1. Minimum Energy Mobile Wireless Networks IEEE JSAC 2001/10/18

2. Outline Introduction Network layer requirements The power consumption model Minimum power networks Distributed network protocol Simulations Conclusion

3. Introduction This paper present a position-based algorithm to set up and maintain a minimum energy network between users that are randomly deployed over an area and are allowed to move with random velocities. Each node has a low-power globe positioning system (GPS) receiver on board. The protocol is self-reconfiguring in mobile scenarios.

4. Network Layer Requirements A network graph is said to be “strongly connected” if there exists a path from any node to any other node in the graph. This paper take one of the nodes to be the information sink for all nodes in the network. They call this node the “master- site.”

5. The Power Consumption Model This model has three components –Small-scale variations –Large-scale variations –Path loss

6. The Power Consumption Model Small-scale variations –These are modeled by a Rayleigh distribution. –A wireless communication receiver is designed with diversity reception to combat small-scale variations. (Rake receiver) –In a rake receiver, a technique called maximum ratio combining (MRC) is used to optimally combine these independent stream.

7. The Power Consumption Model Large-scale variations –The received signal power averaged over small- scale variations. –A outage probability is specified for large-scale variations. The transmitter must adjust its transmit power to satisfy the specification.

8. The Power Consumption Model Path loss –The received signal power averaged over large- scale variations has been found to have a distance dependence which is well modeled by 1/d n. –The path loss may normally depend on the heights of the transmit antenna

9. The Power Consumption Model Directly transmit form A to C will consume more power than relay the message through node B.

10. Minimum Power Networks Consider three node i(transmitter), r(relay), and j(destination). The position of j is (x,y). Definition 1- relay region: the relay region R i→j of the transmit-relay node pair (i,j) is defined to be

11. Minimum Power Networks Definition 2-deployment region: any bounded set in R 2 that has the position of the nodes in Ñ as a subset is said to be a deployment region. Definition 3-enclosure and neighbor: the enclosure of a transmit node i is define as the nonempty solution ε i to the set of the equations

12. Minimum Power Networks

13. Definition 4-enclosed node: a node i is said to be enclosed if it has communication links to each of its neighbors. Definition 5-enclosure graph: the enclosure graph of a set of nodes Ñ is the graph whose vertex set is Ñ and whose edge set is where l i→k is the directed communications link from i to k.

14. Minimum Power Networks Theorem 1-strong connectivity: fix the deployment region D Ñ for a set of node Ñ. The enclosure graph of Ñ is strongly connected.

15. Distributed Network Protocol The main idea of this protocol is that a node does not need to consider all the nodes in the network to find the globe minimum power path to the master-site. This protocol can divide into two parts: –Phase1: search for enclosure –Phase2: cost distribution

16. Distributed Network Protocol Phase1 : Search for Enclosure –Each node in the algorithm starts a search by sending out a beacon search signal that include the position information. –Every node runs exactly the same algorithm. Then it will concentrate on a particular node and call it the transmit node. –The transmit node listens for nearby nodes and calculates the relay region for them.

17. Distributed Network Protocol –The transmit node must keep only those nodes that do not lie in the relay region of previously found nodes. –Each time new nodes are found, the transmit node must update it relay graph.

18. Distributed Network Protocol If a node found (call it k) falls in the relay region of some other found (call it j), then we mark k “dead”. We say that j “blocks” k. If a node is not blocked by any other node found in this search, then we mark the node “alive”. The set of alive nodes constitutes the set of neighbors for transmit node i when the search terminates.

19. Distributed Network Protocol Phase2 : Cost Distribution –The algorithm finds the optimal links on the enclosure graph. –The cost of a node i is defined as the minimum power necessary for i to establish a path to the master-site.

20. Distributed Network Protocol –Each node calculates the minimum cost it can attain given the cost of its neighbors. Let n N(i). When i receives the information Cost(n), it computes: then i compute

21. Simulations

22. Conclusion This paper present a routing protocol which find the minimum power topology for a stationary ad hoc network environment. Brief and to the point, this paper modeled the ad hoc network as the spanning tree then find the minimum spanning tree.