臺灣博碩士論文加值系統

在無線感測網路中，當感測節點在空間中平均分佈的時候泊松節點程序可以良好的模擬他們的位置及數量，然而因為地理因素，節點分佈在環境發生點周遭區域形成群集分佈的情形是很常見的，因此在這情況下，泊松節點程序不再能對此分佈提供精準的模型，這啟發了我們使用泊松群集程序來模擬這些感測節點。在此篇論文中，我們設定每個節點的傳輸能量大小一致，通道為瑞利衰落，並且考慮了兩個情境，在第一個情境裡我們設置資料收集點為一個與感測節點互相獨立的泊松節點程序，並結合之前參考文獻的結果，我們推導提供了傳輸成功機率以及平均傳輸量的積分表示式和他們各自的下界。從模擬以及分析結果我們發現這個情境設定下的系統表現很差且很沒有效率，因此我們在第二個情境裡把資料收集點擺放在感測節點形成的群集中心，也就是泊松群集程序的母程序，在這個情境我們是第一個推導出此情境的干擾拉普拉斯轉換和傳輸者及接收者間的距離的機率密度函數，我們也推導出了此情境下的傳輸成功機率和平均傳輸量的下界，最後從模擬分析圖中可以明顯觀察到第二個情境的效能是遠大於第一個情境的，也代表我們這個改動是正確且有效的。

In wireless sensor networks, the homogeneous Poisson Point Process (PPP)
assumption holds when the sensor nodes are uniformly distributed in space. However,
due to geographic factors, it may be common for sensor nodes to cluster
around some region where the physical or environmental conditions often occur.
Therefore, the PPP assumption does not provide an accurate model for the interference
in these conditions. This motivates the need to characterize the SINR
of wireless sensor networks when the nodes are clustered. Due to the cluster
property, we use Poisson Cluster Process (PCP) to model the location of sensor
nodes. In this thesis, we set the transmission power of each node the same, fading
is modeled as Rayleigh. We consider two kinds of sensor networks. In the first
one, the data collectors are randomly deployed and follow another PPP, which is
independent to the PPP sensor nodes following. Combining some mathematical
models from reference papers, we provide numerically integrable expression for the
success probability and the average achievable rate, and some lower bounds. From
both the analytic and simulation results, we found the performance of this setting
of the position of each data collectors is bad and inefficient. This inspires us to
deploy the data collectors on the center of the cluster distribution of the PCP, that
is, the parent process in the PCP. In this scenario, the interference model and the
probability density function of the distance between the transmitter and receiver
proposed from the reference papers are not applicable. As a consequence, we analyze
these mathematical formulas by ourselves and to the best of our knowledge
we are the first to provide these formulas. We also provide numerically integrable
expression for the success probability and the average achievable rate, and some
lower bounds for this scenario. The results outperform the setting that data collectors
are randomly deployed on these metrics we concerned.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1
CHAPTER 2 BACKGROUND AND RELATED WORK . . . . . 3
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Stochastic Geometry . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Poisson Point Process . . . . . . . . . . . . . . . . . . . . . 4
2.1.3 Probability Generating Functional . . . . . . . . . . . . . . 5
2.1.4 Palm Distribution . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.5 Neyman-Scott cluster processes . . . . . . . . . . . . . . . . 8
2.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . 9
2.2.2 Wireless Sensor Networks with Poisson Cluster Process . . 10
CHAPTER 3 SYSTEM MODEL AND ASSUMPTION . . . . . . 13
3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Random Deployment of Data Collectors . . . . . . . . . . . 13
3.1.2 Data collector located in cluster center . . . . . . . . . . . 14
3.2 Success Probability for Nakagami-m Fading . . . . . . . . . . . . . 15
CHAPTER 4 RANDOM DEPLOYMENT OF DATA COLLECTORS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1 Probability Density Function of kzk . . . . . . . . . . . . . . . . . 17
4.2 Laplace Transform of The Interference . . . . . . . . . . . . . . . . 17
4.2.1 Tighter Lower Bound . . . . . . . . . . . . . . . . . . . . . 17
4.2.2 Closed-form Lower Bound . . . . . . . . . . . . . . . . . . . 22
4.3 Success Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.4 Average Achievable Rate . . . . . . . . . . . . . . . . . . . . . . . 27
CHAPTER 5 DATA COLLECTORS LOCATED IN CLUSTER
CENTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.1 Probability Density Function of kzk . . . . . . . . . . . . . . . . . 29
5.2 Laplace Transform of The Interference . . . . . . . . . . . . . . . . 32
5.2.1 Probability Generating Functional . . . . . . . . . . . . . . 32
5.2.2 Mathematical Expression for the Laplace Transform of Interference
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.2.3 The Closed-Form Lower Bound . . . . . . . . . . . . . . . . 39
5.3 Success Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 44
CHAPTER 6 PERFORMANCE EVALUATION . . . . . . . . . . 50
6.1 Evaluation for the Mathematical Lower Bound . . . . . . . . . . . 50
6.1.1 Random Deployment of Data Collectors . . . . . . . . . . . 50
6.1.2 Data Collectors Located in Cluster Center . . . . . . . . . 53
6.2 Some Discussions for Poisson Cluster Process . . . . . . . . . . . . 55
CHAPTER 7 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . 58

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