(3.92.96.236) 您好!臺灣時間:2021/05/07 15:19
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:張志宏
研究生(外文):Chang,Chi-Hong
論文名稱:使用鬆弛Givens旋轉之可管線化遞迴最小平方演算法
論文名稱(外文):Pipelined Recursive Least-Square Algorithm Using Relaxed Givens Rotations
指導教授:馮武雄馮武雄引用關係周煌程
學位類別:碩士
校院名稱:長庚大學
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:94
中文關鍵詞:適應性演算法遞迴最小平方Givens旋轉可管線化架構
相關次數:
  • 被引用被引用:0
  • 點閱點閱:135
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本篇論文提出一個使用鬆弛Givens旋轉之遞迴最小平方演算法(RGR-RLS)及其管線化的架構(Pipelined RGR-RLS)來實現RLS (Recursive Least Square)演算法。而此演算法是由QRD-RLS(QR-Decomposition-RLS)演算法為出發點,指對Givens Rotations所衍生的複雜運算,利用簡單的數學式子來近似,並推導出具有管線化特性的架構。
本論文中會舉一個Pipelined RGR-RLS演算法做五級管線化的例子,套用在Adaptive Equalizer的系統中,再利用軟體來模擬整個演算法在系統中收斂的特性和誤差值,並和其他類似的演算法做一個比較。最後由模擬結果可證明出所推導出來的演算法和理想的RLS演算法在最小平均平方誤差(minimum mean square error)和學習曲線(learning curve)方面很相近,因此Pipelined RGR-RLS演算法可以說是另一種實現RLS演算法的途徑。
This paper proposed a RGR-RLS (Relaxed Givens Rotations Recursive Least-Square) VLSI architecture which is implemented by RLS algorithm. The RGR-RLS is based on QRD-RLS (QR-Decomposition-RLS) algorithm to improve complex computation due to Givens Rotations. The key point is that complex computation can be approximated by a simple mathematic equation, and it creates a new PRGR-RLS (Pipelined RGR-RLS) algorithm. Thus, the PRGR-RLS has pipeline, no matrix-inverse operation and square-root free. So it is suitable for VLSI implementation.
The software simulation uses an adaptive equalizer as a system model, and adaptive algorithm operates a five-level pipelined RGR-RLS algorithm. The simulation results show that convergence speed and mean square error (MSE) are close to QRD-RLS algorithm. The proposed algorithm is compared with other similar algorithms, and the performances are not worse than them.
So PRGR-RLS will be an alternative VLSI architecture to implement RLS algorithm.
目錄
Abstract1
摘要2
第一章 緒論3
第二章 QRD-RLS演算法的簡介7
2.1 矩陣的QR分解(Givens Rotations)7
2.2 適應性等化器的架構及RLS演算法10
2.3 QRD-RLS演算法15
2.4 QRD-RLS Systolic Array架構18
2.5 模擬結果23
2.6 結論25
第三章STAR-RLS演算法的簡介26
3.1 固定角度旋轉的RLS演算法27
3.2 STAR-RLS演算法及其Systolic Array架構29
3.3 PSTAR-RLS演算法及其Systolic Array架構32
3.4 模擬結果34
3.5 結論35
第四章 使用Relaxed Givens Rotations RLS演算法及架構37
4.1 Relaxed Givens Rotation矩陣38
4.2 RGR-RLS的架構圖44
4.3 RGR-RLS的模擬結果46
4.4 結論49
第五章 PRGR-RLS演算法和架構50
5.1硬體管路化的方法50
5.1.1 Look Ahead方法及驗證結果51
5.1.2 Retiming的原理53
5.1.3 Relaxed Look-Ahead方法55
5.2管線化遞迴及非遞迴架構的方法57
5.3 PRGR-RLS演算法及其管線化架構65
5.4 PRGR-RLS架構的模擬結果76
5.5結論77
第六章 結果及討論79
參考文獻81
[1] S. Haykin, Adaptive filter theory, 2nd Ed., Englewood Cliffs, NJ: Prentice-Hall, 1991.
[2] I. K. Proudler, J. G. McWhirter, and T. J. Shepherd,“Computationally efficient QR decomposition approach to least squares adaptive filters,” Proc. Inst. Elec. Eng., pt, F, vol. 138, pp. 341-353, Aug. 1991.
[3] S. Y. Kung, VLSI Array Processors, Englewood Cliffs, N.J. Prentice Hall, 1988.
