Orthogonal frequency division multiplexing (OFDM) has been investigated for the high-speed transmission of data in radio frequency and optical wireless communications. The OFDM systems usually experience high amplitude variations called peak-to-average power ratio (PAPR). The high PAPR makes non-linear distortion and performance degradation because of clipping the signal. To alleviate the high PAPR, we introduce a new technique based on the compressive sensing approach. In the offered method, the OFDM signal is compressed in the time domain and then transmitted. At the receiver, a G-LASSO (group least absolute shrinkage and selection operator) recovery algorithm is applied to reconstruct the original signal. The reconstruction accuracy of the suggested G-LASSO algorithm is compared with the original LASSO algorithm. Numerical results indicate the effectiveness of the offered approach in terms of PAPR reduction and bit error rate performance.
