On the Topology of Wireless Sensor Networks

1. On the Topology of Wireless Sensor Networks Sen Yang, Xinbing Wang, LuoyiFu Department of Electronic Engineering, Shanghai Jiao Tong University, China Email: {twood,xwang8,fly}@sjtu.edu.cn

2. Outline Introduction Motivations Objectives System Models Topology of Heterogeneous WSNs Without Obstacles Topology of Heterogeneous WSNs With Obstacles Summary On the Topology of Wireless Sensor Networks 2

3. Motivation • Capacity of wireless network is not scalable: in a static wireless network with nodes, the per-node capacity is . Interference is the main reason behind. • Helping nodes are introduced to increase the network capacity [2]. [1] P. Gupta and P. R. Kumar, “The capacity of wireless networks”, in IEEETransactionon Information Theory, 2000. [2] P. Li and Y. Fang, “TheCapacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010. On the Topology of Wireless Sensor Networks

4. Motivation • Network Topology • We investigate throughput capacity of networks with the following topologies and then generalize the results to get some useful conclusions. Uniform Distribution Centralized Distribution Multi-centralized Distribution On the Topology of Wireless Sensor Networks

5. Motivation • In practice, sensor nodes may not be placed uniformly, which could have a huge impact on network performance, including the capacity [3]. Wireless Networks with Inhomogeneous Node Density. [3] [3] G. Alfano, M. Garetto, E. Leonardi, “Capacity Scaling of Wireless Networks with Inhomogeneous Node Density: Upper Bounds,”IEEE Journal on Selected Areas in Communications, vol. 27, no. 7, Sept. 2009. On the Topology of Wireless Sensor Networks

6. Motivation • In practice, sensor nodes may not be placed uniformly, which could have a huge impact on network properties, including the capacity [3]. • Also, sensor networks are often deployed in complex environments, such as battle fields or mountainous areas, and there are often many obstaclesdistributed in these regions. What are the best network topologies for given network regions, especially for networks with obstacles? [3] G. Alfano, M. Garetto, E. Leonardi, “Capacity Scaling of Wireless Networks with Inhomogeneous Node Density: Upper Bounds,” IEEE Journal on Selected Areas in Communications, vol. 27, no. 7, Sept. 2009. On the Topology of Wireless Sensor Networks

7. Objective • We study • How does the node distribution influence the throughput capacity? • What’s the optimal nodes distribution on given conditions? • We obtain • Some guidelines on generating the optimal topology for flat network areas. • An algorithm of linear complexity to generate optimal sensor nodes’ topologies for any given obstacle distributions. On the Topology of Wireless Sensor Networks

8. Outline Introduction System Models Topology of Heterogeneous WSNs Without Obstacles Topology of Heterogeneous WSNs With Obstacles Summary On the Topology of Wireless Sensor Networks 8

9. System Model • We consider dense networks with sensor nodes and helping nodes in a planar unit area. • All the sensor nodes are sources while only sensor nodes are randomly chosen as destinations. • The network is divided into non-overlapping cells with equal size. Nodes can communicate with each other only when they are in the neighboring cells. • We apply a TDMA rotating scheduling scheme to bound the interference. On the Topology of Wireless Sensor Networks

10. System Model • Obstacles • We assume there are number of obstacle nodes in the network area, which can be arbitrarily or randomly distributed. • Cells are blocked when there are obstacle nodes in them. • Here, “blocked” has two implications: • No sensor node can be distributed in these cells; • Nodes’ communication cannot cross them directly. On the Topology of Wireless Sensor Networks

11. System Model • Interference Model • The channel power gain is given as , where denotes the distance of transmission, represents the path-loss exponent. • Each cell in the network can work at a transmission rate , where is a deterministic positive constant relevant to the cells’ scale and is the channel bandwidth.[2] [2] P. Li and Y. Fang, “TheCapacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010. On the Topology of Wireless Sensor Networks

12. System Model • Network Topology • We investigate throughput capacity of networks with the following topologies and then generalize the results to get some useful conclusions. Uniform Distribution Centralized Distribution Multi-centralized Distribution On the Topology of Wireless Sensor Networks

13. Introduction • System Models • Topology of Heterogeneous WSNs Without Obstacles • Capacity of Heterogeneous WSNs without Obstacles • General Properties of “Combined Networks” • Impact of Network Topology on Throughput Capacity • Topology of Heterogeneous WSNs With Obstacles • Summary On the Topology of Wireless Sensor Networks

14. Capacity of WSNs w.o. Obstacles • Achievable throughput in normal mode Maximal number of flows across a cell Virtual destination nodes [2] P. Li and Y. Fang, “TheCapacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010. On the Topology of Wireless Sensor Networks

15. Capacity of WSNs w.o. Obstacles • Achievable throughput in helping mode • In the first phase • In the second phase • In the third phase [2] P. Li and Y. Fang, “TheCapacity of heterogeneous wireless networks,” in Proc. IEEE INFOCOM, 2010. On the Topology of Wireless Sensor Networks

