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 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