跳頻無線電系統之低複雜度盲蔽式頻率及轉換時間估測演算法

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傅國清(Kuo-Ching Fu) 查詢紙本館藏

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通訊工程學系

論文名稱

跳頻無線電系統之低複雜度盲蔽式頻率及轉換時間估測演算法
(Reduced Complexity Blind Frequency and Transition Time Estimation in Frequency Hopping Systems)

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摘要(中)

在跳頻轉換時間及頻率估測演算法中，最大相似演算法(Maximum Likelihood)中通常有較佳的估測效能，然而其缺點為計算複雜度較高。為了解決這個問題，一個基於兩個跳頻模型(Two-Hop Model)的疊代(Iteration)演算法被提出來用來降低計算複雜度[37]，這個方法看起來很棒，並且得到一個不錯的結果，但由於其推導的方程式中包含了多個零點，並且由於其疊代方法需要設定初始值，如此可能造成錯誤估測至其它零點而產生收斂性問題。此外，一般跳頻頻率估測方法並未考慮到頻率轉換時間接近邊界(Boundary)的問題（即在兩個接收到的頻率中，一個頻率取樣個數較多，另一個頻率取樣個數較少的狀況），由於跳頻頻率及轉換時間對接收端來說為未知，因此若取樣的待估測資料區塊，其訊號轉換時間接近邊界，便產生了取樣個數不平衡(Unbalance)的狀況，在這種情境下，取樣個數較少的頻率估測效能將會嚴重下降。
在第一個方法中，我們提出訊號子空間架構運用在最大相似函數法則上，在不需要參考訊號的情況下，用來估測頻率及跳頻轉換時間。我們也討論了相關參數該如何選定。另外，我們利用資料區塊選擇演算法(Block Selection Algorithm)來解決了現存方法中取樣頻率訊號不平衡所造成誤差變大的問題。傳統搜尋式(Greedy Search)最大相似演算法相比，所提的方法大量降低了計算複雜度。並且在計算複雜度類似的情況下，與已知的疊代式最大相似演算法（Iterative ML-Based Algorithm）相比，估測效能很明顯有較好的表現。
在第二種方法當中，我們利用交互投影的概念(Alternative Projection)，將多變數搜尋問題降低為單一變數搜尋問題，這種方法不需要同時搜尋時間及頻率等多個變數，因此大大降低了計算複雜度。同樣地，所提出的方法仍然考慮到頻率轉換時間接近邊界(Boundary)的問題，利用交互投影方法一次估測一個參數的特性，將不平衡的資料區塊調整至平衡的狀態，這樣作的好處是不管我們截收到的訊號是否處於平衡狀態，估測效能都能達到一致。相反地，傳統方法中只要是在不平衡的狀態下，則無法有效估測其中一個頻率及轉換時間。我們所提的方法可以進一步運用在追蹤上面，特別是前一區塊追蹤到的參數亦可以用於下一個區塊的估測當中，所以可以進一步降低計算複雜度。模擬結果也顯示，此方法的估測效能在平衡狀況下，與傳統最大相似貪婪搜索演算法方式效能相當，同時也與推導出的Cramer-Rao下限接近。而在不平衡的狀況下，我們所提的方法更能突顯出強健性
第三個方法使用疊代分解及結合演算法(Iterative Disassemble and Assemble, IDNA)，所提方法與一般疊代演算法不同的是不需要設定初始值，因為不適當的初始值可能造成錯誤地收斂至局部最大值(Local Maximum)而非全域最大值，所提方法可以收斂至全域最大值(Global Maximum)，這個方法是利用類似分治法(Divide And Conquer)的概念，將一個高階多項式函式分解成許多單項式函式，並且將這些單項式函式疊代計算，最後將這些結果結合而成。這個方法計算複雜度遠低於最大相似貪婪搜索演算法，並且能保持住一定的效能。除此之外，我們的方法可以進一步利用近似的方式來降低計算複雜度。

摘要(英)

