渦輪等化器(Turbo Equalizer, TEQ)可有效的對抗碼際干擾(InterSymbol Interference, ISI)和多重路徑雷利衰減通道，我們已知目前有使用線性等化器(Linear Equalizer, LE)、對數最大事後機率(Logarithm Max a-posteriori, Log-MAP)演算法、軟輸出維特比(Soft Output Viterbi Algorithm, SOVA)演算法、輻射基底函數(Radial Basis Function, RBF)…等來實現等化器。在輻射基底函數等化器中，雖然我們已知其效能與貝氏等化器的效能為相等的，但是計算複雜度對電路實現而言，是相當高的，雖然我們可以使用Jacobian演算法和決策回饋(Decision feedback)來簡化計算複雜度，但是其計算複雜度在高階數等化器中，加法器仍然會呈現指數成長，並不適用於現實應用中。在本論文中，我們提出了利用模糊濾波器(Fuzzy Filter)來簡化渦輪等化器的複雜度，結合模糊濾波器和對數最大事後機率解碼器，我們稱為“模糊渦輪等化器”，利用不同的會員函數(Membership function)，我們可以得到不同的效能。同樣的訊號雜訊比(Signal-to-Noise Ratio, SNR)下，在第一次疊代後，輻射基底渦輪等化器的效能會比模糊渦輪等化器好，經過數次疊代之後，經由觀察我們可以發現，模糊渦輪等化器只要比輻射基底等化器多疊代一次，雖然我們需付出較多的運算量，但是由於整體運算量仍然非常的低，所以我們只要多疊代一次，就可以非常的貼近其效能，但是對於計算複雜度而言，卻有非常多的簡化。

Turbo equalizer (TEQ) was shown to against inter symbol interference (ISI) and multipath Rayleigh fading channel effective. That had been implement using linear filter, Logarithm-Maximum a-posteriori algorithm (Log-MAP), Soft Output Viterbi algorithm (SOVA), and Radial Basis Function algorithm (RBF). In RBF-TEQ, which has high computational complexity, in order to reduce computational complexity, we can use Jacobian logarithmic algorithm and Decision-feedback technology, but in high order equalizer, the number of adder is exponential increase, so the computational complexity still too high for materializing. In this paper, we present fuzzy algorithm to reduce computational complexity. We joint fuzzy-filter equalizer and log-MAP decoder (Fuzzy-TEQ). The fuzzy equalizer is shown to perform close to the Bayesian equalizer (RBF). Using different membership function, we get different performance. However, in first iteration, the RBF-TEQ performance is better than Fuzzy-TEQ . After several iteration, the fuzzy-TEQ just need increase one iteration, the performance will be very close RBF-TEQ, almost same performance, but computational complexity can be reducing effective.

中文摘要
………………………………………………………………… iv
英文摘要 ………………………………………………………………… vi
誌謝 ………………………………………………………………… vii
目錄 ………………………………………………………………… ix
表目錄 ………………………………………………………………… x
圖目錄 ………………………………………………………………… xi
第一章 緒論…………………………………………………………… 1
1.1 前言…………………………………………………………… 1
1.2 等化器(Equalizer)的分類………………………………… 4
1.3 最小均方 (Least mean square)演算法…………………… 7
1.4 衰減通道(Fading channel) ………………………………… 10
第二章 錯誤更正碼(Error Correction Code, ECC) ……………… 13
2.1 遞迴系統迴旋碼(Recursive Systematic Code, RSC)編碼器………………………………………………………………
13
2.2 最大事後機率(Maximum a-posteriori, MAP)解碼器………… 15
2.3 對數最大事後機率(Log-Maximum a-posteriori, Log-MAP)解碼器……………………………………………………………
18
第三章 輻射基底函數(Radial Basis Function)…………………… 20
3.1 前言…………………………………………………………… 20
3.2 輻射基底函數架構…………………………………………… 20
3.3 輻射基底等化器……………………………………………… 22
第四章 模糊系統(Fuzzy system)…………………………………… 26
4.1 前言…………………………………………………………… 26
4.2 模糊等化器…………………………………………………… 28
第五章 渦輪等化器(Turbo equalizer)…………………………… 23
5.1 前言…………………………………………………………… 30
5.2 輻射基底渦輪等化器………………………………………… 32
5.3 模糊渦輪等化器……………………………………………… 35
5.4 利用Decision Feedback來簡化複雜度…………………… 37
5.5 Jacobain RBF-TEQ & Fuzzy-TEQ複雜度比較……………… 40
第六章 模擬結果……………………………………………………… 43
第七章 結論…………………………………………………………… 49
參考文獻 ………………………………………………………………… 52

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