在過去的文獻中, 大部分分散式檢測的發展主要是基於在固定樣本數的測試規範之下. 然而, 在現實情況下, 連續測試更適合被使用, 由於它可以利用比較少的樣本數並且達
到與固定樣本大小測試相同的檢測效能。因此, 此篇論文將提出一個新的分散式連續檢測方法可以應用在無線傳感器網絡(WSNs) 和認知無線電(CRS)。首先, 連續性的檢測已經在1994年被Wald 提出, 就是著名的順序概率比檢驗(SPRT)。而SPRT 也確切被證明是能減少所需的平均樣本數或降低平均檢測時間。實際上, 當觀測樣本是獨立的和相同的分佈(IID) 時, 若給定限制的錯誤警報機率以及失誤偵測的概率, 則SPRT 在於減少所需要的樣本數量將會是一個最佳的順序檢測。然而, 如果觀察樣品是不相同的分佈, 通過模擬的結果證明,SPRT 將不會是一個最佳的測試方法。基於啟發式的方法, 本論文將開發了一種新的分佈式檢測方案基於排序的樣品。最後, 可以由模擬結果來說明, 本論文所提出的方法比起傳統的SPRT 可以更進一步減少最後決策所需要的樣本數量。

In the literature, most distributed detection developed so far mainly focuses on the test rule based on fixed sample size. However, in the real situations, sequential tests are more suitable to be utilized since it might achieve the same detection performance by using fewer number of samples as compared with the fixed-sample-size test. Thus, this theses will propose a new distributed sequential detection approach for the applications in wireless sensor networks(WSNs) and cognitive radios(CRs). First we refer to the sequential detection, and it has been developed by Wald in 1994, which is well known as the sequential probability ratio test (SPRT). The SPRT is proved to be able to decrease the required average sample numbers or reducing the average detection time. Indeed, the SPRT is the optimal sequential detection in terms of the minimizing the required number of samples given the constraint of false alarm and miss probabilities when the observation samples are independent and identical distributed (i.i.d.). However, if the observation samples are not dentically distributed, by simulation results show that the SPRT is not the optimal test. Based on a heuristic approach, this thesis then developed a new distributed detection scheme based on the sorted samples. Finally , the simulation results obtained by this thesis shows that the proposed scheme can further reduce the number of samples required for making the final decision as compared with SPRT.

Contents
1. Introduction ...4
2. Sequential Detection : Wald’s Test ...7
3. System Model...12
4. Simulation Result ...17
5. Conclusion ...26
6. Reference...27

[1] T. Rappaport, Wireless Communications: Principles and Practice. Upper Saddle River:
NJ: Prentice-Hall, 1996.
[2] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood
Cliffs: NJ: Prentice-Hall, 1993.
[3] R. N. M. A. D. Whalen, Detection of Signals in Noise. New York: Academic Press, 1971.
[4] F. L. LEWIS, Wireless Sensor Networks1. Smart Environments, 2004.
[5] A. Wald, “Sequential tests of statistical hypotheses,” vol. 16, no. 2, pp. 117–186, Mar 1945.
[6] A. J. Jerri, “The shannon sampling theorem - it’s various extensions and applications: A
tutorial review,” Proceeding of IEEE, vol. 65, no. 11, pp. 1565–1596, July 1989.
[7] K. S. Fu, Sequential Methods in Pattern Recognition and Machine Learning. New York:
Academic Press, 1986.
[8] A. Qiyue Zou; Songfeng Zheng; Sayed, “Cooperative sensing via sequential detection,” Signal Processing, IEEE Transactions on, vol. 58, no. 12, p. 18, Dec. 2010.
[9] E. L. Lehmann., Testing Statistical Hypotheses. New York: Wiley, 1986.
[10] S. Zacks, Parametric Statistical Inference. Oxford: Pergamon Press, 1981.
[11] I. JULIAN J.BUSSGANG, SENIOR MEMBER, “Sequential methods in radar detection,”
PROCEEDINGS OF THE IEEE, vol. 58, no. 5, p. 16, MAY 1970.
[12] H. . S. E. Fleisher, S. ; Singh, “A generalized two-threshold detection procedure,” Information
Theory, IEEE Transactions on, vol. 34, no. 11, p. 347, Mar 1988.