Frequency hopping spread spectrum (FHSS) is a technology for combating narrow band interference. Two important parameters required for estimation in FHSS are transition time and hopping frequency. We proposed three algorithms for estimating transition time and hopping frequency in FHSS.
In the first algorithm, blind subspace-based schemes with a maximum likelihood (ML) criterion for estimating frequency and transition time without using reference signals are proposed. The selection of the related parameters is discussed. Subspace-based algorithms are applied with the help of the proposed block selection scheme. The performance is improved with a block selection algorithm (BSA) to overcome the unbalanced processing block problems in various algorithms. The proposed method significantly reduces computational complexity compared with a greedy search ML-based algorithm. The performance is shown to outperform an existing iterative ML-based algorithm with a comparable complexity.
Another proposed algorithm uses the concept of the alternative projection algorithm, which reduces a multi variable search problem to a single variable search problem. The proposed algorithm does not require the simultaneous search of all times and frequencies. Therefore, the computation complexity is reduced tremendously. The scheme is robust in the sense that it can avoid the unbalanced sampling block problem that occurs in existing maximum likelihood-based schemes. The unbalanced sampling block problem would cause large errors in one of the estimates of frequency. The proposed scheme has a lower computational cost than the maximum likelihood-based greedy search method. The estimated parameters are also used for the subsequent time and frequency tracking.
The third proposed algorithm presents a blind scheme for estimating frequency and transition time in an iterative fashion: the iterative disassemble and assemble (IDNA) algorithm. The algorithm is developed on the basis of the “divide and conquer” approach. The proposed scheme disassembles a high order polynomial into several monomial functions. The solutions for the monomial functions are calculated iteratively, and are then assembled into a final estimation result. The proposed scheme does not require initial random guesses as with common iterative algorithms. Improper initial guesses may suffer from the problem of convergence to the local maximum. The proposed approach can converge to the global maximum in order to achieve the solution. The proposed scheme offers a much lower computational complexity than that of the maximum likelihood greedy search algorithm. Moreover, it also outperforms existing schemes with a comparable complexity. Moreover, an approximation version of the proposed scheme is derived and can be used to further reduce the computational complexity.

關鍵字(中)

★ 頻率估測
★ 同步
★ 跳頻
★ 展頻
★ 疊代
★ 分治法
★ 盲蔽式估測
★ 最大似然估測

關鍵字(英)

★ Frequency estimation
★ synchronization
★ frequency hopping
★ spread spectrum
★ iterative
★ blind estimation
★ maximum likelihood (ML)

論文目次

中文摘要 ii
Abstract iv
致謝 vi
List of Contents vii
List of Figures ix
List of Tables xi
List of Notations and Symbols xii
Chapter 1. Introduction 1
Chapter 2. Subspace-based Algorithms for Blind ML Frequency and Transition Time Estimation in Frequency Hopping Systems 6
2.1 Signal Model and Problem Formulation 6
2.2 Subspace-Based Schemes for Reduced Complexity ML-Based Estimation 9
2.2.1 ML-Based Exhaustive Search Methods with Frequency Scanning Vectors 10
2.2.2 Reduced Complexity Processing Schemes with Subspace-Based Estimation Algorithm 11
2.3 Proposed Block Selection Algorithm 13
2.4 Analysis of Computational Complexity 15
2.5 Simulation Results 18
2.5.1 Balanced-Block Scenario: 18
2.5.2 Unbalanced-Block Scenario with The Block Selection Algorithm: 21
Chapter 3. Robust Blind Frequency and Transition Time Estimation for Frequency Hopping Systems by Using Alternative Projection Algorithm 26
3.1 Proposed Estimation Algorithm Based on Maximum Likelihood Principle 27
3.1.1 Synchronization Phase 27
3.1.2 Robust Estimation in the Synchronization Phase 29
3.1.3 Tracking Phase 33
3.1.4 Algorithm Summary 34
3.2 Analysis of Computational Complexity 36
3.3 Simulations Results 38
Chapter 4. Blind Iterative ML-based Frequency and Transition Time Estimation for Frequency Hopping Systems 50
4.1 Proposed Iterative Disassemble and Assemble (IDNA) Algorithm 51
4.1.1 Analysis of the Nonlinear Objective Function 51
4.1.2 The Proposed IDNA Algorithm for Frequency Estimation 56
4.2 Reduced Computational Complexity for the Iterative Frequency Updating Scheme and an Approximation Method 61
4.3 Algorithm Summary 63
4.4 Analysis of Computational Complexities 65
4.5 Simulations Results 66
Chapter 5. Conclusion 77
References 79
Appendix 84
Appendix A. Derivation of Multiroots in (2.10) and (2.11) 84
Appendix B. Derivation of (2.13) 86
Appendix C. The Cramer Rao Lower Bound (CRLB) for the Balanced Block 87

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指導教授

陳永芳(Yung-Fang Chen)

審核日期

2013-7-29

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