在本論文中, 我們考慮在正交分頻多工合作式中繼解碼網路的資源分配,
我們的目的是對主要使用者干擾適當管理下最大化在次要使用者的總通道容量,
此最佳化包含子載波配對與功率分配, 因此最佳化問題為一混合整數規劃問題(MIP)。
為了在合理的成本下解決此複雜的混合整數規劃問題, 我們應用混合基因演算法,
其主要動機來自減少前人為了簡化問題所設的假設之缺陷。
在我們所提出的混合基因演算法中, 染色體可以切割成兩個部份來討論, 前半部分為整數
型的子載波配對基因, 後半部分為實數型的功率分配基因。 基於凸函數最佳化理論的啟發,
我們亦提出兩種新型的染色體初始化方法、新式的交配運算與突變計算以適應增加對主要使用者干擾限制式。其中在對偶問題部份, 使用替代型次梯度法替代傳統型次梯度法增加對偶變數收斂速度, 在不須使拉格朗日對偶問題最佳化就可以保證對偶變數收斂, 進而得到較小的對偶間隙。此外, 隨著子載波增加, 計算複雜度亦隨之增加, 我們亦提出兩階段低複雜度分離式演算法, 此演算法把功率分配與子載波配對分開到兩個不同基因演算法分離運算。最後我們的模擬將比較我們提出的混合演算法、兩階段低複雜度分離式演算法與最新的論文比較, 提出功率、主要使用者個數對系統整體傳輸速率, 子載波個數對CPU 時間計算複雜度的模擬圖。

This paper considers the resource allocation for an orthogonal frequency-division multiplexing (OFDM)-based cognitive decode-and-forward (DF) relay network. Our objective is to maximize the sum rate (over subcarriers) of the cognitive radio (CR) user with the interference introduced to the primary
users (PUs) being managed. The optimization is over the subcarrier pairing and power allocation, which leads to a mixed integer programming (MIP) problem. To resolve this complicated MIP problem with reasonable cost, we adopt the heterogeneous genetic algorithm (HGA) framework. The main motivation of the HGA framework comes from the idea that it can reduce the impact of extra assumptions made in previous works to simplify the problem. In our HGA, the chromosome is divided into an integer string for subcarrier pairing, and a real number string for power allocation. Two new initialization methods of these chromosomes, motivated by the convex optimization theory, are proposed. New crossover and mutation schemes are also devised to accommodate these new chromosomes as well as to manage the interference to the PUs. For dual problem part, we replace subgradient method by surrogate subgradient method to converge the dual variables without optimal dual value, and then get the low dual gap. Furthermore, we also propose a two-stage low-complexity GA, which separately determines the proper subcarrier pairs and power allocations. Our simulations show that the proposed HGAs and the two-stage algorithm provide competing performance compared with similar state-of-the-art works.

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