검색 상세

최적의 컨트롤 파라미터를 이용한 분산 적응신호처리 알고리즘에 관한 연구

Distributed Adaptive Signal Processing Algorithms with Optimal Control Parameters

이한솔 (Han-Sol Lee, 포항공과대학교)

원문보기

초록 moremore
In this thesis, we develop novel algorithms which deal with a distributed estimation problem. The goal of the distributed estimation problem is to estimate a common vector from measurements of a sensor network whose sensor is distributed over a geographical region. In this regard, a diffusion LMS al...
In this thesis, we develop novel algorithms which deal with a distributed estimation problem. The goal of the distributed estimation problem is to estimate a common vector from measurements of a sensor network whose sensor is distributed over a geographical region. In this regard, a diffusion LMS algorithm has been proposed and its variants have been developed recently. Among them, we focus on controlling user parameters of the diffusion LMS algorithm to enhance the adaptation capabilities. We first propose a novel variable step-size diffusion LMS algorithm which adjusts step sizes across the network. Each variable step size is derived to achieve the minimum mean square deviation of an intermediate estimate. The algorithm thus adapts the different node environments and profiles across the networks, and requires relatively less user interaction than existing algorithms. In experiments, the algorithm achieves both fast convergence speed and low misadjustment by remarkable improvement in an adaptation stage. We analyze the mean square performance of the proposed algorithm. Also, the proposed algorithm works well even in non-stationary environments. We also propose a new diffusion LMS algorithm that utilizes adaptive gains in the adaptation stage for the sparse distributed estimation problem. We derive the optimal gains that attain a minimum mean square deviation and also propose an adaptive gain control method from it. Computationally efficient gain control method is also derived. We provide the mean stability analysis to establish a sufficient condition for the algorithm to converge in the mean sense and also perform the mean square performance analysis. The algorithm achieves higher convergence speed than the sparsity-constrained algorithms, regardless of the sparsity of the vector of interest.
목차 moremore
Notation 1
1 Introduction 2
1.1 Introduction 2
...
Notation 1
1 Introduction 2
1.1 Introduction 2
1.2 Application of the Distributed Estimation Problem . 3
1.2.1 Moving-Average Model 3
1.2.2 Collaborative Spectral Sensing 5
1.2.3 Distributed Beamforming 8
1.3 Scope of Thesis 12
1.4 Thesis Outline 16
2 Diffusion LMS Algorithm 19
2.1 Introduction 19
2.2 Centralized Solution 20
2.2.1 Global Cost Function and Optimal Solution 20
2.2.2 Global Iterative Solution 20
2.3 Local Solution 22
2.3.1 Local Cost Function and Optimal Solution 22
2.3.2 Local Iterative Solution 22
2.4 Diffusion Strategy 23
2.4.1 Cost Function and Steepest Descent Solution 24
2.4.2 Diffusion LMS Algorithm 26
3 A Variable Step-size Diffusion LMS Algorithm 31
3.1 Introduction 31
3.2 Conventional Variable Step-size Diffusion LMS Algorithms 32
3.3 Proposed algorithm 34
3.3.1 An Optimal Step-size 34
3.3.2 Proposed VSS Diffusion LMS Algorithm 35
3.4 Mean Square Performance Analysis 39
3.4.1 Assumptions 39
3.4.2 Signal Modeling 42
3.4.3 Transient Analysis 43
3.4.4 Steady-state Analysis 48
3.5 Simulation Results 51
3.5.1 Stationary environments 53
3.5.2 Non-stationary environments 60
3.6 Summary 64
4 Sparseness Exploiting Diffusion LMS Algorithm 65
4.1 Introduction 65
4.2 Conventional Algorithm 66
4.3 Proposed Algorithm 68
4.3.1 Optimal Gain 68
4.3.2 Practical Implementation 72
4.3.3 Simplified Algorithm 74
4.4 Performance Analysis of the Proportionate Diffusion LMS Algorithm 78
4.4.1 Assumptions 78
4.4.2 Signal Modeling 79
4.4.3 Mean Stability 81
4.4.4 Mean Square Performance Analysis of the z2-proportionate Diffusion LMS Algorithm 82
4.5 Simulation Results 89
4.6 Summary 98
5 Conclusion 99
Appendices 101
A Derivation of (3.12) 101
B Effect of Different Forgetting Factors 102
C Derivation of (4.10) 104
D Solution of (4.15) 108
References 111