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

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 (Ad-hoc) Wireless Networks Instant deployment No wired backbone No centralized control Nodes may cooperate in routing each other’s data packets 2

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Example: Wireless Sensor Networks Sensor Node Components Sensor Data Processor Wireless Communication Module Characteristics Small Size Low-cost Low-Power 3

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Example: Wireless Sensor Networks – cont’ 4 Wireless Multimedia Sensor Networks (Image Source:

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Example: Wireless Sensor Networks – cont’ 5 Volcano monitoring (Image Source:

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Example: Ad-hoc Network 6 Vehicular Ad-hoc Networks (Image Source:

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Example: Ad-hoc Network – cont’ 7 Military Ad-hoc Network (Image Source:

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Research Issues 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 8

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Arbitrary Networks 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 9

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Unit Disk Graph (UDG) 10

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Unit Disk Graph – cont’ 11

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Protocol Model Let X i denote the location of a node A transmission is successfully received by X j if: For every other node X k simultaneously transmitting is the guarding zone specified by the protocol 12

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Physical Model – cont’ 13

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Physical Model – cont’ Let be a subset of nodes simultaneously transmitting Let P k be the power level chosen at node X k Transmission from node X i is successfully received at node X j if: Also called signal to interference and noise ratio (SINR) model. 14

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Topology Control in UDG (under Protocol Interference Model) 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… 15

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Topology Control in UDG – cont’ It is a static problem! 16 Topology Control Protocol

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Topology Control in SINR A schedule to actually realize selected links (transmission requests), to successfully transmit message over them 17 Minimum signal-to- interference ratio Power level of sender u Path-loss exponent Noise Distance between two nodes Received signal power from sender Received signal power from all other nodes (=interference)

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Cross Layer Aspects of Power Control 18 Physical Layer MAC Layer Network Layer Power Control Incorporating Physical Layer Characteristics Cross Layer Design Effect of MAC-Layer Interference Dynamic Topology Control w.r.t. Network Traffic Network Capacity Network Lifetime Critical Power Analysis Network Capacity Network Lifetime Critical Power Analysis Physical Layer Incorporating Physical Layer Characteristics

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.

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Capacity of Wireless Network 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 20

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Overview of Contributions 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 21

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Limitations of Graph-model- based topology control 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) 22

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Notations : 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 23

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Assumptions 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 24

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Network Graph Model 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. 25

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Interference Model A node is said to be an interfering node for link if 26 NOTE: Very loose – simultaneous transmissions of non interfering nodes can cause interference.

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Interference Model – cont’ 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 27

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Interference Link Graph A link interference graph represents the interference of a link as, where, and is the set of edges such that 28

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Interference Degree vs. Node Degree 29 Interference degree does not necessarily related to the node degree.

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Result 1 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. 30

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Topology Control To Maximize Spatial Reuse 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 31

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Topology Power Assignment: T4P 32

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Topology Control To Maximize Spatial Reuse – cont’ 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 33

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Power Assignment to Topology: P4T 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 34

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Topology Control To Maximize Spatial Reuse – cont’ 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 35

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Spatial Reuse Maximizer (MaxSR) : power level of nodes (optimized by T4P) T : topology of nodes (optimized by P4T) Theorem: MaxSR converges to an optimal point 36

Department of Mathematics and Computer Science North Carolina Central University Donghyun (David) Kim September 23, 2011 Discussion SINR model with loose interference model vs Construction of static topology in dynamic SINR model 37