臺灣博碩士論文加值系統

這篇論文主要目的是利用數學的方式來分析多重模數盲蔽等化(blind equalization)演算法應用在非正方形(non-square)信號星狀圖的正交振幅調變。主要的分析將針對於兩種非正方形信號星狀圖做研究 : 一、我們提出一種增益控制補償方法改善使用多重模數盲蔽等化演算法用在交叉信號星狀圖(cross signal constellations)的正交振幅調變之效能。這種方法可以改善載子相位回復因此可以比原始使用多重模數盲蔽等化演算法用在交叉信號星狀圖的正交振幅調變較為降低符號錯誤率(SER)。二、根據長方形信號星狀圖分析結果顯示,使用多重模數盲蔽等化演算法用在長方形信號星狀圖上似乎會比用在交叉信號星狀圖好,雖然我們知道前者需要比後者多付出一些平均傳輸功率。分析亦指出使用長方形的星狀圖沒有任何的不想要的最小值(undesirable minimum)並且因為長方形星狀圖的鞍點比交叉星狀圖和正方形星狀圖少所以長方形星狀圖也較少被鞍點(saddle points)吸引的機率。

This thesis mathematically analyzes a multimodulus blind equalization algorithm (MMA) for non-square quadrature amplitude modulation (QAM) signal constellations. The analyses will focus on two different non-square constellations: i) we propose a gain control (GC) compensation scheme that improves the performance of a multimodulus blind equalization algorithm for cross QAM signal constellations. The scheme may improve carrier-phase recovery, which in turn generates a lower symbol-error rate (SER) than the original MMA for cross QAM signal constellations. ii) The analysis of rectangular constellations indicates that the MMA that uses non-square rectangular constellations may be better able to recover the phase rotation introduced by channels than the MMA that uses the cross constellations, although the former is known to require more average transmitted power than the latter two. The analysis also demonstrates that the MMA that uses non-square rectangular constellations does not have any undesirable minimum and may be less likely attracted to saddle points than the MMA that uses both square and cross constellations, because the former has fewer saddle points than the latter two constellations.

Abstract (in Chinese) i
Abstract ii
Contents...………………………………………………………….……………………..………...iii
List of tables v
List of figures vi
1. Introduction to Blind Channel Equalization 1
1.1 The Baseband Equivalent Model 2
1.2 The Channel Model 3
1.3 Constant Modulus Algorithm (CMA) 5
1.4 Multiple Modulus Algorithm (MMA) 8
1.5 Non-Square Constellations 11
2. Analysis of the Multimodulus Blind Equalization Algorithm for Non-Square Cross QAM Signal Constellations 15
2.1 Stationary points of MMA for QAM Cross Constellations 17
2.1.1 MMA Cost Function for QAM Cross Constellations 17
2.1.2 Stationary Points of MMA for Cross Constellations 19
2.1.3 Saddle Points and Desired Global Minima 22
2.2 Proposed Gain Control for Compersion 26
2.3 Computer Simulations 28
3. Analysis of the Multimodulus Blind Equalization Algorithm for Non-Square Rectangular QAM Signal Constellations 46
3.1 MMA Cost Functions Using Non-Square Constellations 48
3.1.1 General Formulation of MMA Cost Function 48
3.1.2 MMA Cost Function of Non-Square Rectangular Constellations 48
3.2 Analysis of MMA Using Rectangular Constellations 51
3.2.1 Stationary Points of MMA Using Rectangular Constellations 51
3.2.2 Unstable Equilibria of the MMA when 54
3.2.3 Phase-Tracking capability 55
3.2.4 Desired Global Minima and Unstable equilibria of MMA for Non-Square Rectangular Constellations when M = 1 63
3.3 Computer Simulations 67
4. Conclusions 78
References 81
Appendix A 83

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