Cognitive Radio Network (CRN) is an emerging technology to increase usages of the underutilized spectrum. Since cognitive radios (CR) join and leave CRN at will, as a dynamic secondary overlay network operating in the dynamic scenarios, CRN faces many new practical challenges. Spectrum sensing is a key functionality enabling dynamic spectrum management. Distributed cooperative spectrum sensing can effectively overcome the hidden primary user issue. The performance of the distributed sensing scheme is affected by the number of collaborative CRs. In this dissertation, we analyze the performance of cooperative spectrum sensing for the dynamic CRN systems, which is a more realistic application scenario. Closed form exact expressions for the dynamic performance of distributed energy-based cooperative spectrum sensing over different fading channels are derived. These expressions enable the calculation of probability of detection and probability of false alarm efficiently tractable, and also provide a feasible approach for optimization of sensing performance. Quick performance evaluation is essential for CRN to achieve real-time adaptation to guarantee optimal system operations. We also study two promising applications for cognitive radio networks technologies: wireless cellular networks and public safety emergency networks. We analyze the performance of cooperative spectrum sensing in these two scenarios and the closed form expressions provide the framework to apply the cognitive radio networks technologies to perform online learning for self-organizing dynamic ad hoc cellular wireless system and public safety emergency networks system.