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In cognitive radio networks (CRN), secondary users (SUs) are required to detect the presence of the licensed users, known as primary users (PUs), and to find spectrum holes for opportunistic spectrum access without causing harmful interference to PUs. However, due to complicated data processing, non-real-time information exchange and limited memory, SUs often suffer from imperfect sensing and unreliable spectrum access. Cloud computing can solve this problem by allowing the data to be stored and processed in a shared environment. Furthermore, the information from a massive number of SUs allows for more comprehensive information exchanges to assist the resource allocation and interference management at the cloud center while relieving the stringent capacity demands in fronthaul links. Moreover, spectrum resources should be made available to more users, especially when the spectrum is underutilized but occupies a large band. Hence, cloud-based CRN can generate massive sensing samples that will benefit the applications of big data algorithms. The approaches to spectrum sensing and spectrum management can be greatly improved with decision-making capabilities of spectral big data. nonPeerReviewed