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This paper presents the spectrum sharing network consisting of a pair of primary users (PUs) and a pair of cognitive users or secondary user (SUs) in fading wireless channels. Cognitive radio networks are the spectrum utilizing networks. When both the links (primary user link and secondary user link) utilized the spectrum simultaneously networks are called the spectrum sharing networks. During the spectrum sharing, the interference will occur at the primary user link and secondary user degrades the QoS of the primary user link due to same frequency band utilization from the PUs and SUs. The priority of the primary user's spectrum utilization will be higher than secondary user's spectrum utilization. This study discussed about the QoS assurance of primary users, improved the performance of the secondary users and minimization of bit rate in the spectrum sharing cognitive radio network.