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Modeling End-to-end Distance for Given Number of Hops in Dense Planar Wireless Sensor Networks

Modeling End-to-end Distance for Given Number of Hops in Dense Planar Wireless Sensor Networks. April. 2013 Chan- Myung Kim LINK@KoreaTech http://link.koreatech.ac.kr. ABSTRACT.

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Modeling End-to-end Distance for Given Number of Hops in Dense Planar Wireless Sensor Networks

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  1. Modeling End-to-end Distance for Given Number of Hops in Dense Planar Wireless Sensor Networks April. 2013 Chan-Myung Kim LINK@KoreaTech http://link.koreatech.ac.kr

  2. ABSTRACT • We model the end-to-end distance for a given number of hops in dense planar Wireless Sensor Networks in this paper. • We derive that the closed-form formula for single hop distance and postulate Beta distribution for 2-hop distance. • When the number of hops increases beyond three, the multihop distance approaches Gaussian. • Our error analysis also shows the distance error is be minimized by using our model. LINK@KoreaTech

  3. INTRODUCTION AND MOTIVATION • In Wireless Sensor Networks (WSN), knowledge of node location is often required in many applications. • Generally, the distances from a node with unknown location to several anchor nodes are estimated, and then a multilateration is applied to estimate the node location. • For those applications where the sensor nodes are overdensely deployed, the distance between the nodes are short and the variance of such distance is also small. • Therefore, it is quite promising to estimate the end-to-end distance based on the number of hops. • In this paper, we study the hopdistance relation in the planar WSN. LINK@KoreaTech

  4. PRELIMINARIES • A. Skewness and Kurtosis • Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or sample set, is symmetric if it looks the same to the left and right of the center point. LINK@KoreaTech

  5. PRELIMINARIES • A. Skewness and Kurtosis • Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. LINK@KoreaTech

  6. PRELIMINARIES • B. Chi-Square Test • Chi-square test is widely used to determine the goodness of fit of a distribution to a set of experimental data. LINK@KoreaTech

  7. MODELING END-TO-END DISTANCE FOR GIVEN NUMBER OF HOPS • A. Problem Formulation • Firstly, our study on end-to-end distance for given number of hops is based on local coordinate system, which could be translated into a global coordinate system if enough nodes in the local coordinate system have known global coordinates. • Secondly, we assume the beacon packets are distributed in an ad hoc fashion. Under such circumstances, we have to assume the beacon packets are simply flooded throughout the sensor network LINK@KoreaTech

  8. MODELING END-TO-END DISTANCE FOR GIVEN NUMBER OF HOPS • A. Problem Formulation • The problem of interest is to find the distance from a specific node to the anchor given this node is within i hops from the anchor. LINK@KoreaTech

  9. MODELING END-TO-END DISTANCE FOR GIVEN NUMBER OF HOPS • B. Single-Hop Case • The problem of interest is to find the distance from a specific node to the anchor given this node is within i hops from the anchor. • And the conditional mean and variance are 2R/3 and R^2/18, respectively, LINK@KoreaTech

  10. MODELING END-TO-END DISTANCE FOR GIVEN NUMBER OF HOPS • C. Two-Hop Case • . LINK@KoreaTech

  11. MODELING END-TO-END DISTANCE FOR GIVEN NUMBER OF HOPS • C. Two-Hop Case • . LINK@KoreaTech

  12. MODELING END-TO-END DISTANCE FOR GIVEN NUMBER OF HOPS • C. Two-Hop Case • . LINK@KoreaTech

  13. STATISTICAL ANALYSIS • All the simulation data are collected from such a scenario that N sensor nodes were uniformly distributed in a circular region of radius of 300 meters.Theanchor node was placed at (0, 0). • We ran simulations for extensive settings of node density λ and transmission range R. • And for each setting of (N,R), we ran 300 simulations, in each of which all nodes are re-deployed from the beginning. LINK@KoreaTech

  14. STATISTICAL ANALYSIS • . LINK@KoreaTech

  15. STATISTICAL ANALYSIS • . LINK@KoreaTech

  16. STATISTICAL ANALYSIS • Optimum Estimation and Error Analysis LINK@KoreaTech

  17. CONCLUSIONS • In this paper, we study the modeling of the end-to-end distance for given number of hops in WSN. • The experiments showed that the distance does not increase linearly with the number of hops. Therefore, the distance should be analyzed for each number of hops. • We derived the distribution for single-hop distance and also showed that the complexity of derivation for multiple-hop distance is beyond practical interest. • Thus, we postulate Beta distribution for two-hop end-to-end distance and Gaussian distribution for three-and-more-hop end-to-end distance. • Computer simulations showed our postulated distributions agree well with the histograms. • We also show that the distance error can be minimized by exploiting the distribution knowledge. LINK@KoreaTech

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