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Cellular networks are the most diffuse type of wireless networks; however, they suffer from spectrum shortage due to the recent increase in smartphone wireless applications and services. Cognitive radios offer a key technology to successfully maintain, optimize and upgrade wireless networks and effectively address spectrum overcrowding problem. CRs have the ability to sense the frequency spectrum, learn from history, and make intelligent decisions to adjust their transmission parameters, and hence, perfectly integrate themselves into the existing wireless networks. The main challenges for implementing cellular CR networks (CCRNs) include the coexistence between CR devices and external wireless cellular networks, and the self-coexistence among these devices. The coexistence/self-coexistence problem in CCRNs can be seen as a channel assignment problem among the network cells. Considering IEEE 802.22 as the standard reference for cellular network mechanisms, this article addresses the coexistence/self-coexistence issues, and proposes two channel assignment schemes for cooperative and non-cooperative CR devices along with their pros and cons. An experimental study and comparison with a random channel assignment demonstrate that a robust and efficient channel assignment scheme is a critical feature in CCRNs.