The agility of any cognitive radio system largely depends on the performance of the spectrum sensing technique used. While the Energy Detector (ED) is considered to be a very simple technique in practice, it suffers from noise and measurement uncertainty. To overcome this uncertainty, the Eigenvalue Based Detector (EBD) is currently proposed as a promising technique for spectrum sensing. In this paper, we propose to analyze the performance of such a detector in a finite context. More specifically, we derive the analytical form of the cumulative density function (CDF) and the probability density function (PDF) of the 3xN MIMO like signal based on Wishart matrix. Then, we evaluate the performance of the EBD detector with 2 and 3 antennas in terms of CDF, probability of false alarm, and probability of detection.