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A key technology in cognitive radio (CR) is spectrum sensing that senses the spectrum and reports the available vacant channels. However, due to some effects such as fading or shadowing, an individual sensor may not be able to reliably detect the existence of a primary user (PU). Cooperative spectrum sensing that is proposed to solve such problem, uses a distributed detection system to overcome the severe decadent of received signal strength at some locations in the network. This paper considers the performance of a distributed Neyman-Pearson (N-P) detection system consisting of N sensors and a fusion center, in which the decision rules of the sensors have been given and the decisions of different sensors are mutually independent conditioned on both hypotheses. Theoretical analysis on the performance of this fusion center is carried out. We obtain the conditions for the fusion center to achieve an overall probability of detection that is greater than the local probability of detection of each sensor. Numerical results show that the AND, OR and majority decision fusion rules are the special cases of the N-P fusion rule.