[4] K. K. Parhi, VLSI Digital Signal Processing Systems:Design and Implementation, John Wiley & Sons, Inc. 1999
[5] S. F. Hsieh, K. J. R. Liu, and K. Yao, “ A unified square-root-free Givens rotation approach for QRD-based recursive least squares estimation,” IEEE Tran. Signal Processing, vol.41, pp. 1405-1409, Mar. 1993.
[6] E. Franrzeskakis and K. J. R. Liu, “ A class of square-root and division free algorithms and architectures for QRD-based adaptive signal processing,” IEEE Trans. Signal Processing, vol. 42, pp.2455-2469, Sept. 1994
[7] J. M. Cioffi, “The fast adaptive ROTOR’s RLS algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 631-653, Apr. 1990.
[8] C. L. Lawson an R. J. Hanson, Solving Least Squares Problems, Englewood Cliffs, NJ: Prentice-Hall, 1995
[9] A. Y. Wu and K.J.R. Liu, “Split Recursive Least-Squares: algorithms, architectures, and applications,” IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, Vol. 43 , pp. 645 —658, Sept. 1996.
[10] Y. H. Hu, “The CORDIC trigonometric computing technique,” IEEE Trans. Electron. Comput. , pp. 330-334, July 1992.
[11] K. K. Parhi and D. G. Messerschmitt, “Pipeline interleaving and parallelism in recursive digital filters-Part II: Pipelined incremental block filtering,” IEEE Trans. Acoust. , Speech, Signal Processing, vol. 37, pp. 1099-1117, July 1989.
[12] N. R. Shanbhag and K. K. Parhi, “Relaxed look-ahead pipelined LMS adaptive filters and their application to ADPCM coder,” IEEE Trans. Circuits Syst. II, vol. 40, pp. 753-766, Dec. 1993.
[13] K. K. Parhi and D. G. Messerschmitt, “Pipeline interleaving and parallelism in recursive digital filters-Part I: Pipelining using scattered look-ahead and decomposition,”IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 1118-1134, July 1989.
[14] J. Ma, K. K. Parhi and E. F. Deprettere,”Annihilation-Reordering Look-Ahead Pipelined CORDIC-Based RLS Adaptive Filters and Their Application to Adaptive Beamforming,” IEEE Transactions on Signal processing, vol. 48, no 8,pp. 2414-2431, AUGUST 2000.
[15] J. Ma, E. F. Depretter and K. K. Parhi, “Pipelined CORDIC based QRD-RLS adaptive filtering using matrix lookahead,” in Proc. IEEE Workshop Signal Process. Syst. , Nov. 1997, pp. 131-140.
[16] J. J. Raghunath and L. L. Parhi, “Pipelined RLS adaptive filtering using scaled tangent rotations (STAR),”IEEE Trans. Signal Processing, vol. 40, pp.2591-2604, Oct. 1996.
[17]N. R. Shanbhag and K. K. Parhi, “A pipelined adaptive lattice filter architecture,” IEEE Trans. Signal Processing, vol. 41, pp. 1925-1939, May 1993.
[18] N. R. Shanbhag and K. K. Parhi, “A high-speed architecture for ADPCM coder and decoder,” in Proc. Int. Symp. Circuits Syst., May 1992, pp. 1499-1502.
[19] G. H. Golub and C. F. V. Loan, Matrix Computation. Baltimore, MD: Johns Hopkins Univ. Press, 1989.
[20] B.Farhang-Boroujeny, Adaptive Filters, Baffins Lane, Chichester, West Sussex PO19 1UD, England, John Wiley & Sons Ltd , 1999.
[21] M. L. Honig and D. G. Messerschmitt, Adaptive Filters: Structures, Algorithms, and Applications, Kluwer Academic Publishers, 1984.
[22] B. Parhami ,Computer Arithmetic:Alogrithms and Hardware Designs, Oxford University Press ,1999.
[23] Diniz Paulo and Sergio Ramirez , Adaptive filtering algorithms and practical implementation, Boston Kluwer Academic Publishers, 1997.
[24] Widrow Bernard, and Stearns Samuel, Adaptive signal processing, Englewood Cliffs, N.J. Prentice-Hall, 1985 .
[25] L. D. Van, "Design of efficient VLSI architectures: multipliers, 2-D digital filter, and adaptive digital filter," Ph. D. dissertation, Dept. Elect. Eng., National Taiwan University, Taipei, Taiwan, R.O.C., 2001.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關論文
 
系統版面圖檔 系統版面圖檔