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A channel allocation mechanism for cognitive radios (CRs) with finite user population to enable maximum throughput and minimum forced termination probability for CR users (CUs) that are not capable of spectrum handover (SH) is presented. SH is an optimal scheme used by CUs to evacuate from time-slots that will be used by primary users (PUs) based on time-slot assignment (TA) information obtained in advance. Commonly it is not easy to obtain PU TA information in advance. The channel allocation scheme for CR-networks without SH enables a remarkable throughput performance, equivalent to the level of when SH is used. In this paper, we analyze the scheme using the finite user population model. This model provides a more precise solution for network scalability.