A new BDDEE （Blind Detector based on Difference of Extreme Eigenvalues） multi-antenna spectrum sensing algorithm based on the difference between the extreme eigenvalues of the received signal sample covariance matrix （SCM） is proposed. It uses the ratio of the difference between the maximum and minimum eigenvalues of the SCM and the average energy of the received signal as the sensing decision. The proposed BDDEE algorithm breaks away from the dependence on the noise variance in the detection process and does not need to use the relevant parameters such as the primary user signal and the wireless transmission channel. On this basis， using the results of the ordered eigenvalue distribution of the finite-dimensional Wishart random matrix， an accurate analysis and calculation method for false-alarm probability and decision threshold is proposed theoretically. Furthermore， considering the limitation of computing and storage resources of secondary users， a decision threshold calculation method with low computational complexity is proposed by combining the decision threshold corresponding to the maximum and minimum eigenvalue limiting distribution by using the distribution theory of limiting eigenvalues in the high-dimensional Wishart random matrix. From the comprehensive consideration of detection performance and false-alarm performance， the proposed BDDEE algorithm has better sensing performance than the traditional CAV （Covariance Absolute Value）， MME （Maximum Minimum Eigenvalue） and DMME （Difference between the Maximum and the Minimum Eigenvalues） algorithms， and can obtain more robust detection results under the condition of limited sample number， which is verified by the various numerical simulation results.