Special Topics on Algorithmic Aspects of Wireless Networking

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## Special Topics on Algorithmic Aspects of Wireless Networking

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**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**Instant deployment**• No wired backbone • No centralized control • Nodes may cooperate in routing each other’s data packets (Ad-hoc) Wireless Networks**Sensor Node Components**• Sensor • Data Processor • Wireless Communication Module • Characteristics • Small Size • Low-cost • Low-Power Example: Wireless Sensor Networks**Example: Wireless Sensor Networks – cont’**Wireless Multimedia Sensor Networks(Image Source: http://www2.ece.ohio-state.edu/~ekici/res_wmsn.html)**Example: Wireless Sensor Networks – cont’**Volcano monitoring(Image Source: http://fiji.eecs.harvard.edu/Volcano)**Example: Ad-hoc Network**Vehicular Ad-hoc Networks(Image Source: http://monet.postech.ac.kr/research.html)**Example: Ad-hoc Network – cont’**Military Ad-hoc Network(Image Source: http://www.atacwireless.com/adhoc.html)**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**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**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**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’**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’**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)**Topology**Control Protocol • It is a static problem! Topology Control in UDG – cont’**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)**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**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.**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**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**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**: 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**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**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**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**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’**A link interference graph represents the interference of a**link as , where , and is the set of edges such that Interference Link Graph**Interference degree does not necessarily related to the node**degree. Interference Degree vs. Node Degree**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**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**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**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’**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**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’**: 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)**SINR model with loose interference modelvs**• Construction of static topology in dynamic SINR model Discussion