The problem of multiple antenna spectrum sensing in cognitive radio (CR) networks is studied in this paper. We propose two new invariant constant false-alarm rate eigenvalue-based (EVB) detectors, using the higher order moments of the sample covariance matrix eigenvalues, by exploiting the separating function estimation test framework. We find closed-form expressions for the false-alarm and detection probabilities of the proposed detectors by providing moment-based approximations of their statistical distributions. The accuracy of the obtained closed-form expressions is validated by Monte Carlo simulations. In addition, we compare the performance of the proposed detectors with that of their two counterparts, i.e., John's and the arithmetic to geometric mean (AGM) detectors, in terms of the asymptotic relative efficiency. This comparison enables us to demonstrate the superiority of our proposed detectors over those detectors within the typical range of signal-to-noise ratio in CR application. The comparative simulation results also illustrate the superiority of the proposed detectors over John's and the AGM detectors as well as some other state-of-the-art EVB algorithms given in the literature.