再一個多輸入多輸出的上行鏈路中，強制歸零(Zero-forcing, ZF)或是最小均方誤差(Minimum mean-square error, MMSE)兩者都是廣泛被利用來做線性解調，然而這樣的線性解調會因為逆矩陣而使整體的運算複雜度提高，特別是再增加天線以及使用者時會更加明顯。於是會採用一些線性的近似解來降低複雜度，當一個用戶進入或者是離開服務範圍，依據其上行或是下行鏈路提出不同的演算法，然而這些方法只能簡單的用於更新強制歸零解調器，再我們的論文中會將奇異值分解(Singular value decomposition, SVD)運用再強制歸零或是最小均方誤差解調器，並且提出兩種演算法來更新通道矩陣，我們分別使用吉文斯旋轉(Given rotation)和Golub Kahan以遞迴的方式來近似奇異值分解的對角矩陣，模擬結果顯示出我們提出的方法比現有的其他方法來的好並且有較低的複雜度。

For the uplink of multiuser massive multi input multi output (MIMO) systems, linear detection
such as Zero Forcing or minimum mean-square error (MMSE) detectors are widely adopted.
However the computational complexity of the linear detectors is still high due to the matrix
inversion, especially with increasing number of antennas and users. Hence some strategies to
approximate the linear detectors have been adopted to reduce complexity. Among them updating
and downdating algorithm were proposed for the case when one user join or leaves the cell.
Nevertheless, these strategies simply applicable to update or downdate the ZF detector. In the
thesis we adopt Singular Value Decomposition(SVD) based ZF or MMSE detector and propose
two algorithm to update and downdate the SVD of channel matrix. We used Given Rotation and
Golub Kahan to approach the diagonal matrix of the singular value recursively. It is shows through
simulation results that the proposed scheme outperforms the existinf schemes with lower
complexity.

摘要 ii
ABSTRACT iii
TABLE OF CONTENT iv
LIST OF FIGURE vi
LIST OF TABLE vii

CHAPTER I Introduction 1
CHAPTER II Related Works 4
2.1 Large scale MIMO Detection for 3GPP LTE: Algorithm and FPGA Implementation, its journal is the basis of large MIMO detection 4
2.2 Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method 6
2.3 A Near-Optimal Detection Scheme Based on Joint Steepest Descent and Jacobi Method for Uplink Massive MIMO Systems 8
2.4 High Precision Low Complexity Matrix Inversion Based on Newton Iteration 11
2.5 Robust Update Algorithms for Zero Forcing Detection in Uplink Large-Scale MIMO Systems 13

CHAPTER 3 Updating And Downdating Using SVD 17
3.1 System Model 17
3.2 Channel Equalization using MMSE 18
3.3 Channel Equalization using Zero Forcing 19
3.4 Proposed Algorithm................................................................ 20
3.4.1 Given Rotation 21
3.4.2 Householder Transform 22
3.4.2.1 Householder Transform for Column 23
3.4.2.2 Householder Transform for Row 23
3.4.3 Bidiagonal Matrix to be Diagonal Matrix 24
3.4.3.1 Given Rotation for Converge Bidiagonal Matrix 25
3.4.3.2 Golub Kahan SVD Algorithm 26
3.5 Updating user 27
3.6 Dowdating user 28
3.7 Computational Complexity 30

CHAPTER 4 Simulations 33
4.1 Simulation Result 33
4.2 Error Analysis 37
4.3 Comparison Result 41
CHAPTER 5 Conclusion 46
Reference. 47

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