For the purpose of enhancing the spectrum efficiency, cognitive radio (CR) technology has been recently proposed as a promising dynamic spectrum allocation paradigm. In CR, spectrum sensing is the key capability of secondary users in a cognitive radio network that aims for reducing the probability of harmful interference with primary users. However, the individual CRs might not be able to carry out reliable detection of the presence of a primary radio due to the impact of channel fading or shadowing. This paper studies the cooperative spectrum sensing scheme as means of optimizing the sensing performance in AWGN and Rayleigh channels. Results generated from simulation provide evidence of the impact of channel condition on the complementary receiver operating characteristic (ROC). Based on the results, it was found that with constant local SNRs at the secondary users, the probability of missed detection ($P_m$) of cooperative spectrum sensing in a cognitive radio network, calculated using a closed form expression, can be significantly minimized. Thus, the paper illustrates that improvement of the detection performance of the CR network can be achieved by establishing a centralized cooperation among neighboring cognitive radio users. Finally, verification of the validity of the fusion schemes utilized for combining the individual CR decisions is provided.