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，最後再將使用者的數目從兩個推廣到N個。由於以前都是探討在完美通道資訊的情況下，但實際情況下，通道的估測會有誤差，精確的系統傳送容量不存在解析解(closed-form)，所以我們轉而尋找系統傳送容量的下限(lower bound)，目標為讓系統傳送容量下限最大化之最佳化問題有解。再經由卡羅需-庫恩-塔克條件(Karush-Kuhn-Tucker conditions)可以得到解來做系統的功率分配，但是不知道這個系統傳送容量下限和實際系統傳送容量的差距多大，所以我們會再去求得一個系統傳送容量上限(upper bound)，經由電腦模擬結果顯示，他們之間的差距是非常小的，這也代表我們去最大化系統傳送容量下限所做的功率分配是很貼近實際系統的。

In this thesis, we investigate power allocation for a downlink non-orthogonal multiple access (NOMA) system with a base station and N users under imperfect channel state information (CSI). We first derive the capacity lower bound and upper bound for a single-input single-output (SISO) scenario and show that they are tight for Gaussian inputs. Accordingly, the capacity lower bound can be used as an approximate capacity expression for the SISO case under imperfect CSI. Similar results are also derived for a multiple-input multiple-output (MIMO) scenario. Then, we formulate optimization problems for both the SISO and MIMO cases in terms of power allocation among N users for maximizing the corresponding capacity lower bounds under a total power constraint and a quality-of-service condition such that the minimum rate requirement of each user is satisfied. Low-complexity closed-form optimal power allocation solutions are derived based on the Karush-Kuhn-Tucker (KKT) conditions. Computer simulation results under imperfect CSI show that the proposed methods offer a better average bit error rate performance for all users than the fixed power allocation approach and the previous related optimal schemes under perfect CSI.

Abstract i
Contents ii
List of Figures iii
I. Introduction 1
II. System Model 4
A. SISO Structure 4
B. MIMO Structure 6
III. Closed-From Expressions For Capacity Bounds 7
A. Lower Bound and Upper Bound Derivation for SISO 7
B. Lower Bound and Upper Bound Derivation for MIMO 11
IV. Proposed Power Allocation Methods Baesd on Capacity Lower Bound 15
A. Problem Formulation 15
B. Proposed Power Allocation 16
V. Simulation Results 20
VI. Conclusion 28
Appendix. 29
References 30

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