臺灣博碩士論文加值系統

本篇論文主要應用在高階QAM調變系統中使用纜線數據機(cable modem)通道模型的環境下，藉由盲蔽式等化器估計出通道效應，將接收到的訊號進行振幅與相位的補償。盲蔽式等化器的特性在於不需要使用訊號符元(training symbol)，藉由傳輸訊號的統計特性便能有效的校正受到干擾的訊號，而盲蔽式等化器相關演算法中，主要是以固定模數演算法(Constant Modulus Algorithm，CMA)為基礎，再延伸出廣義多模數演算法(Generalized Multi-Modulus Algorithm，GMMA)，為了使等化器在高階QAM調變系統下也能有較低的符元錯誤率(Symbol Error Rate，SER)，因此我們設計了一個兩階段式混合廣義多模數演算法及軟性決策運算(Soft Decision-Directed，SDD)的等化器演算法，其中，第一階段為結合廣義多模數演算法與軟性決策運算來提升收斂的速度，當等化器收斂到一定的程度後，在由收斂偵測器(convergence detector)將等化器從第一階段切換到第二階段，第二階段等化器使用的演算法為軟性決策運算來降低穩態的均方誤差(Mean Square Error，MSE)。
在不同QAM調變系統下，藉由數學式的分析以及Matlab的模擬，將我們所設計的演算法與其他的演算法比較後，可以得到較快的收斂速度與較低的均方誤差以及在相同的訊號雜訊比(Signal to Noise Ratio，SNR)環境下也可以得到較低的符元錯誤率，因此我們所設計的兩階段式混合廣義多模數演算法與軟性決策運算為最佳的組合方式。
接著，為了要解決通信系統中傳送與接收兩端振盪頻率不同所產生的載波偏移現象，因此我們將等化器與載波回復器(carrier recovery)整合模擬，由於廣義多模數演算法與載波回復器會互相產生干擾的現象，因此將等化器演算法改良成多階模數演算法(Multi-Level Modulus Algorithm，MLMA)。整個系統主要是由等化器消除部分的通道效應與雜訊的干擾，使載波回復器有較乾淨的環境進行載波偏移補償，最後再搭配決策回授等化器(Decision Feedback Equalizer，DFE)，來得到更低的均方誤差與符元錯誤率。在整合模擬中，64QAM可補償的頻率範圍為-250kHz ~ 250kHz，256QAM可補償的頻率範圍為-150kHz ~ 200kHz，而1024QAM雖然可以收歛，不過必須先估計出載波頻率偏移約為多少的情況下，才可以有效的進行載波回復。

This thesis mainly presents the blind equalization for high-order QAM cable modem systems. By applying the blind equalization, the inverse channel impulse response can be accurately found and the amplitude and phase of the received symbols can also be corrected. Blind equalizations operate the computations and adjust equalizer coefficients without training symbols by only using received symbols. The generalized multi-modulus algorithm (Generalized Multi-Modulus Algorithm, GMMA) is an extension of the typical blind equalization algorithm, which is called the constant modulus algorithm (CMA). In order to let the equalizer have a lower symbol error rate (SER) in high-order QAM systems, we design a two-stage joint GMMA and Soft Decision-Directed (SDD) blind equalizer. In the first stage, the joint GMMA and SDD scheme is applied for the purpose of fast convergence. When the equalization approaches the threshold of convergence, the convergence detector switches the first stage equalization to the second stage equalization, where the SDD scheme is applied merely for the purpose to reduce the stable mean square error (MSE) in the second stage.
In difference QAM modulations, through the mathematical analysis and Matlab simulations, our proposed scheme can achieve faster convergence speed and lower MSE than other blind algorithms. Meanwhile, at the same signal to noise ratio (SNR) environment, our proposed equalization can also obtain lower SER than other blind algorithms.
In order to solve the carrier offset problem where the transmitter and receiver generate two different oscillation frequencies, we propose the joint adaptive equalization and carrier recovery algorithm for high-order QAM systems. Because the GMMA and the carrier recovery interfere with each other, we replace the GMMA equalization with the Multi-Level Modulus Algorithm (MLMA). By applying the MLMA equalizer to eliminate some channel effects and noise interferences, the carrier recovery loop can effectively eliminate the carrier offset, and finally a decision feedback equalizer (DFE) is also applied to obtain lower MSE and SER.

誌謝 i
中文摘要 ii
英文摘要 iii
目錄 iv
表目錄 vi
圖目錄 vii

第一章 簡介 1
1.1 動機 1
1.2 頻帶限制傳輸通道 1
1.3 多路徑效應 1
1.4 等化器 2
1.5 載波回復器 4
第二章 盲蔽式等化器相關演算法介紹 6
2.1 固定模數演算法(CMA) 7
2.2 改良式固定模數演算法(MCMA) 8
2.3 多模數演算法 10
2.3.1 多模數演算法(MMA) 10
2.3.2 廣義多模數演算法(GMMA) 11
2.4 決策運算 13
2.4.1 增強型決策運算(Enhanced DD) 14
2.4.2 軟性決策運算(SDD) 15
2.5 兩階段混合GMMA與SDD演算法 18
第三章 兩階段GMMA+SDD/SDD的效能分析 20
3.1 GMMA+SDD/SDD 穩態分析 21
3.1.1 第一階段GMMA+SDD 22
3.1.2 第二階段SDD 25
3.2 理論MSE與實驗MSE比較 26
3.2.1 64QAM 26
3.2.2 256QAM 27
3.2.3 1024QAM 28
第四章 相關演算法模擬與GMMA+SDD演算法硬體簡化 31
4.1 相關演算法的模擬與比較 32
4.1.1 64QAM 32
4.1.2 256QAM 33
4.1.3 1024QAM 34
4.2 脈波塑型濾波器與等化器組合及模擬 35
4.2.1 64QAM 36
4.2.2 256QAM 38
4.2.3 1024QAM 40
4.3 從硬體簡化GMMA+SDD演算法 41
4.3.1 GMMA+SDD演算法除法器取代 43
4.3.2 GMMA+SDD演算法exponential函數取代 45
4.4 相關演算法的浮點數與定點數模擬與比較 46
第五章 多階模數演算法(MLMA)與決策回授等化器(DFE) 53
5.1 多階模數演算法 53
5.1.1 64QAM 55
5.1.2 256QAM 56
5.1.3 1024QAM 57
5.2 決策回授等化器 58
5.2.1 64QAM 60
5.2.2 256QAM 61
5.2.3 1024QAM 62
第六章 等化器與載波回復器整合模擬 63
6.1 載波回復器架構 63
6.2等化器與載波回復器整合與模擬 68
6.2.1 64QAM 70
6.2.2 256QAM 71
6.2.3 1024QAM 73
第七章 結論與未來工作 75
7.1結論 75
7.2未來工作 75
參考文獻 76

中文參考資料
[1] 梁文軒,“應用於高階QAM調變系統之快速收斂盲蔽式等化器設計與實
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[2] 胡皓峻,“應用於高階QAM通信系統之混合廣義多模數與軟性決策快速盲蔽式等化器設計與模擬”, 國立中興大學論文, 民國98年7月
[3] 白政達,“高階QAM通信系統的盲蔽式等化器與載波回復協同設計與模擬”,國立中興大學論文，民國97年6月

英文參考資料
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