在本論文中，我們探討一個包含兩個使用者之下行多輸入多輸出非正交多重接取(MIMO-NOMA)系統的位元錯誤率(BER)分析，其中發射端採用正交相移鍵控(QPSK)調變，而接收端則使用線性最小均方誤差偵測。不同於現有的單輸入單輸出 NOMA 系統之相關分析研究，本論文同時考量了 MIMO-NOMA 傳輸所引起的多重接取干擾以及連續干擾消除所造成的錯誤傳播效應。我們首先針對完美通道狀態信息(CSI)情境推導使用者的 BER 公式，然後在已知通道估測均方誤差的情況下，將推導方式擴展至非完美 CSI 情境，以獲得使用者的 BER 上界公式。根據這些 BER 結果，我們建立兩個功率分配優化問題，以分別最小化平均 BER 和最小化平均 BER 上界，再藉由現有之具有高複雜度的迭代式演算法求得理論最佳解。為了簡化數學運算，我們進而使用最小平方曲線擬合方法來逼近兩個優化問題中的平均 BER 和平均 BER 上界，並據以設計兩個閉合式的功率分配解決方案。電腦模擬結果顯示，所推導出的 MIMO-NOMA 系統之使用者 BER 公式足夠準確，且每個閉合式功率分配解決方案之 BER 效能僅略遜於理論最佳解之效能，但卻具有明顯較低的運算複雜度。相較於另一種基於廣義奇異值分解和訊號對干擾雜訊比平衡技巧之迭代式 MIMO-NOMA 功率分配演算法，所提出之閉合式解決方案亦可大幅降低複雜度，並達到接近的平均 BER 效能。

In this thesis, we investigate bit-error-rate (BER) performance for a two-user downlink multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) system. The quadrature phase shift keying (QPSK) modulation is used at the transmitter, and the linear minimum mean-squared error detection is adopted at the receiver sides. Unlike existing related works for single-input single-output NOMA systems, this thesis takes account of both multiple access interference in MIMO-NOMA transmission and error propagation from successive interference cancellation. We first derive BER expressions for both users under the availability of perfect channel state information (CSI), and then extend the derivations to an imperfect CSI scenario to obtain BER upper bounds by assuming that the mean-squared errors of channel estimation are known a priori. Based on the BER results, two power allocation optimization problems are respectively formulated for minimization of the average BER and for minimization of the average BER upper bound, where the theoretically optimal solutions can be found by well-known complicated iterative algorithms. To simplify the computational complexity, we further use the least-squares curve fitting method to approximate the average BER and the average BER upper bound in both optimization problems and then design two closed-form power allocation solutions accordingly. Computer simulation results show that the derived BER expressions are sufficiently accurate and each of the closed-form solutions offers slightly worse performance with much lower complexity than the corresponding theoretically optimal one for the MIMO-NOMA system. As compared with another iterative MIMO-NOMA power allocation algorithm based on generalized singular value decomposition and signal-to-interference-plus-noise ratio balancing, the proposed two closed-form schemes also achieve close average BER performance with significantly reduced complexity.

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