摘要
本論文探討一個再生能源的分散式估計系統。在此系統中，每個感測器量測一個共同的參數，並乘上一放大倍率後，通過正交的通道回傳至匯流中心估測。感測器將會隨機收取附近的再生能源，作為傳輸之用。由於現有電量的不確定性，將影響傳送訊號是否失真，在論文中，我們考慮三種傳送接收的架構。第一種考慮的架構是在避免訊號失真下，在現有電量不夠時，感測器不進行傳輸，匯流中心無法得知傳送資訊，感測器不進行傳輸則匯流中心收到雜訊。第二種狀況下同樣在現有電量不夠時，感測器不進行傳輸，匯流中心擁有傳送資訊，能夠知道哪些感測器未進行傳輸。第三種則在現有電量不夠時，傳送既有的最大電量，匯流中心擁有傳送資訊，能夠知道哪些感測器未進行傳輸。在論文中，我們推導了個架構下最大似然估計器的型式以及相對應的現有電量統計特性。同時，我們嘗試在第二種架構下，找尋一個較佳放大倍率，增進估測的方根差值。最後，我們根據蒙地卡羅模擬分析不同架構的趨勢。

Distributed estimation in energy-harvesting wireless sensor networks is examined in this
work. Here, each sensor takes a local measurement of the common parameter of interest
and forwards a scaled version of it to the fusion center through orthogonal channels. The
energy available for transmission at each sensor is converted from ambient energy, whose
arrival is random. Two analog forwarding transmission schemes, clipping avoidance and
best effort are proposed. Based on the information of whether the sensors transmit, we
propose three transmission-reception schemes, transmission unaware clipping avoidance
(TUCA), transmission aware clipping avoidance (TACA) and transmission aware best
effort (TABE) schemes. In TUCA and TACA, each sensor transmits only when its required
transmission energy is less than its available battery energy. Besides, in TABE, each sensor
transmits regardless of its available battery energy, in which case, clipping errors may occur.
The information of whether the sensors transmit is known by the fusion center in TACA
and TABE, but not in TUCA. The maximum-likelihood estimator is adopted at the fusion
center and is derived based on the statistics of the energy arrival process. The transmission
policy parameters of TACA are sub-optimized by average of mean square error bound. The
effectiveness of our proposed schemes is demonstrated through Monte Carlo simulations.

Abstract i
Contents ii
1 Introduction 1
2 System Model and Problem Formulation 6
2.1 Sensor Transmission Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Estimation at Fusion Center . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Maximum Likelihood Estimator for the Case with Bernoulli Energy Arrival
11
3.1 Bernoulli Energy Arrival . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Scheme I: Transmission Unaware Clipping Avoidance . . . . . . . . . . . . . 15
3.3 Scheme II: Transmission Aware Clipping Avoidance . . . . . . . . . . . . . . 17
3.4 Scheme III: Transmission Aware Best Effort . . . . . . . . . . . . . . . . . . 18
3.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Transmission Policy Parameters Optimization 22
4.1 Amplifying Factor Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 TACA Amplifying Factor Optimization . . . . . . . . . . . . . . . . . 25
4.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Conclusion 31
6 Appendix 32
6.1 Markov process static state probability . . . . . . . . . . . . . . . . . . . . . 32
6.2 Derivation for probability density function of transmission unaware clipping
avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.3 Derivation for the differentiation of PDF of transmission unaware clipping
avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.4 Derivation for probability density function of transmission aware clipping
avoidance) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6.5 Derivation for the differentiation of PDF of transmission aware clipping avoidance
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.6 Derivation for probability density function of transmission aware best effort 40
6.7 Derivation for the differentiation of PDF of transmission aware best effort . 42
6.8 Expansion of the PDF of of transmission aware best effort . . . . . . . . . . 46
6.9 CRLB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.10 Derivation for fisher function of transmission aware clipping avoidance . . . . 48
6.11 Derivation of theta expectation in BCRB . . . . . . . . . . . . . . . . . . . . 49
6.12 Derivation of fisher function with parameter observation . . . . . . . . . . . 50

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