Spectrum sensing methods and systems for detecting spectrum holes for use in cognitive radio secondary transmissions are disclosed. In one method, an indication of an assignment of a set of subcarriers to a primary user is received. The method further includes determining multitaper spectral estimates for at least a subset of the set of subcarriers based on the assignment of the set of subcarriers to the primary user by processing samples for the at least a subset of the set of subcarriers. In addition, a test statistic that is based on the multitaper spectral estimates is compared to a threshold to determine whether the set of subcarriers is utilized for primary transmissions to the primary user. Moreover, data signals are received on at least one of the subcarriers in the set of subcarriers if the set of subcarriers is not utilized for primary transmissions to the primary user.