A novel spectrum sensing algorithm is proposed for environments characterized by symmetric Alpha-stable （SαS） noise， combining fractional low-order preprocessing with eigenvalue harmonic mean detection. The proposed algorithm employs the ratio of the difference between the maximum eigenvalue and the harmonic average of all eigenvalues to the minimum eigenvalue （DMHMM） as the test statistic. These eigenvalues are calculated from the sample covariance matrix of the received signal， which is preprocessed using fractional lower-order techniques. This algorithm reduces the impact of the non-Gaussian characteristics of SαS noise through fractional low-order operations in the preprocessing stage； and in the detection stage， it uses extreme eigenvalues and eigenvalue harmonic mean to design test statistic. The detection process of the proposed algorithm does not depend on SαS noise parameters and has a wide range of adaptability. On this basis， based on the moment theory of geometric mean of Wishart matrix eigenvalues and the asymptotic distribution theory of maximum and minimum eigenvalues in high-dimensional random matrices， an effective theoretical decision threshold calculation method is proposed for the proposed DMHMM algorithm. This method reduces the complexity of theoretical threshold calculation while improving the reliability of detection results of the primary user signal in SαS noise under non-asymptotic conditions. Monte Carlo simulation results show that the proposed DMHMM algorithm can obtain more reliable decision results than semi-blind DMGM algorithm， and does not require statistical parameters of SαS noise in the detection stage. Due to the comprehensive utilization of the extreme eigenvalues and the harmonic mean of all eigenvalues of the sampled covariance matrix after fractional low order preprocessing， the new algorithm can better reflect the changes in the primary user signal， resulting in high detection probabilities than the traditional MME and CHME algorithms.