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Purpose The tremendous growth of wireless applications and the demand for high data rate, the spectrum utilization improvement has been the most crucial challenges for wireless communication. Adapting cognitive radio with orthogonal frequency division multiplexing or offset quadrature amplitude modulation (OFDM/OQAM) improves the spectrum and energy efficiencies. Design/methodology/approach Thus, it overcomes the spectral leakage problem at the transmitter side and leads to less interference from secondary user (SUs) to primary user (PUs) and between the SUs in cognitive radio technology. The benefit of exploiting pulse shape filtering in the OFDM/OQAM is to not only eliminate the requirement of the guard bands but also reduce the out of band energy transmission, which also improves the spectral isolation from the neighboring systems. But the high peak to average power ratio (PAPR) phenomenon is a common issue in the majority of the multicarrier modulation systems and thus OFDM/OQAM is no exception in this case. Findings Therefore, this paper aims to examine the effect of integrating the Walsh–Hadamard Transform (WHT) on the power spectral density and investigates the problem of PAPR in the WHT/OQAM system. Originality/value Thus, it overcomes the spectral leakage problem at the transmitter side and leads to less interference from SUs to PUs and between the SUs in cognitive radio technology. The benefit of exploiting pulse shape filtering in the OFDM/OQAM is to not only eliminate the requirement of the guard bands but also reduce the out of band energy transmission, which also improves the spectral isolation from the neighboring systems. But the high PAPR phenomenon is a common issue in the majority of the multicarrier modulation systems thus OFDM/OQAM is no exception in this case.