Optimal Relay Placement for Indoor Sensor Networks Cuiyao Xue †, Yanmin Zhu †, Lei Ni †, Minglu Li †, Bo Li ‡ † Shanghai Jiao Tong University ‡ HK University of Science and Technology IEEE DCOSS 2012 Hangzhou, China May 17, 2012

Outline Introduction –Relays in indoor environment –Challenge for indoor environment System model –Propagation model Problem statement –Objective –NP-hardness –Radio coverage prediction –RPI algorithm Evaluation Conclusion 2

Relays in indoor environment 3 A typical indoor environment where sensor networks may be deployed. Walls separating sensors and relays can significantly change radio propagation characteristics.

Existing relay placement method Existing relay placement method Many works are for computing relay deployment location in WSN. Many node placement algorithms are for achieve full sensing coverage. They assumed that the target sensor network is deployed in an ideal environment. The radio coverage of a sensor node are modeled as a unit disk. 4

Challenges for indoor environment Obstacles like walls may significantly degrade radio strength. The radio propagation model in an indoor environment is more complex than ourdoor. The existing solutions become inapplicable when indoor. 5

System Model Indoor area –Δ denotes the area needs to be covered –Set W denotes the set of Walls –Each wall presented by two end points of it, – and – denotes the set of all relays which will be deployed, where |K| is not given. 6

Propagation Model 7

Coverage model 8

Objective Minimizing the set of deployed relays Problem definition 9

NP-hardness To prove its NP hardness, we provide a polynomial reduction from the minimum set cover problem (MSC) to the optimal relay placement problem. 10

Overview of the algorithm Basic step of the algorithm 11

Radio coverage prediction Estimate the important parameters and and the mapping function. – First, a set of relays are deployed at given set of locations. –Second, RSS values at a small set of location points are measured and collected. –Finally, these set of RSS values are used as training data and a machine learning. 12

Prediction result The resulting model with estimated parameters can accurately predict RSS values with no more than 9dBm error. We obtain the radio coverage set R of relays being placed at any point within the environment. 13

RPI and its input The RPI algorithm is to select a minimum set of candidate location points for replay placement while meeting the coverage quality requirement. The input of the algorithm –the set of all grid points –the set of all candidate locations for relay placement –the coverage ratio requirement 14

RPI algorithm Divide the whole environment space into small grids of the same size L denote the set of grid points within Δ N denote the set of candidate locations N is L minus the set of grid points falling in unfeasible regions 15

Main steps of RPI The algorithm interactively selects the best candidate location. –C denote the set of remain grid points, which is initialized to the set L. –For each iteration, the one provides the maximum number of remain grid points is selected. –The selected one is inserted into the set K. 16

Details of RPI 17

Performance analysis 18

Evaluation Simulation Setup –Real RSS reading driven simulation RSS readings are recorded in two days and the set of RSS readings is used as the training data. –Default parameters: An office floor of a regular 47m × 66m Includes 65 walls in total Maximum 5 wall classes 28 test relays 100 test points Monte Carlo method to compute real coverage ratios 19

Compared Algorithms Random algorithm(Random) –Randomly selects from the candidate locations until the set of selected relay locations satisfies the coverage requirement. Uniform algorithm(Uniform) –It requires that there is a minimum distance between any pair of selected relay locations. Suppose K relay locations are selected. Then the minimum distance 20

Comparative Results Number of relays vs. coverage ratio requirement 21

Comparative Results Real coverage ratio vs. coverage ratio requirement 22

Comparative Results Number of relays vs. grid size 23

Comparative Results Real coverage ratio vs. grid size 24

Conclusion Conclusion –Propose efficient greedy algorithm to solve the optimal relay placement in realistic indoor environments and explicitly consider wall effects. –The optimal placement of relays in a given indoor environment is NP hard. –Provides an ln(n) + 1 factor approximation to the theoretical optimum, n is the number of all grid points. –Results of simulations have shown that our algorithm is better than other alternative algorithms. 25

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