Distributed Topology Control In Wireless Sensor Networks with Assymetric Links

1. Distributed Topology Control In Wireless Sensor Networks with Assymetric Links • Presenter: Himali Saxena

2. General Outline • Introduction • Model • Algorithm • Performance Analysis • Simulation

3. Introduction • WSN- collection of power conscious wireless capable sensors without the support of pre existing infrastructure • Topology control via per-node Tx power adjustment has been shown to be effective in extending network lifetime and increasing network capacity • With reduced Tx range, basic reachability can be jeopardized • The problem exacerbated with heterogeneous nodes with different maximum transmission ranges with assymetric power links

4. Model • Nodes are deployed in 2-D plane. • Each node is euipped with an omni directional antenna with adjustable Tx power • Nodes have different Tx powers & radio range

5. Pi : Tx Power, Pi max : Max Tx Power • Pij : Tx Power required for I to reach j • P i max != Pj max : Asymetric link → Pj i> Pj max (impossible for j to reach i) • G = (V,L) : Strongly or weakly connected, or disconnected • Objective : To derive a minimum power topology G that bis strongly connected, guaranteeing multi hop reachability from any source to any destination in the directed graph

6. Algorithm • Phase I : Establishing the vicinity topology • Node i broadcasts IRQ msg using Pi max • IRQ includes the location of I & Pi max • Set of nodes receive this msg : vicinity nodes of i (Vi) • each nodej inVi replies to node i with anIRP message, with its location andPjmax j −→ Lji.

7. For a node j ∈ Vi, if Pjmax ≥ Pij , j can reach node I via the single-hop link • If Pj max < Pij , j must find a multi-hop path to reach i. • Having the knowledge of the locations and maximum transmission powers for itself and all its vicinity nodes, it may derive the existence of thevicnity edges • For any two nodes j, k ∈ Vi, link Ljk is defined as one of i’s vicinity edges, if Pj max ≥ Pjk • Consequently, node i constructs its local vicinity topology that includes all its vicinity nodes, itself and the discovered vicinity edges

8. Phase II: Deriving the minimum-power vicinity tree • 1. With the knowledge of the weighted, directed topology Gi, the weight, Wl, of a directed path l = u0 → u1 → . . . → uk from node u0 to uk is the sum of edge weights along the Path • 2. The minimum power for node i to reach j is min(Wp) for all available paths p • 3. Find the shortest path in G from i to j. In this case, node i may execute a single source shortest-paths algorithm to derive the minimum-power vicinity tree Gis = (Vis, Eis) • Property 1. Since there does not exist unreachable nodes in the in Gi, we have Vis = Vi, and Eis ⊆ Ei. • Property 2. The derivation of Gis depends solely on the edge weights, which does not assume a specific propagation model

9. Phase 3: Propagation of transmission powers • 1. In this phase, node i needs to calculate the transmission power needed for itself and each vicinity node in Vi, to ensure that all its minimum-power paths exist in the final minimum power network topology • 2. Specifically, for node i itself and each node in set Vi, the transmission power is assigned as the power required to reach the furthest one-hop downstream nodes in node i’s minimum-power vicinity tree Gis • 3. Node i first adopts the minimum power assigned to itself, and then sends the minimum power required for each vicinity node with a explicit PR message

14. Performance Analysis • Scalability : Execution of the algorithm is limited to its vicnity topology, thus scalable to network composed of large no. of nodes • Convergence of the algorithm : Network converges to the final mimimum power topology once every node completes the execution of the algorithm • Guaranteeing of network connectivity

16. Simulation • N nodes uniformly distributed in 100*100 m network area, where n is in the range of [2,50] • Parameters : Reachability, Power Efficiency, and Scalability

19. Conclusion • 1. Algorithm provides a solution to the topology control problem in a network of heterogeneous wireless devices with different maximum transmission ranges • 2. The resulting minimum-power topology is shown to guarantee that • (a) reachability between any two nodes is guaranteed to be the same as the maximum topology; and • (b) nodal transmission range is minimized to cover the least number of surrounding nodes.