Special Topics on Algorithmic Aspects of Wireless Networking

1. Topology Abstraction of Wireless Networks using Physical Model Special Topics on Algorithmic Aspects of Wireless Networking Donghyun (David) Kim Department of Mathematics and Computer ScienceNorth Carolina Central University

2. Instant deployment • No wired backbone • No centralized control • Nodes may cooperate in routing each other’s data packets (Ad-hoc) Wireless Networks

3. Sensor Node Components • Sensor • Data Processor • Wireless Communication Module • Characteristics • Small Size • Low-cost • Low-Power Example: Wireless Sensor Networks

4. Example: Wireless Sensor Networks – cont’ Wireless Multimedia Sensor Networks(Image Source: http://www2.ece.ohio-state.edu/~ekici/res_wmsn.html)

5. Example: Wireless Sensor Networks – cont’ Volcano monitoring(Image Source: http://fiji.eecs.harvard.edu/Volcano)

6. Example: Ad-hoc Network Vehicular Ad-hoc Networks(Image Source: http://monet.postech.ac.kr/research.html)

7. Example: Ad-hoc Network – cont’ Military Ad-hoc Network(Image Source: http://www.atacwireless.com/adhoc.html)

8. Network Layer • problems are in routing, mobility of nodes and power constraints • MAC layer • problems with wireless signal interference and collision handling protocols such as TDMA, FDMA,CDMA • Physical layer • problems in power control • Convenient to have graph model for the topology of a wireless network Research Issues

9. n nodes are arbitrary located • Each node has a fixed communication power • When does a transmission received successfully? • Allowing for two possible models for successful reception over one hop: The protocol model and the physical model Arbitrary Networks

10. Unit Disk Graph (UDG)

11. Unit Disk Graph – cont’

12. Let Xidenote the location of a node • A transmission is successfully received by Xjif: • For every other node Xksimultaneously transmitting • is the guarding zone specified by the protocol Protocol Model

13. In radio communication, the power p to send a message for a distance l can be simplified aswhere is a constant called path-loss exponent, and is a constant called the reference loss factor. • In other word, given a signal transmission power at the sender, the signal power at the receiver side is proportional to Physical Model – cont’

14. Let be a subset of nodes simultaneously transmitting • Let Pkbe the power level chosen at node Xk • Transmission from node Xi is successfully received at node Xjif: • Also called signal to interference and noise ratio (SINR) model. Physical Model – cont’

15. What is topology control ? • Given node location, find a (static) communication graph with desirable properties • Assume adjustable communication power • Idea: Drop links if possible by adjusting communication power • Goal: Reduces energy and interference!But still stay connected and satisfies other properties: • Low node degree • Low static interference • Etc… Topology Control in UDG(under Protocol Interference Model)

16. Topology Control Protocol • It is a static problem! Topology Control in UDG – cont’

17. A schedule to actually realize selected links (transmission requests), to successfully transmit message over them Received signal power from sender Power level of sender u Path-loss exponent Minimum signal-to-interference ratio Noise Distance between two nodes Topology Control in SINR Received signal power from all other nodes (=interference)

18. Cross Layer Design Dynamic Topology Control w.r.t. Network Traffic Power Control Network Layer Network Capacity Network Lifetime Critical Power Analysis Effect of MAC-Layer Interference MAC Layer Cross Layer Aspects of Power Control Incorporating Physical Layer Characteristics Incorporating Physical Layer Characteristics Physical Layer Physical Layer

19. Topology Control for Maximizing Network Capacity Under the Physical Model Ref: Yan Gao, Jennifer C. Hou, and Hoang Nguyen, “Topology Control for Maintaining Network Connectivity and Maximizing Network Capacity under the Physical Model,” INFOCOM 2008.

