Authors: Yanyan Zhuang, Jianping Pan, Lin Cai University of Victoria

1. Minimizing Energy Consumption with Probabilistic Distance Distributions in Wireless Sensor Networks Authors: Yanyan Zhuang, Jianping Pan, Lin Cai University of Victoria

2. Problem: • Prolong lifetime of wireless sensor network • → • Minimize energy cost in wireless sensor network • → • The main part of energy cost in wireless sensor network is cost by sensor communication

3. Problem: • How to minimum communication cost in wireless sensor network • → • How to measure energy cost by sensor communication

4. Solution • Grid-based clustering model • Calculating average distance between two communicating sensors • Advantage: • Simple and feasible

5. Advantage of the grid-based model • “Once the grid structure is established nodes can communicate locally with their grid head and reach the data processing center, or the sink node, through neighbor grids.”

6. Disadvantage of average distance • Disregard the super-linear path loss exponent of over-the-air wireless transmissions. • Existed models disregard the path loss of wireless communication signals.

7. Path loss • When radiowave transmitted in space, it will be absorbed or diffracted and causes propagation loss.

8. Path loss is a major component in the analysis and design of telecommunication system. • → • Energy cost obtained from average distance between two sensors is not accurate • → • Find a more accurate calculation model

9. Key point • Reflect path loss on communication distance

10. background • Clustering scheme • Equal-divided grid clustering • Variable size clustering

11. Distance distribution model • Based on geometric properties of grid-based clustering • Three steps

12. Step 1 • Classify transceiver locations for a wireless transmission • (1)two random nodes in the same grid • (2)two random nodes in diagonal neighbor grids • (3)two random nodes in parallel neighbor grids

14. Step 2 • Find coordinate distribution of those nodes in the three cases by the Heaviside Step Function on unit square grids. • Step function:

15. Unit step function • The Heaviside step function, H, also called the unit step function, is a discontinuous function whose value is zero for negative argument and one for positive argument. It seldom matters what value is used for H(0), since H is mostly used as a distribution.

16. Dirac delta function • a 'function' δ(x) that has the value zero everywhere except at x = 0 where its value is infinitely large in such a way that its total integral is 1.

17. Step 3 • Apply coordinate distribution on the distance calculating formula • to obtain distance distribution in three cases

18. Distance distribution

19. Distance distribution

20. Simulation • (1)distance verification • Compare results of their distance distribution function to the output of cumulative distribution function

21. Simplify integral calculation • Use high-degree polynomial functions by Least Squares Fitting to approximate the distribution functions.

24. Simulation • (2)compare one-hop energy cost • Result: error of energy calculation of average distance model will increase exponentially as the path loss exponent grows

26. Simulation • (3) compare network energy cost of “simulation” , distance distribution model and average distance model with varied grid length. • Result: there is an optimal grid size

28. Grid size • The closer to the sink the smaller of the cluster • Heavy load of traffic • Sensors around the sink consume much more energy than sensors located far from the sink in the same time duration

29. Conclusion • Traditional energy cost calculating model based on average communication distance between two sensors in grid-based sensor network can not reflect the accurate value for out of consideration of path loss • Distance distribution model is more accurate and useful in finding a suitable grid length to further optimize energy efficiency