The implementation of the Generalized Detector (GD) in Cognitive Radio (CR) systems allows them to improve the spectrum sensing performance in comparison with employment of the conventional detectors. They analyze the spectrum sensing performance for the uncorrelated and spatially correlated receive antenna array elements. Additionally, they consider a practical case when the noise power at the output of GD linear systems (the preliminary and additional filters) is differed by value. The choice of the optimal GD threshold based on the minimum total error rate criterion is also discussed. Simulation results demonstrate superiority of GD implementation in CR system as spectrum sensor in comparison with the Energy Detector (ED), Weighted ED (WED), Maximum-Minimum Eigenvalue (MME) detector and Generalized Likelihood Ratio Test (GLRT) detector.