20. Not well established concept, but there are several commonly used definition • A (kind of) conceptual throughput • Definition in this paper • The number of bytes that can be simultaneously transported by the network Capacity of Wireless Network

21. Show existing graph-model-based topology control captures interference inadequately under SINR model • Cause high interference and low network capacity • Spatial Reuse Maximizer (MaxSR), a combination of • A power control algorithm (T4P) to compute a power assignment that maximizes spatial reuse with a fixed topology • A topology control algorithm (P4T) to generate a topology that maximizes spatial reuse with a fixed power assignment • MaxSR alternatively invokes T4P and P4T alternatively • Converge into a stable status • Via simulation, shows MaxSR outperforms competitors by 50% - 110% in terms of maximizing the network capacity Overview of Contributions

22. The node degree does not capture interference adequately • The interference in the resulting topology may be high, rendering low network capacity • A wireless link that exists in the communication graph may not in practice exist under the physical model (due to the high interference level) Limitations of Graph-model-based topology control

23. : 2-d coordinate of a node v • : the Euclidean distance between two nodes • : the transmit power of a node • : the transmit power assignment of all nodes, where Notations

24. Large-scale path loss model • To describe how signals attenuate along the transmission path • The two conditions of successful transmission • Homogenous network • Same - maximum communication power level Assumptions

25. A link (i, j) is said to exist if and only if • Only consider bidirectional links – an edge exists if and only if and • The communication graph of a network is represented by a graph G = (V, E), where E is a set of undirected edges. • Based on the power assignment, a graph is induced. Network Graph Model

26. A node is said to be an interfering node for link if NOTE: Very loose – simultaneous transmissions of non interfering nodes can cause interference. Interference Model

27. The interference degree of a link is defined as the number of interfering nodes for . • Let denote the set of containing all interfering nodes of , then the interference degree • A link with a high interference degree • multiple nodes can interfere with its transmission activity, causing channel competition and/or collision. • Undesirable since both channel competition and collision degrade the network capacity • Hence, interference degree is a better index than the node degree in quantifying the interference Interference Model – cont’

28. A link interference graph represents the interference of a link as , where , and is the set of edges such that Interference Link Graph

29. Interference degree does not necessarily related to the node degree. Interference Degree vs. Node Degree

30. Given a communication topology, is it possible to find a power assignment such that the communication graph of the topology is identical to the physical-model-based interference graph? • Based on the simulation result, it is not likely to find power assignments to a topology induced by graph-mode-based topology control to represent the corresponding interference graph. Result 1

31. T4P: compute a power assignment that maximizes spatial reuse with a fixed topology • P4T: generate a topology that maximizes spatial reuse with a fixed power assignment • MaxSR: A novel algorithm to maximize spatial reuse and improve network capacity by repeatedly executing T4P and P4T Topology Control To Maximize Spatial Reuse

32. T4P • Hard SINR requirement can be softened by the sigmoid function • After set b, asequentialquadratic programming method [12, 13] can be used to solve this softened problem. Topology Power Assignment: T4P

33. T4P: compute a power assignment that maximizes spatial reuse with a fixed topology • P4T: generate a topology that maximizes spatial reuse with a fixed power assignment • MaxSR: A novel algorithm to maximize spatial reuse and improve network capacity by repeatedly executing T4P and P4T Topology Control To Maximize Spatial Reuse – cont’

34. To generate an optimal connected topology given a fixed power assignment • Similar to the minimum spanning tree algorithm • Differ in that this finds the spanning tree that gives minimal interference degree • Outline (like Prim’s algorithm) • Given a power assignment, for each link, compute its interference degree • Sort the edge in the non-decreasing order of interference degree • Add each edge one by one until all nodes are connected Power Assignment to Topology: P4T

35. T4P: compute a power assignment that maximizes spatial reuse with a fixed topology • P4T: generate a topology that maximizes spatial reuse with a fixed power assignment • MaxSR: A novel algorithm to maximize spatial reuse and improve network capacity by repeatedly executing T4P and P4T Topology Control To Maximize Spatial Reuse – cont’

36. : power level of nodes (optimized by T4P) • T : topology of nodes (optimized by P4T) • Theorem: MaxSR converges to an optimal point Spatial Reuse Maximizer (MaxSR)

37. SINR model with loose interference modelvs • Construction of static topology in dynamic SINR model Discussion