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Cognitive Radio Network (CRN) provides a promising method to expand usage of the underutilized spectrum resources. Spectrum sensing is a key functionality for the operation of secondary overlay CRN systems without causing harmful interference to the licensed primary users. Through the collaboration among spatially distributed CR users, spectrum sensing can provide reliable decisions. However, CRN is not a static network but a dynamic network such that the number of available spatial diversity is time-varying. The performance of cooperative spectrum sensing is thus dynamically changing. Furthermore, the distributed CRs may experience a variety of fading conditions, so identically distributed fading model adopted in most spectrum sensing literatures does not fully characterize the practical CRN application scenarios. Thus, in this paper, we study the cooperative spectrum sensing with opportunistic spatial diversity over non-identical fading channels. We derive the exact closed form expressions for the probabilities of detection and false alarm. These expressions are analytical tractable and hence provide the framework to apply optimization tools to efficiently guarantee the global optimality without computationally costly exhaustive search. Quick efficient performance evaluation is crucial for CRN to perform online adaptation to the wireless links, the primary users' activities, and the CR dynamics simultaneously.