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This paper considers the problem of optimizing the data rate of the cooperative cognitive system subject to the dual constraints of the interference threshold of primary users and power budget of secondary users. In particular, under a single constraint, the rate can reach its peak easily. But under the double restrictions, the peak rate problem becomes complicated and changeable. According to different interference conditions and power supplies, four scenarios are formulated: total interference threshold and total power budget, total interference threshold and separate power budget, separate interference threshold and total power budget, and separate interference threshold and separate power budget. Each scenario needs to be further divided into many situations for discussion due to the sheer particularity. Through careful comparison and classification, we summarize and formulate each situation one by one to …