Many wireless channel behavior exhibits approximate sparse modeling in time domain, therefore compressive sensing (CS) approaches are applied for more accurate wireless channel estimation than traditional least squares approach. However, the CS approach is not applied for multicarrier data information recovery because the transmitted symbol can be sparse neither in time domain nor in frequency domain. In this paper, a new Sparse Frequency Division Multiplexing (SFDM) approach is suggested to generate sparse multicarrier mapping in frequency domain based on the huge combinatorial domain. The subcarriers will be mapped in sparse manner according to data stream for taking advantages of multicarrier modulation with lower number of subcarriers. The number of activated subcarriers is designed to achieve the same as Orthogonal Frequency–Division Multiplexing data rate under lower signal-to-noise ratio. The proposed approach exploits the double sparsity of data symbol in the frequency domain, and channel sparsity in the time domain. The same CS approach for both data recovery and adaptive channel estimation in a unified sparsely manner is used. The suggested framework can be used with any non-orthogonal waveform shaping and can work efficiently without any prior information about neither the channel sparsity order nor searching for the optimum pilot patterns.