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.

[1] I. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey on sensor networks,”
IEEE Commun. Mag., vol. 40, no. 8, pp. 102–114, 2002.
[2] J. Yick, B. Mukherjee, and D. Ghosal, “Wireless sensor network survey,” Comput.
Networks, vol. 52, no. 12, pp. 2292–2330, 2008.
[3] S. Cui, J.-J. Xiao, A. Goldsmith, Z.-Q. Luo, and H. Poor, “Estimation diversity and
energy efficiency in distributed sensing,” IEEE Trans. Signal Process., vol. 55, no. 9,
pp. 4683–4695, 2007.
[4] D. Steingart, “Power sources for wireless sensor networks,” in Energy Harvesting Technologies.
Springer US, 2009, pp. 267–286.
[5] J. A. Paradiso and T. Starner, “Energy scavenging for mobile and wireless electronics,”
IEEE Pervasive Comput., vol. 4, no. 1, pp. 18–27, 2005.
[6] S. Sudevalayam and P. Kulkarni, “Energy harvesting sensor nodes: survey and implications,”
IEEE Commun. Surveys & Tutorials, vol. 13, no. 3, pp. 443 – 461, 2011.
[7] O. Ozel, K. Tutuncuoglu, J. Yang, S. Ulukus, and A. Yener, “Transmission with energy
harvesting nodes in fading wireless channels: Optimal policies,” IEEE J. Sel. Areas
Commun., vol. 29, no. 8, pp. 1732–1743, 2011.

[8] A. Kansal, J. Hsu, S. Zahedi, and M. B. Srivastava, “Power management in energy
harvesting sensor networks,” ACM Trans. Embed. Comput. Syst., vol. 6, no. 4, 2007.
[9] R. Rajesh, V. Sharma, and P. Viswanath, “Information capacity of energy harvesting
sensor nodes,” in IEEE ISIT, 2011, pp. 2363–2367.
[10] D. Niyato, E. Hossain, and A. Fallahi, “Sleep and wakeup strategies in solar-powered
wireless sensor/mesh networks: Performance analysis and optimization,” IEEE Trans.
Mobile Computing, vol. 6, no. 2, pp. 221–236, 2007.
[11] B. Medepally and N. B. Mehta, “Voluntary energy harvesting relays and selection in
cooperative wireless networks,” IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3543
– 3553, 2010.
[12] A. Ribeiro and G. B. Giannakis, “Bandwidth-constrained distributed estimation for
wireless sensor networks-part I: Gaussian case,” IEEE Trans. Signal Process., vol. 54,
no. 3, pp. 1131 – 1143, 2006.
[13] S. Cui, J.-J. Xiao, A. J. Goldsmith, Z.-Q. Luo, and H. V. Poor, “Estimation diversity
and energy efficiency in distributed sensing,” IEEE Trans. Signal Process., vol. 55, no. 9,
pp. 4683 – 4695, 2007.
[14] J. Li and G. AlRegib, “Distributed estimation in energy-constrained wireless sensor
networks,” IEEE Trans. Signal Process., vol. 57, no. 10, pp. 3746 – 3758, 2009.
[15] C. Huang, Y. Zhou, T. Jiang, P. Zhang, and S. Cui, “Power allocation for joint estimation
with energy harvesting constraints,” in IEEE ICASSP, 2013, pp. 4804–4808.
[16] A. Nayyar, T. Basar, D. Teneketzis, and V. V. Veeravalli, “Optimal strategies for communication
and remote estimation with an energy harvesting sensor,” IEEE Trans.
Autom. Control, vol. 58, no. 9, pp. 2246 – 2260, 2013.

[17] Y. Zhao, B. Chen, and R. Zhang, “Optimal power allocation for an energy harvesting
estimation system,” in IEEE ICASSP, 2013, pp. 4549 – 4553.
[18] B. K. Chalise, Y. D. Zhang, and M. G. Amin, “Energy harvesting in an OSTBC based
amplify-and-forward MIMO relay system,” in IEEE ICASSP, 2012, pp. 3201 – 3204.
[19] M. Avriel, Nonlinear Programming: Analysis and Methods. Courier Dover, 2003.
[20] J. Dauwels, “Computing bayesian cram´er-rao bounds,” in IEEE ISIT, 2005, pp. 425 –
429.
[21] H. Van Trees, Detection, Estimation, and Modulation Theory: Part I. Wiley, 2004.
[22] J. Tabrikian and J. Krolik, “Efficient computation of the bayesian cramer-rao bound
on estimating parameters of markov models,” in IEEE ICASSP, 1999, pp. 1761–1764
vol.3.
[23] H. Messer, “The hybrid cramer-rao lower bound - from practice to theory,” in IEEE
Workshop on Sensor Array and Multichannel Processing, 2006, pp. 304–307.
[24] A. Wachter and L. T. Biegler, “On the implementation of an interior-point filter linesearch
algorithm for large-scale nonlinear programming,” Mathematical Programming,
vol. 106, no. 1, pp. 25–57, 2006.
[25] J. J. Mor´e and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,”
ACM Trans. Math. Softw., vol. 20, no. 3, pp. 286–307, 1994.
[26] S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory.
Prentice Hall, 1993.