在本篇論文中，我們對於非正交多重接取下行系統之功率分配作探討，系統中包含一個單一天線基地台(Base Station)作為訊號源，以及兩個單一天線使用者作為接收端，而兩個使用者中，通道增益較大的一方稱為強使用者(strong user)，另一方為弱使用者(weak user)。首先我們會證明此系統的傳送容量為一嚴格遞增函數，因此可以得知，在總功率以及兩個使用者各自都有功率與傳輸率要求的限制條件下，目標為讓系統傳送容量最大化之最佳化問題確實有解。再經由卡羅需-庫恩-塔克條件(Karush-Kuhn-Tucker conditions)，就能夠得出封閉形式的解來做系統的功率分配。而根據此結果，我們可以由不同情況下，某一方使用者傳輸率要求，得出最佳之功率分配法，並進一步找到另一方使用者所能達到的傳輸率，因此能讓整體的傳送容量在系統的限制條件下達到最大化的結果。
　　我們將此方法與相關研究中提到之疊代演算法以及低複雜度之次最佳功率分配法做比較，電腦模擬結果顯示我們提出之方法能比次最佳功率分配法達到更佳的表現，並且可以達到與疊代演算法相同的系統傳送容量。

In this thesis, we investigate power allocation for a downlink non-orthogonal multiple access (NOMA) system with a base station and two users, where the user with a larger channel gain is called the strong user and the other one is called the weak user. We first formulate an optimization problem for power allocation to maximize the sum capacity of both users under the constraints that the weak one must have greater transmit power than the strong one (i.e., the NOMA principle) and the minimum rate requirements of each user must be satisfied. Then we derive two closed-form power allocation solutions for the two users based on the Karush-Kuhn-Tucker conditions. Simulation results show that the proposed schemes can significantly outperform an arbitrary power allocation method. Also, as compared to the optimal approach described in a recent work, the proposed approaches achieve the same sum capacity with much lower computational complexity; in contrast to the suboptimal method, they provide better performance with similar complexity.

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