這篇碩論探討無線感知多重跳躍網路的能量使用最佳化問題。這
涵蓋了能量控制、頻道共用、流量分配和路由，所以這個最佳化問題
觸及OSI 模型的實體層、資料連結層和網路層。我們的原始模型是個
NP-hard 混合整數非線性分數規劃。我們需要對原始模型做線性化才有
辦法求解。
我們用沈農公式來計算通道容量，此公式為非凸。我們用切線和割
線線性化此公式。另一個造成限制式非線性的原因是變數相乘項。這
部分我們引用了逐段地重新線性化技術來解決。以上兩步讓所有限制
式為線性。我們用Charnes-Cooper Transform(CCT) 使目標函式不再是
分數型態。再把部分變數做還原，最後得到一個混合整數線性規劃的
模型。

This thesis study optimal power efficiency problem of the multi-hop CR network. The topic contains power control, bands sharing and routing. Thus, OSI model such as physical layer, data link layer, and network layer are included
in our optimal programming. The original model is a mixed-integer nonlinear fractional , it is NP-hard and hardly solvable. We should process some transforms on it than we can solve it.
We compute channel capacity by Shannon’s information theorem, and the constraint is nonconvex. We use tangent lines and a secant line to make it convex. Bilinear term is another cause of nonliearity of the constraint. For this part, we apply piecewise reformulation-linearization technique. These relaxation make all the constrains to be linear. And we use Charnes-Cooper transform to reduce the fractional form of objective function, then doing adjustment
over some variable. After series of transform we get a mixed-integer linear programming problem.

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