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標題: 使用QR分解和交錯近似法 於奇異值分解之硬體實現
SVD Hardware Implementation Using QRD and Interleaver Approximation Method
作者: 陳志勝
Chen, Chih-Sheng
關鍵字: SVD;奇異值分解;QRD;Interleaver;eigenvalue and eigenvector;QR分解;交錯近似法;特徵值;特徵向量
出版社: 電機工程學系所
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奇異值分解( SVD )已成為標準線性代數的工具,在數位訊號處理上
一個矩陣,都化簡成對角矩陣。這樣在Beamforming的應用上,將會非常的方便,也就是降低困難度。大部分的奇異值分解演算法,都是以大量的運算式來求出奇異值的解,例如矩陣的特徵值與特徵向量就是以不斷的乘法之化簡最後達到結果。本篇論文,是以QR為基礎,配合交錯式近似法,來求得奇異值的解,QR分解是以Given Rotation 為基礎,這種方式是建構在CORDIC演算法上,只利用很簡單的加法以及位移達到分解目的,而交錯式近似法 ,則完全使用位移暫存的方式,故用這兩種方式的配合,可達得到低複雜度的奇異值分解之目的。

本篇論文電路實現是採用聯電0.18um 1P6M CMOS製程。實體面積為1000x930 ,執行速度為7MHz

SVD is a standard tool of linear algebra. SVD in digital signal processing based on the CORDIC is the most popular algorithm now. The fundamental concept of SVD is to simplify every matrix to be a diagonal matrix. On the application of beamforming, this method will be very convenient for calculation. Most SVD algorithm used a lot of calculation to find out the solution. For example, matrix's eigenvalues and eigenvectors are obtained by using multiplication continuously.
At last, we can get the most simplified result. In this thesis, QR base and
Interleaver approximation method is used to obtain the solution of SVD. Given Rotation is utilized for QR. Furthermore, Given Rotation method is established on CORDIC algorithm. Not only CORDIC algorithm uses very simple additions and shift registers to achieve the goal, but also Staggered Approximation uses shift registers toaccomplish.
As the result, the SVD hardware by using QR and Interleaver approximation method is very simple and small in area. The SVD circuit is designed by using UMC 0.18um 1P6M CMOS technology. The chip area is 1000x930 at 7MHz execution speed.
其他識別: U0005-1408200816491300
Appears in Collections:電機工程學系所

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