Energy efficient convergecasting

1. Energy efficient convergecasting Bhushan Pendharkar ASU ID 993934582

2. Introduction • Convergecasting in wireless sensor networks • It refers to the process of aggregation or collection of data from several sensors (nodes) in a network towards a root node or the base station. • Nodes or sensors are battery powered • The lifetime of a network is decided by the life of the nodes • Nodes have a limited battery life, consequently networks have a limited lifetime. • Challenge in designing these networks  Reduction in the energy consumption of the network • Achieve maximization of network lifetime

3. Approach • Initially, a convergecast tree is considered consisting of nodes which send data to the central root node. • Formulation of a method to optimally assign power levels to each and every node in the tree to maximize the lifetime of the tree. • Binary Search Algorithm • This algorithm forms the base of this approach which performs optimal power assignment among nodes . • A power consumption model is considered initially for specifying certain parameters for the binary search algorithm.

4. Power Consumption Model • Em  minimum energy to decode an information bit conveyed by a transmitter. • d  distance between transmitter and receiver • α  path loss exponent • Pg  scaling factor • Eu  energy per unit operation per bit to run the decoder Total transmitter energy/ bit = Pt = Pg.Em.dα Total receiver energy/ bit = Pr = Eu.f(Pg) • f(Pg) is a non linear function

5. Initial conditions • Suppose there are n number of nodes in the network with each node using a transmission energy Pt(i) to transmit data. • Let T be the lifetime of the network. • Lifetime denotes the time until the first node in the network (or the tree) runs out of energy. • The goal is to find an optimal set of power settings of nodes (Pt(1), Pt(2), ..Pt(n)) that maximizes network lifetime

6. Constraints • The constraints are: • Flow conservation : An interior node forwards traffic at a rate equal to the sum of incoming rates from children and its own data rate. • Energy constraint : Total energy consumption of a node i over the lifetime of the network is less than or equal to its initial total remaining energy. • Transmission energy constraint: The transmission energy per bit of node i must be greater than or equal to minimum transmission energy required for decoding at node located at a distance d.

7. Binary Search Algorithm • This algorithm follows an iterative approach. • In each iteration, the root node chooses a target life time T that network seeks to achieve • Initially the leaf nodes determine their power settings by satisfying the energy constraint. • The parent nodes then determine the power settings by solving the energy constraint. • If the power settings of all the nodes do not violate any constraint, then lifetime T is feasible and the optimal lifetime must be greater than or equal to T. • As a result, a higher lifetime is sought in next iteration

8. Binary Search Algorithm (cont’d) • If the power assignment may require a node to transmit a power smaller than required minimum. In this case , the lifetime is too large to be achieved • A smaller lifetime needs to be sought in next iteration • Thus, the process of finding optimal lifetime represents a binary search process. • The data tree and an error margin that determines the desired accuracy of the solution are the input to the algorithm. • The output is a lifetime within the error margin of optimal lifetime and power setting of each node

9. Binary Search Algorithm (cont’d) • Suppose ‘tu’ and ‘tl’ represent upper and lower bounds of optimal lifetime respectively. • The values of ‘tu’ and ‘tl’ are updated after every iteration • The algorithm terminates with a lifetime within the error margin of the optimal lifetime when the difference between ‘tu’ and ‘tl’ is less than the error margin.

10. Conclusion • The Binary Search Algorithm works in an iterative manner to ultimately assign a power level to the nodes corresponding to the optimal lifetime. • A small margin of error is considered while computing the power levels. • This approach attempts to maximize the network lifetime by optimum energy consumption of the nodes.

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