Report

On the Implications of the Log-normal Path Loss Model: An Efficient Method to Deploy and Move Sensor Motes Yin Chen, Andreas Terzis November 2, 2011 Connected region Transitional region • What to do about the transitional region? – Place motes in the transitional region vs in the connected region 2 Our Proposal • Occupy the transitional region – Perform random trials to construct links with high PRR – Based on the Log-normal radio model 3 Motivation: Placing Relay Nodes 4 Outline • Introduce log-normal path loss model • Discuss pitfalls • Present the experimental results – reality check 5 Log-normal Path Loss Model distance Sender Receiver • Received signal strength Power of the transmitted signal – at a distance is Path loss at distance 0 Path loss exponent Random variation , is a Gaussian random variable • Due to artifacts in the environment (occlusions, multipath, etc.) – Does not consider temporal variation 6 Three Regions of Radio Links • As the distance increases, we go through 3 regions – Connected: – Transitional: – Disconnected: P ≥ 85% ≥ 95% 5% < P ≥ 85% < 95% P ≥ 85% ≤ 5% • Observation – The packet reception ratio at any given location is random 7 Connected Region Sender 5 meters Receiver • In connected region • PRR is very likely to be high • Trying one location will likely produce good link 8 Transitional Region Sender 15 meters Receiver • In transitional region • PRR may or may not be high • Trying a few spots should yield a good link 9 Disconnected Region Sender 40 meters Receiver • In disconnected region • PRR is very unlikely to be high • Trying multiple spots seems worthless 10 Outline • Introduce log-normal path loss model • Discuss pitfalls • Present the experimental results – reality check 11 Pitfalls • Log-normal path loss model is not perfect • The Gaussian variation in signal strength is a statistical observation • Signal strengths at nearby locations are correlated 12 Reality Check • Verify log-normal path loss model • Quantify spatial correlations • Count number of trials to construct good links • Investigate temporal variations 13 Experimental Setup • Devices – TelosB motes – iRobot with an Ebox-3854 running Linux • Environments – – – – – Outdoor parking lot Lawn Indoor hallway Indoor testbed Two forests 14 Evaluations on the Log-normal Model • Holds well in all the environments – Example figure for the parking lot – We can subtract the solid line from the raw RSSI readings • The residual RSSI values are samples of the random variable : 15 Q-Q Plot of the Residual RSSI Values 16 Reality Check • Verify log-normal path loss model • Quantify spatial correlations • Count number of trials to construct good links • Investigate temporal variations 17 Spatial Correlation • PRR measurements at a parking lot – – iRobot moves in a 2-d plane (the ground) Black cell : PRR below 85%; Gray cell : PRR above 85% • PRR are correlated • Trying two adjacent locations ≠ flipping two coins • In all of our experiments, 1 meter is sufficient to remove most correlation 18 Reality Check • Verify log-normal path loss model • Quantify spatial correlations • Count number of trials to construct good links • Investigate temporal variations 19 Number of Trials - Configuration 1 meter distance • Grid sampling – Bernoulli trials • Number of trials to find a good PRR is geometrically distributed 20 Number of Trials - Results • Measure and compute the length of connected region – Place motes at distances longer than Number of Trials Expected Number of Trials 3.5 3 Distance to the Sender (Normalized by lc) 2.5 3.5 2 3 2.5 1.5 2 1 1.5 1 0.5 0.5 0 0 Parking Lot Hallway 1 Hallway 2 Office Forest 21 Number of Trials – Fitting Geometric Distribution Suggests that 1 meter ensures independent trials. 22 Connecting Two Motes Relay Mote A Mote B TAR TBR TARB TAR multiplied by TBR 4.5 TAR: number of trials to connect to A TBR: number of trials to connect to B TARB: number of trials to connect to both A and B 4 3.5 3 2.5 2 1.5 1 0.5 0 Hallway 1 Hallway 2 Parking Lot 1 Parking Lot 2 Parking Lot 3 TARB ≈ TAR × TBR 23 Reality Check • Verify log-normal path loss model • Quantify spatial correlations • Count number of trials to construct good links • Investigate temporal variations 24 Temporal Variation • Box plots of residual RSSI values for two forests 25 Conclusion • Log-normal model fits sensornets • Signal correlation vanishes at 1 meter separation • Easy to find good links in the transitional region – Rule of thumb: at twice the length of connected region, number of trials is less than 5 with high probability 26 Application – Placing Relay Nodes • Number of relay nodes at large scale – Place 120 sensor motes in an area of size 800m by 800m – Run Steiner Tree algorithm to place relay nodes 27 Application – Mobile Sensor Networks • Mobile sink – If the current spot yields low PRR, move 1 meter – Minimize travel distance • Mobile motes Signal variation in the space domain Signal variation in the time domain 28 Thank you! Questions? 29