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研究生(外文):Che-Ming Kuo
論文名稱(外文):Low-Complexity Remote Compressive Sensing Schemes for Machine-to-Machine Networks with Stochastic Sources
外文關鍵詞:Machine-to-Machine networksCapillary networksCompressive sensingPower exponential modelsStrictly sub-Gaussian random variables
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在最近幾年,互聯網 (M2M) 被廣泛應用於無限通訊系統中。機器本身會有功率限制,處理和通訊能力也都會有限。壓縮感測技術可以避免傳多餘的資訊出去,進而降低傳輸功率。在此篇論文中,在雙層架構下,我們於互聯網中針對隨機訊號源提出一個遠程的壓縮感知架構,目的是要省閘道 (gateway) 的傳輸功率,並且我們將原本問題簡化成隨機壓縮感知的問題。進一步,針對訊號源我們選擇一個非常實用的共變異數矩陣 (covariance matrix),並且驗證指數遞減的性質。最後,和目前已被驗證效能可以很好的高斯 (Gaussian),伯努力(Bernoulli) 感知矩陣做比較,我們選擇一個低複雜度的感知矩陣應用於我們所提出的的系統中,並且驗證我們所選擇的這個感知矩陣可以達到傳統訊號傳輸所能達到的最佳效果。

In recent years, machine-to-machine (M2M) networks are widely considered in wireless communication system. Machines typically have constrained power, and their processing and communication capabilities are limited. Compressive sensing is especially useful for avoiding the redundant information to be transmitted such that the transmission power can be reduced. In this thesis, under the two-tier architecture, to begin with, we propose remote compressive sensing schemes for M2M networks with stochastic sources to save the transmission power at the gateway, and simplify the original problems to the stochastic compressive sensing problems. Furthermore, we select a very practical covariance matrix model of the sources, and verify the power low property. Finally, comparing with the sensing matrices such as Gaussian and Bernoulli sensing matrices that have been verified to have good performances, we select a low-complexity sensing matrix to apply to the proposed systems, and we have verified that the selected sensing matrix can achieve the optimal MMSE sense in the traditional signal transmission.

1 Introduction ... 1
1.1 Machine-to-Machine Networks ... 1
1.2 Compressive Sensing ... 3
1.3 Contributions ... 6
1.4 Notations ... 6

2 System Model ... 7
2.1 Proposed Remote Compressive Sensing Schemes for Machineto-Machine Networks with Stochastic Sources ... 8
2.2 Problem Formulations ... 10

3 Stochastic Compressive Sensing for Gaussian Signals ... 14
3.1 The Optimal Decoder for Gaussian Signals ... 15
3.2 Power Law for Stochastic Compressive Sensing ... 15
3.2.1 Exponential Decay for Power Exponential Models ... 17
3.2.2 Checking Power Law for Gaussian Signals ... 24
3.3 Selected Low-Complexity Sensing Matrix ... 25
3.4 Analysis of the Average Reconstruction Error ... 32
3.4.1 Mean Square Error ... 34
3.4.2 Mean Absolute Error ... 39

4 Simulation Results ... 43
4.1 Simulation Environment ... 43
4.2 Performance Comparison ... 43
4.2.1 Comparison between Stochastic Compressive Sensing
and Conventional Compressive Sensing ... 43
4.2.2 Stochastic Compressive Sensing ... 47
4.2.3 Remote Compressive Sensing ... 50

5 Conclusions ... 56

6 Future Works ... 58
6.1 Problems Formulation 1 ... 60
6.2 Problems Formulation 2 ... 65

Bibliography ... 67

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