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Spectrum congestion problem is mainly caused by the inefficient spectrum usage. Cognitive radio (CR) and emerging soft decision CR (SDCR) have attracted wide interest as candidates to solve this problem. The former determines unused spectral regions and transmits overlay signals in these bands. The latter exploits both unused and occupied spectral regions simultaneously and dynamically adapts its spectra response according to time-varying environmental conditions. However, enabling waveforms of SDCR are sinusoidal signals and can not be separated from licensed signals completely. In this paper, we provide a novel waveform design method for CR based on the fractional Fourier transform. We first present a novel hybrid underlay/overlay waveform design method and then propose a system model for CR using the derived results. Moreover, theoretical analysis is also given. The validity of the theoretical derivations is demonstrated via simulations.