16. Capacity of WSNs w.o. Obstacles • Throughput capacity of the network • Uniform Network • Centralized Network • Multi-centralized Network On the Topology of Wireless Sensor Networks

17. Properties of “Combined Networks” • Impacts of combination: • The interference of different sub-networks • Flows passing through a cell • Theorem 4: For network composed of some isomorphic sub-networks, the throughput capacity of the overall network, denoted by , and the throughput capacity of sub-network of same network scales, denoted by , have the following relationship. On the Topology of Wireless Sensor Networks 20

18. Impact of Topology on Capacity • Sensor Nodes’ Topology • Theorem 5: For the topology of sensor nodes, if the value range of nodes distribution’s PDF is bounded, the gap in achievable throughput of non-uniform networks and uniform networks is at most a constant time. • For networks without helping nodes, uniform sensor nodes’ distribution is order optimal on maximizing throughput capacity. On the Topology of Wireless Sensor Networks

19. Impact of Topology on Capacity • Helping Nodes’ Topology On the Topology of Wireless Sensor Networks

20. Impact of Topology on Capacity • Helping Nodes’ Topology – for uniform sensor nodes • Theorem 6: For networks with uniformly distributed sensor nodes, regularly distributed helping nodes are optimalto maximize the network throughput capacity. On the Topology of Wireless Sensor Networks

21. Impact of Topology on Capacity • Helping Nodes’ Topology – for non-uniform sensor nodes • Theorem 7: For networks with non-uniformly distributed sensor nodes, though regularly distributed helping nodes are no longer optimal, any improvement on the helping nodes’ topology cannot change the scale of network throughput capacity. • Regularly distributed helping nodes are optimal on maximizing the throughput capacity in the sense of scaling law. On the Topology of Wireless Sensor Networks

22. Introduction • System Models • Topology of Heterogeneous WSNs Without Obstacles • Topology of Heterogeneous WSNs With Obstacles • Algorithm to Obtain the Optimal Network Topology • Complexity of the Algorithm • Summary On the Topology of Wireless Sensor Networks

23. The OptimizationAlgorithm • Algorithm - “Wall with Gate”: • Step 1) Transform the original problem to a simple scenario - “Wall with Gate”. On the Topology of Wireless Sensor Networks

24. The OptimizationAlgorithm • Algorithm - “Wall with Gate”: • Step 2) Transform the problem with obstacles to a problem without obstacles. Virtual destination nodes On the Topology of Wireless Sensor Networks

25. The OptimizationAlgorithm • Algorithm - “Wall with Gate”: • Step 2) Transform the problem with obstacles to a problem without obstacles. On the Topology of Wireless Sensor Networks

26. The OptimizationAlgorithm • Algorithm - “Wall with Gate”: • Step 3) For the degraded sub-network, use techniques and conclusions given in previous sections to generate an optimal sub-network topology On the Topology of Wireless Sensor Networks

27. The OptimizationAlgorithm • Algorithm - “Wall with Gate”: • Step 4) Combine all of the sub-networks’ topology to obtain the overall topology of the network On the Topology of Wireless Sensor Networks

28. The OptimizationAlgorithm • More words about the algorithm: • This is a centralized algorithm which results in a global optimal solution • Since the gate areas here might be relatively large, nodes distribution in these areas can no longer be ignored and Step 2 – 3 must be applied to these gate areas. On the Topology of Wireless Sensor Networks

29. Complexity of the Algorithm • How to divide the network? • Method I: take blocked cells in a row (either vertical or horizontal) as a wall and cells without obstacles in this row as gates. On the Topology of Wireless Sensor Networks

30. Complexity of the Algorithm • How to divide the network? • Method II: Firstly construct a wall in the row with the most number of blocked cells, dividing the network area into two parts. For each part, repeat this step iteratively until all the blocked cells are crossed by at least one wall. On the Topology of Wireless Sensor Networks

31. Complexity of the Algorithm • Complexity of the Algorithm • The algorithm complexity is when using network dividing method I and is when using method II. On the Topology of Wireless Sensor Networks

32. Introduction • System Models • Topology of Heterogeneous WSNs Without Obstacles • Topology of Heterogeneous WSNs With Obstacles • Summary On the Topology of Wireless Sensor Networks

33. Summary • For networks without obstacles, we find that uniformly distributed sensor nodes and regularly distributed helping nodes have some advantages in improving the throughput capacity. • For networks without obstacles, we propose an algorithm of linear complexity to generate optimal sensor nodes’ topology for any given obstacle distribution. On the Topology of Wireless Sensor Networks

34. Thank you for listening SenYang, Xinbing Wang, LuoyiFu Email: {twood,xwang8,fly}@sjtu.edu.cn On the Topology of Wireless Sensor Networks