隨著5G標準化，多用戶大規模多輸入多輸出系統（MU M-MIMO system）的設計為一項關鍵技術，其中迫零預編碼器為常見的簡單預編碼方式，在高信噪比情境下，可將多用戶大規模多輸入多輸出系統y=nHFx+n改寫為y=x+n，使得y容易解碼為x。一般而言，迫零預編碼器的主要困難在於赫米特威沙特矩陣HH^H的逆運算，但藉由Chebyshev多項式加速方法，可利用HH^H的特徵值直接推估x，降低運算複雜度。
已知近來研究中，多有以深度學習途徑求解矩陣特徵值之研究，惟其往往對矩陣尺寸與特性有諸多限制，雖取得良好成果，但也缺代應用性。本篇研究試圖以並聯的神經網路架構，增進深度學習方法在矩陣特徵值問題的適用性，並以條件篩選方式增進資料的特徵。

With the standardization of 5G, the design of a multi-user large-scale multi-input multi-output system (MU M-MIMO system) has became a key technology. And the zero-forcing precoder is a simple precoding method. In high signal-to-noise ratio, the received signal y is decoded into the  transmitted signal x easily. Generally speaking, the main difficulty of the zero-forcing precoder is the inverse operation of the Hermitian Wishart matrix, HH^H. However, by the Chebyshev polynomial acceleration method, the eigenvalues of  HH^Hcan be used to directly estimate x, reducing the computational complexity.

In recent studies, there are many studies on solving matrix eigenvalues by deep learning. However, those studies often have many restrictions on the size and property of the matrix. Although good performances have been achieved, those studies are also lacking in applicability.  This study attempts to improve the applicability of deep learning methods to matrix eigenvalue problems with a parallel neural network architecture and use conditional sorting to improve the features of the data.

目錄
致謝	Ⅰ
中文摘要	Ⅱ
英文摘要	Ⅲ
目錄	ⅠⅤ
圖目錄	ⅤⅠ
表目錄	ⅤⅢ
第一章	緒論	1
1.1	研究動機與目的	1
1.2	研究方法	3
1.3	論文章節架構	5
第二章	相關研究與背景資料	6
2.1 	問題描述	6
2.2 	估測編碼後訊號之研究途徑	7
2.2.1 	逆矩陣近似法與定點迭代方法	8
2.2.2 	結合漸進特徵值機率分佈函數之Chebyshev加速方法	10
2.3 	以深度學習途徑估測矩陣特徵值	14
第三章	倡議之神經網路	20
3.1 	輸入層	20
3.2 	分類條件與正規化	20
3.3 	隱藏層與啟動函數	24
3.4 	前向傳遞與後向傳遞	25
第四章	實驗結果	31
4.1 	估測矩陣特徵值	31
4.1.1 	天線相關性ρ=0	32
4.1.2 	天線相關性ρ=0.2	35
4.1.3 	天線相關性ρ=0.5	38
4.1.4 	天線相關性ρ=0.8	41
4.2 	位元錯誤率	44
第五章	結論與未來展望	49
參考文獻	52

圖目錄
圖1.1  分別以1個、5個、10個及20個神經元擬合拋物線函數	4
圖2.1  不同天線相關性下的單邊克羅內克模型之AEPDF	13
圖2.2  單一輸出之全連結神經網路	18
圖2.3  多輸出之全連結神經網路	19
圖3.1  倡議之神經網路結構	22
圖3.2  多輸出之神經網路結構	26
圖3.3  單一輸出之神經網路結構	26
圖4.1  ρ=0時，矩陣W相應特徵值λ_1	32
圖4.2  ρ=0時，矩陣W相應特徵值λ_2	32
圖4.3  ρ=0時，矩陣W相應特徵值λ_8	33
圖4.4  ρ=0時，矩陣W相應特徵值λ_15	33
圖4.5  ρ=0時，矩陣W相應特徵值λ_16	34
圖4.6  ρ=0.2時，矩陣W相應特徵值λ_1	35
圖4.7  ρ=0.2時，矩陣W相應特徵值λ_2	35
圖4.8  ρ=0.2時，矩陣W相應特徵值λ_8	36
圖4.9  ρ=0.2時，矩陣W相應特徵值λ_15	36
圖4.10  ρ=0.2時，矩陣W相應特徵值λ_16	37
圖4.11  ρ=0.5時，矩陣W相應特徵值λ_1	38
圖4.12  ρ=0.5時，矩陣W相應特徵值λ_2	38
圖4.13  ρ=0.5時，矩陣W相應特徵值λ_8	39
圖4.14  ρ=0.5時，矩陣W相應特徵值λ_15	39
圖4.15  ρ=0.5時，矩陣W相應特徵值λ_16	40
圖4.16  ρ=0.8時，矩陣W相應特徵值λ_1	41
圖4.17  ρ=0.8時，矩陣W相應特徵值λ_2	41
圖4.18  ρ=0.8時，矩陣W相應特徵值λ_8	42
圖4.19  ρ=0.8時，矩陣W相應特徵值λ_15	42
圖4.20  ρ=0.8時，矩陣W相應特徵值λ_16	43
圖4.21  ρ=0時，BER-SNR作圖	45
圖4.22  ρ=0.2時，BER-SNR作圖	46
圖4.23  ρ=0.5時，BER-SNR作圖	47
圖4.24  ρ=0.8時，BER-SNR作圖	48

 
表目錄
表2.1  三個代表性逆矩陣近似法	9
表2.2  三個代表性定點迭代方法	10
表2.3  常見的損失函數	15
表3.1  針對不同天線相關性之統計	21

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